Works (80)

Updated: June 22nd, 2024 05:05

2024 article

New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties

Chertock, A., Herty, M., Iskhakov, A. S., Janajra, S., Kurganov, A., & Lukacova-Medvid'ova, M. (2024, June 4). COMMUNICATIONS ON APPLIED MATHEMATICS AND COMPUTATION, Vol. 6.

By: A. Chertock n, M. Herty*, A. Iskhakov n, S. Janajra n, A. Kurganov* & M. Lukacova-Medvid'ova*

author keywords: Hyperbolic conservation and balance laws with uncertainties; Finite-volume methods; Central-upwind schemes; Weighted essentially non-oscillatory (WENO) interpolations
Sources: Web Of Science, NC State University Libraries
Added: June 17, 2024

2023 article

A diffuse-domain-based numerical method for a chemotaxis-fluid model

Wang, C., Chertock, A., Cui, S., Kurganov, A., & Zhang, Z. (2023, February 23). MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES, Vol. 2.

By: C. Wang*, A. Chertock n, S. Cui*, A. Kurganov* & Z. Zhang*

author keywords: Chemotaxis; Navier-Stokes equations; bioconvection; diffuse-domain approach; finite-volume method; finite-difference method
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation (OpenAlex)
Sources: Web Of Science, NC State University Libraries
Added: March 13, 2023

2023 article

Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator

Chertock, A., Chu, S., & Kurganov, A. (2023, April 12). EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, Vol. 4.

By: A. Chertock n, S. Chu* & A. Kurganov

author keywords: Local smoothness indicator; scheme adaption; strong stability preserving Runge-Kutta methods; hyperbolic systems of conservation laws; A-WENO schemes
Sources: Web Of Science, NC State University Libraries, ORCID
Added: May 9, 2023

2023 journal article

Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS, 13(3), 576–609.

By: A. Chertock, S. Chu & A. Kurganov

author keywords: Local smoothness indicator; scheme adaption; strong stability preserving Runge-Kutta methods; hyperbolic systems of conservation laws; A-WENO schemes
Sources: Web Of Science, NC State University Libraries
Added: July 24, 2023

2023 journal article

Denoising convolution algorithms and applications to SAR signal processing

Communications on Analysis and Computation, 1(2), 135–156.

By: A. Chertock n, N. Mathematics, C. Leonard n, S. Tsynkov n, S. Utyuzhnikov* & A. Mechanical

Source: ORCID
Added: September 19, 2023

2023 journal article

Local characteristic decomposition based central-upwind scheme

JOURNAL OF COMPUTATIONAL PHYSICS, 473.

By: A. Chertock*, S. Chu, M. Herty, A. Kurganov & M. Lukacova-Medvid'ova

author keywords: Local characteristic decomposition; Central-upwind schemes; Hyperbolic systems of conservative laws; Euler equations of gas dynamics
Sources: Web Of Science, NC State University Libraries
Added: November 21, 2022

2023 journal article

Stochastic Galerkin method for cloud simulation. Part II: A fully random Navier-Stokes-cloud model

Journal of Computational Physics, 479, 111987.

By: A. Chertock n, A. Kurganov*, M. Lukáčová-Medvid'ová*, P. Spichtinger* & B. Wiebe*

TL;DR: A fully random Navier-Stokes-cloud model in which randomness in the macroscopic fluid dynamics as well is included, and a generalized polynomial chaos stochastic Galerkin method is derived and implemented. (via Semantic Scholar)
Source: ORCID
Added: September 19, 2023

2023 journal article

Well-balanced numerical method for atmospheric flow equations with gravity

APPLIED MATHEMATICS AND COMPUTATION, 439.

By: A. Chertock n, A. Kurganov*, T. Wu* & J. Yan n

author keywords: Atmospheric flow equations with gravity; Well-balanced central -upwind scheme; Equilibrium variables; Quadrilateral mesh; Irregular domains
Sources: Web Of Science, NC State University Libraries
Added: December 5, 2022

2022 journal article

On a hybrid continuum-kinetic model for complex fluids

Partial Differential Equations and Applications, 3(5).

UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Source: ORCID
Added: September 19, 2023

2022 journal article

Well-Balancing via Flux Globalization: Applications to Shallow Water Equations with Wet/Dry Fronts

JOURNAL OF SCIENTIFIC COMPUTING, 90(1).

By: A. Chertock n, A. Kurganov*, X. Liu*, Y. Liu* & T. Wu*

author keywords: Flux globalization; Central-upwind schemes; Well-balanced schemes; "Lake-at-rest" steady states; "Dry lake" steady states
Sources: Web Of Science, NC State University Libraries
Added: November 29, 2021

2021 journal article

Hybrid Multifluid Algorithms Based on the Path-Conservative Central-Upwind Scheme

JOURNAL OF SCIENTIFIC COMPUTING, 89(2).

By: A. Chertock n, S. Chu* & A. Kurganov*

author keywords: Path-conservative scheme; Central-upwind scheme; Compressible multifluids; Pressure evolution model
Sources: Web Of Science, NC State University Libraries
Added: October 26, 2021

2020 chapter

Central-upwind scheme for a non-hydrostatic Saint-Venant system

In Hyperbolic problems: theory, numerics, applications (Vol. 10, pp. 25–41). Am. Inst. Math. Sci. (AIMS), Springfield, MO.

By: A. Chertock, A. Kurganov, J. Miller & J. Yan

Source: ORCID
Added: September 19, 2023

2020 journal article

Finite-Volume-Particle Methods for the Two-Component Camassa-Holm System

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 27(2), 480–502.

By: A. Chertock*, A. Kurganov & Y. Liu

author keywords: Two-component Camassa-Holm system; finite-volume method; deterministic particle method; finite-volume-particle method; central-upwind scheme
Sources: Web Of Science, NC State University Libraries
Added: December 30, 2019

2020 journal article

Operator splitting based central-upwind schemes for shallow water equations with moving bottom topography

Communications in Mathematical Sciences, 18(8), 2149–2168.

By: A. Chertock n, A. Kurganov* & T. Wu*

TL;DR: A robust andcient numerical method for shallow water equations with moving bottom topography consisting of the Saint-Venant system governing the water coupled with the Exner equation for the sediment transport and an operator splitting approach for the underlying coupled system is developed. (via Semantic Scholar)
Source: ORCID
Added: April 28, 2021

2019 journal article

A New Approach for Designing Moving-Water Equilibria Preserving Schemes for the Shallow Water Equations

JOURNAL OF SCIENTIFIC COMPUTING, 80(1), 538–554.

By: Y. Cheng*, A. Chertock n, M. Herty*, A. Kurganov* & T. Wu*

author keywords: Shallow water equations; Central-upwind scheme; Well-balanced method; Steady-state solutions (equilibria); Moving-water and still-water equilibria
Sources: Web Of Science, ORCID, NC State University Libraries
Added: June 17, 2019

2019 journal article

Adaptive moving mesh upwind scheme for the two-species chemotaxis model

Computers & Mathematics with Applications, 77(12), 3172–3185.

By: A. Chertock*, A. Kurganov*, M. Ricchiuto & T. Wu

author keywords: Two-species chemotaxis system; Adaptive moving mesh (AMM) method; Finite-volume upwind method; Singular (spiky) solutions
TL;DR: An adaptive moving mesh (AMM) finite-volume semi-discrete upwind method for the two-species chemotaxis system and an alternative approach relying on mesh adaptation, which helps to improve the approximation of the singular structures evolved bychemotaxis models are considered. (via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Sources: Web Of Science, Crossref, ORCID, NC State University Libraries
Added: July 1, 2019

2019 journal article

An asymptotic preserving scheme for kinetic chemotaxis models in two space dimensions

Kinetic & Related Models, 12(1), 195–216.

By: A. Chertock*, A. Kurganov, M. Lukáčová-Medvid’ová & Ș. Nur Özcan

author keywords: Chemotaxis; kinetic equations; multiscale models; asymptotic preserving (AP) methods; operator splitting
UN Sustainable Development Goal Categories
Sources: ORCID, Crossref, NC State University Libraries
Added: September 8, 2019

2019 journal article

An asymptotic preserving scheme for the two-dimensional shallow water equations with Coriolis forces

JOURNAL OF COMPUTATIONAL PHYSICS, 391, 259–279.

By: X. Liu*, A. Chertock n & A. Kurganov*

author keywords: Saint-Venant system of shallow water equations; Coriolis forces; Asymptotic preserving scheme; Central-upwind scheme; Flux splitting; Implicit-explicit approach
TL;DR: Numerical experiments demonstrate that the developed AP scheme achieves the theoretical second-order rate of convergence and the time-step stability restriction is independent of the Froude number, which makes the proposed AP scheme an efficient and robust alternative to fully explicit numerical methods. (via Semantic Scholar)
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation (OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: June 17, 2019

2019 article

High-Resolution Positivity and Asymptotic Preserving Numerical Methods for Chemotaxis and Related Models

ACTIVE PARTICLES, VOL 2: ADVANCES IN THEORY, MODELS, AND APPLICATIONS, pp. 109–148.

By: A. Chertock n & A. Kurganov*

TL;DR: Many microorganisms exhibit a special pattern formation at the presence of a chemoattractant, food, light, or areas with high oxygen concentration, so a multiscale chemotaxis models can be used to describe collective cell movement. (via Semantic Scholar)
Sources: Web Of Science, NC State University Libraries
Added: March 30, 2020

2019 journal article

Incompressible limit of a continuum model of tissue growth with segregation for two cell populations

MATHEMATICAL BIOSCIENCES AND ENGINEERING, 16(5), 5804–5835.

By: A. Chertock n, P. Degond*, S. Hecht* & J. Vincent*

author keywords: tissue growth; two cell populations; incompressible limit; free boundary problem
MeSH headings : Biological Phenomena; Cell Proliferation; Computer Simulation; Developmental Biology; Elasticity; Epidermis / physiopathology; Epithelium / physiology; Humans; Models, Biological; Models, Theoretical; Neoplasms / physiopathology; Porosity; Stress, Mechanical
TL;DR: The influ-ence of the model parameters are studied thanks to one-dimensional simulations using a finite-volume method for a relaxation approximation of the fourth order diffusion and formal arguments are provided that the model approximates a free boundary Hele Shaw type model. (via Semantic Scholar)
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID, NC State University Libraries
Added: July 8, 2019

2019 journal article

Incompressible limit of a continuum model of tissue growth with segregation for two cell populations

Math. Biosci. Eng., 16(5), 5804–5835.

By: A. Chertock n, P. Degond, S. Hecht & J. Vincent

Source: ORCID
Added: September 8, 2019

2019 journal article

One-Dimensional/Two-Dimensional Coupling Approach with Quadrilateral Confluence Region for Modeling River Systems

Journal of Scientific Computing.

Alina Chertock

author keywords: Shallow water flow in river systems; One-dimensional; two-dimensional coupling; Quadrilateral confluence region; Well-balanced central-upwind scheme
TL;DR: A new 1-D/2-D river junction model is proposed, in which each reach of the river is modeled by the1-D shallow water equations, while the confluence region, where the mixing of flows from the different directions occurs, is modeling by the 2-D ones. (via Semantic Scholar)
Source: ORCID
Added: September 10, 2019

2019 journal article

Preface to the Special Issue in Memory of Professor Saul Abarbanel

Journal of Scientific Computing.

Alina Chertock; Semyon Tsynkov

Source: ORCID
Added: December 4, 2019

2019 journal article

Stochastic Galerkin method for cloud simulation

Mathematics of Climate and Weather Forecasting, 5(1), 65–106.

By: A. Chertock n, A. Kurganov n, M. Lukáčová-Medvid’ová*, P. Spichtinger* & B. Wiebe n

TL;DR: A stochastic Galerkin method is developed for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds to explicitly describe the evolution of uncertainties that arise due to unknown input data, such as model parameters and initial or boundary conditions. (via Semantic Scholar)
Sources: Crossref, NC State University Libraries
Added: December 11, 2019

2018 journal article

A second-order finite-difference method for compressible fluids in domains with moving boundaries

Commun. Comput. Phys., 23(1), 230–263.

By: A. Chertock, A. Coco, A. Kurganov & G. Russo

Sources: NC State University Libraries, ORCID
Added: August 6, 2018

2018 journal article

AN ASYMPTOTIC PRESERVING SCHEME FOR KINETIC MODELS WITH SINGULAR LIMIT

KINETIC AND RELATED MODELS, 11(4), 735–756.

By: A. Chertock*, C. Tan & B. Yan

author keywords: Kinetic models; singular limit; asymptotic-preserving schemes; velocity scaling; aggregation equation; flocking phenomena
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2018 journal article

High-order positivity-preserving hybrid finite-volume-finite-difference methods for chemotaxis systems

ADVANCES IN COMPUTATIONAL MATHEMATICS, 44(1), 327–350.

By: A. Chertock n, Y. Epshteyn*, H. Hu & A. Kurganov*

author keywords: Patlak-Keller-Segel chemotaxis system; Advection-diffusion-reaction systems; High-order finite-difference; Finite-volume methods; Positivity-preserving algorithms
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2018 chapter

Well-Balanced Central-Upwind Schemes for 2x2 Systems of Balance Laws

In Theory, Numerics and Applications of Hyperbolic Problems I (Vol. 236, pp. 345–361).

By: A. Chertock n, M. Herty* & Ş. Özcan n

Sources: Crossref, ORCID
Added: August 30, 2019

2018 journal article

Well-balanced schemes for the Euler equations with gravitation: Conservative formulation using global fluxes

JOURNAL OF COMPUTATIONAL PHYSICS, 358, 36–52.

By: A. Chertock n, S. Cui*, A. Kurganov*, S. Ozcan n & E. Tadmor*

author keywords: Euler equations of gas dynamics with gravitation; Well-balanced scheme; Equilibrium variables; Central-upwind scheme; Piecewise linear reconstruction
TL;DR: A new paradigm based on a purely conservative reformulation of the Euler equations using global fluxes is advocated, capable of exactly preserving steady-state solutions expressed in terms of a nonlocal equilibrium variable. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2018 journal article

Well-balanced schemes for the shallow water equations with Coriolis forces

NUMERISCHE MATHEMATIK, 138(4), 939–973.

By: A. Chertock n, M. Dudzinski*, A. Kurganov* & M. Lukacova-Medvid'ova*

Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2017 chapter

A Practical Guide to Deterministic Particle Methods

In Handbook of Numerical Analysis (Vol. 18, pp. 177–202).

By: A. Chertock n

author keywords: Deterministic particle methods; Particle function approximations; Remising techniques; Linear transport equations; Convection-diffusion equation; Dispersion equations
TL;DR: This chapter provides a mathematical introduction to deterministic particle methods and review different aspects of their practical implementation such as recovering an approximate solution from its particle distribution and an investigation of various particle redistribution algorithms. (via Semantic Scholar)
Sources: Crossref, ORCID
Added: August 6, 2018

2017 chapter

A Simple Finite-Volume Method on a Cartesian Mesh for Pedestrian Flows with Obstacles

In Springer Proceedings in Mathematics & Statistics (Vol. 199, pp. 43–55).

By: Y. Cheng*, A. Chertock n & A. Kurganov*

author keywords: Pedestrian flow model; Hyperbolic conservation laws; Finite-volume method; Interface tracking method; Eikonal equation; Fast sweeping method
TL;DR: Though the method is only first-order accurate near the obstacles, it is robust and provides sharp resolution of discontinuities as illustrated in a number of numerical experiments. (via Semantic Scholar)
Sources: Crossref, ORCID
Added: August 6, 2018

2017 journal article

An asymptotic-preserving method for a relaxation of the Navier-Stokes-Korteweg equations

JOURNAL OF COMPUTATIONAL PHYSICS, 335, 387–403.

By: A. Chertock n, P. Degond* & J. Neusser*

author keywords: Asymptotic-preserving scheme; Diffuse-interface model; Compressible flow with phase transition
TL;DR: It is proved that the new scheme provides a consistent discretization of the NSK system in the relaxation limit and it is demonstrated that it is capable of accurately and efficiently computing numerical solutions of problems with realistic density ratios and small interfacial widths. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2017 journal article

Hybrid Finite-Volume-Particle Method for Dusty Gas Flows

SMAI Journal of Computational Mathematics, 3, 139–180.

By: A. Chertock*, S. Cui & A. Kurganov

Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019

2016 journal article

Central-upwind scheme for shallow water equations with discontinuous bottom topography

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 47(1), 91–103.

By: A. Bernstein n, A. Chertock n & A. Kurganov*

author keywords: hyperbolic system of conservation and balance laws; semi-discrete central-upwind scheme; Saint Venant system of shallow water equations
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2015 journal article

A Finite-Volume Method for Nonlinear Nonlocal Equations with a Gradient Flow Structure

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 17(1), 233–258.

By: J. Carrillo*, A. Chertock n & Y. Huang*

author keywords: Finite-volume method; gradient flow; nonlinear nonlocal equations
TL;DR: The proposed scheme is able to cope with non-smooth stationary states, different time scales including metastability, as well as concentrations and self-similar behavior in- duced by singular nonlocal kernels. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2015 article

Elastic collisions among peakon solutions for the Camassa-Holm equation

Chertock, A., Liu, J.-G., & Pendleton, T. (2015, July). APPLIED NUMERICAL MATHEMATICS, Vol. 93, pp. 30–46.

By: A. Chertock n, J. Liu* & T. Pendleton*

author keywords: Camassa-Holm equation; Particle method; Peakon solutions; Elastic collisions; Conservation laws; Completely integrable systems
UN Sustainable Development Goal Categories
7. Affordable and Clean Energy (OpenAlex)
14. Life Below Water (Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2015 journal article

Steady State and Sign Preserving Semi-Implicit Runge--Kutta Methods for ODEs with Stiff Damping Term

SIAM Journal on Numerical Analysis, 53(4), 2008–2029.

By: A. Chertock*, S. Cui, A. Kurganov & T. Wu

author keywords: ordinary differential equations with stiff damping terms; semi-implicit methods; strong stability preserving Runge-Kutta methods; implicit-explicit methods; shallow water equations with friction terms
TL;DR: A family of second-order semi-implicit time integration methods for systems of ordinary differential equations (ODEs) with stiff damping term that are capable of exactly preserving the steady states as well as maintaining the sign of the computed solution under the time step restriction determined by the nonstiff part of the system only. (via Semantic Scholar)
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation (OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries, Crossref
Added: August 6, 2018

2015 journal article

Well-balanced positivity preserving central-upwind scheme for the shallow water system with friction terms

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, 78(6), 355–383.

By: A. Chertock n, S. Cui*, A. Kurganov* & T. Wu*

author keywords: shallow water equations with friction terms; central-upwind scheme; well-balanced scheme
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities (OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2014 journal article

An Eulerian-Lagrangian method for optimization problems governed by multidimensional nonlinear hyperbolic PDEs

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS, 59(3), 689–724.

By: A. Chertock n, M. Herty* & A. Kurganov*

author keywords: Optimal control; Multidimensional hyperbolic partial differential equations; Numerical methods
TL;DR: A hybrid method is developed, which utilizes advantages of both the Eulerian finite-volume central-upwind scheme and the Lagrangian discrete characteristics method for solving the adjoint transport equation for hyperbolic balance laws in one and two space dimensions. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2014 journal article

Central-upwind schemes for the system of shallow water equations with horizontal temperature gradients

NUMERISCHE MATHEMATIK, 127(4), 595–639.

By: A. Chertock n, A. Kurganov* & Y. Liu*

Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2014 journal article

Solving Two-Mode Shallow Water Equations Using Finite Volume Methods

COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 16(5), 1323–1354.

By: M. Castro Diaz, Y. Cheng*, A. Chertock n & A. Kurganov*

author keywords: Two-mode shallow water equations; nonconservative products; conditional hyperbolicity; finite volume methods; central-upwind schemes; splitting methods; upwind schemes
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation (OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2013 journal article

PEDESTRIAN FLOW MODELS WITH SLOWDOWN INTERACTIONS

Mathematical Models and Methods in Applied Sciences, 24(02), 249–275.

By: A. Chertock n, A. Kurganov*, A. Polizzi* & I. Timofeyev*

author keywords: Pedestrian traffic flow; stochastic cellular automata model; mesoscopic and macroscopic models; exclusion process; nonlinear diffusion
TL;DR: Numerical experiments demonstrate that the nonlinear diffusion is essential for reproducing the behavior of the stochastic system in the nonhyperbolic regime. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries, Crossref
Added: August 6, 2018

2013 journal article

Three-Layer Approximation of Two-Layer Shallow Water Equations

MATHEMATICAL MODELLING AND ANALYSIS, 18(5), 675–693.

By: A. Chertock n, A. Kurganov*, Z. Qu* & T. Wu*

author keywords: two-layer shallow water equations; central-upwind scheme; well-balanced scheme; conditional hyperbolicity
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation (OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2012 journal article

CONVERGENCE OF A PARTICLE METHOD AND GLOBAL WEAK SOLUTIONS OF A FAMILY OF EVOLUTIONARY PDES

SIAM JOURNAL ON NUMERICAL ANALYSIS, 50(1), 1–21.

By: A. Chertock n, J. Liu & T. Pendleton*

Contributors: A. Chertock n, J. Liu & T. Pendleton*

author keywords: Camassa-Holm equation; Degasperis-Procesi equation; Euler-Poincare equation; global weak solution; particle method; space-time BV estimates; peakon solutions; conservation laws; completely integrable systems
TL;DR: From this result, the existence of a unique global weak solution in some special cases is proved and stronger regularity properties of the solution are obtained than previously established. (via Semantic Scholar)
UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2012 chapter

Convergence Analysis of the Particle Method for the Camassa-Holm Equation

In Series in Contemporary Applied Mathematics (Vol. 18, pp. 365–373).

By: A. Chertock n, J. Liu* & T. Pendleton n

Sources: Crossref, ORCID
Added: July 20, 2019

2012 journal article

INTEGRATION OF THE EPDIFF EQUATION BY PARTICLE METHODS

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 46(3), 515–534.

By: A. Chertock n, P. Du Toit* & J. Marsden*

Contributors: A. Chertock n, P. Du Toit* & J. Marsden*

author keywords: Solitons; peakons; integrable Hamiltonian systems; particle methods; weak solutions; variational principle; momentum maps; shallow water and internal waves
UN Sustainable Development Goal Categories
14. Life Below Water (Web of Science)
15. Life on Land (OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2012 journal article

ON A CHEMOTAXIS MODEL WITH SATURATED CHEMOTACTIC FLUX

KINETIC AND RELATED MODELS, 5(1), 51–95.

By: A. Chertock n, A. Kurganov n, X. Wang n & Y. Wu n

Contributors: A. Chertock n, A. Kurganov n, X. Wang n & Y. Wu n

author keywords: Chemotaxis; saturation of flux; spiky steady states; local and global existence; bifurcation; hybrid finite-volume-finite-difference method; second-order positivity preserving upwind scheme
UN Sustainable Development Goal Categories
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2012 journal article

Sinking, merging and stationary plumes in a coupled chemotaxis-fluid model: a high-resolution numerical approach

Journal of Fluid Mechanics, 694, 155–190.

By: A. Chertock n, K. Fellner*, A. Kurganov*, A. Lorz* & P. Markowich*

Contributors: A. Chertock n, K. Fellner*, A. Kurganov*, A. Lorz* & P. Markowich*

author keywords: bioconvection; computational methods; micro-organism dynamics
UN Sustainable Development Goal Categories
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019

2011 chapter

Central-upwind schemes for Boussinesq paradigm equations

In Computational science and high performance computing IV (Vol. 115, pp. 267–281).

By: A. Chertock n, C. Christov* & A. Kurganov*

UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Sources: NC State University Libraries, ORCID, NC State University Libraries
Added: August 6, 2018

2010 journal article

A Fast Explicit Operator Splitting Method for Passive Scalar Advection

JOURNAL OF SCIENTIFIC COMPUTING, 45(1-3), 200–214.

By: A. Chertock n, C. Doering*, E. Kashdan* & A. Kurganov*

Contributors: A. Chertock n, C. Doering*, E. Kashdan* & A. Kurganov*

TL;DR: A fast explicit operator splitting method is extended, recently proposed, for solving deterministic convection-diffusion equations, to the problems with random velocity fields and singular source terms. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2010 chapter

On splitting-based numerical methods for convection-diffusion equations

In Numerical Methods for Balance Laws, Quaderni di Matematica, Aracne editrice S.r.l (Vol. 24, p. 303). Roma.

By: A. Chertock & A. Kurganov

Source: NC State University Libraries
Added: July 28, 2019

2010 chapter

On splitting-based numerical methods for convection-diffusionequations

In G. Puppo & G. Russo (Eds.), Numerical Methods for Balance Laws (p. 303). Caserta: Dipartimento di matematica della Seconda Universitá di Napoli.

By: A. Chertock & A. Kurganov

Ed(s): G. Puppo & G. Russo

Source: NC State University Libraries
Added: December 22, 2020

2009 journal article

Computing multivalued solutions of pressureless gas dynamics by deterministic particle methods

Commun. Comput. Phys., 5(2-4), 565–581. http://global-sci.org/intro/article_detail/cicp/7750.html

By: A. Chertock & A. Kurganov

Source: ORCID
Added: September 8, 2019

2009 conference paper

Computing multivalued solutions of pressureless gas dynamics by deterministic particle methods

Communications in Computational Physics, 5(2-4), 565–581.

By: A. Chertock & A. Kurganov

Source: NC State University Libraries
Added: August 6, 2018

2009 article

Fast explicit operator splitting method for convection-diffusion equations

Chertock, A., Kurganov, A., & Petrova, G. (2009, January 30). INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Vol. 59, pp. 309–332.

By: A. Chertock n, A. Kurganov* & G. Petrova*

Contributors: A. Chertock n, A. Kurganov* & G. Petrova*

author keywords: convection-diffusion equations; operator splitting; polymer systems; finite-volume methods; heat kernel
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2009 chapter

On splitting-based numerical methods for convection-diffusion equations

In Numerical methods for balance laws (Vol. 24, pp. 303–343). Dept. Math., Seconda Univ. Napoli, Caserta.

By: A. Chertock & A. Kurganov

Source: ORCID
Added: September 8, 2019

2008 journal article

A SIMPLE EULERIAN FINITE-VOLUME METHOD FOR COMPRESSIBLE FLUIDS IN DOMAINS WITH MOVING BOUNDARIES

COMMUNICATIONS IN MATHEMATICAL SCIENCES, 6(3), 531–556.

By: A. Chertock n & A. Kurganov*

author keywords: Compressible Enter equations; ghost-cell extrapolation; moving boundaries; semi-discrete finite-volume schemes
Sources: Web Of Science, ORCID
Added: August 6, 2018

2008 journal article

A second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models

NUMERISCHE MATHEMATIK, 111(2), 169–205.

By: A. Chertock n & A. Kurganov*

Contributors: A. Chertock n & A. Kurganov*

TL;DR: Numerical results demonstrate high accuracy, stability, and robustness of the proposed second-order central-upwind scheme, which is applied to a number of two-dimensional problems including the most commonly used Keller–Segel chemotaxis model and its modern extensions. (via Semantic Scholar)
UN Sustainable Development Goal Categories
15. Life on Land (OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2008 journal article

INTERFACE TRACKING METHOD FOR COMPRESSIBLE MULTIFLUIDS

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 42(6), 991–1019.

By: A. Chertock n, S. Karni* & A. Kurganov*

Contributors: A. Chertock n, S. Karni* & A. Kurganov*

author keywords: Compressible Euler equations; multicomponent fluids; material interfaces; finite-volume schemes
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2008 journal article

Modified Optimal Prediction and its Application to a Particle-Method Problem

JOURNAL OF SCIENTIFIC COMPUTING, 37(2), 189–201.

By: A. Chertock n, D. Gottlieb* & A. Solomonoff*

Contributors: A. Chertock n, D. Gottlieb* & A. Solomonoff*

author keywords: Optimal prediction; Particle methods; Multiscale computations
TL;DR: This paper applies the original and modified optimal prediction methods to a system of ODEs obtained from a particle method discretization of a hyperbolic PDE and demonstrates their performance in a number of numerical experiments. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2008 chapter

Propagation of Diffusing Pollutant by a Hybrid Eulerian–Lagrangian Method

In Hyperbolic Problems: Theory, Numerics, Applications (pp. 371–379).

By: A. Chertock n, E. Kashdan*, A. Kurganov*, S. BenzoniGavage & D. Serre

Contributors: S. BenzoniGavage, A. Chertock n, E. Kashdan*, A. Kurganov* & D. Serre

Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019

2007 journal article

A new sticky particle method for pressureless gas dynamics

SIAM JOURNAL ON NUMERICAL ANALYSIS, 45(6), 2408–2441.

By: A. Chertock*, A. Kurganov & Y. Rykov

Contributors: A. Chertock*, A. Kurganov & Y. Rykov

author keywords: nonstrictly hyperbolic systems of conservation laws; pressureless gas dynamics; mass concentration; strong singularities; delta-shock; sticky particle method
TL;DR: The authors' simulations demonstrate the superiority of the results obtained by the sticky particle method that accurately tracks the evolution of developing discontinuities and does not smear the developing $\delta$-shocks. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2006 article

Finite-volume-particle methods for models of transport of pollutant in shallow water

Chertock, A., Kurganov, A., & Petrova, G. (2006, June). JOURNAL OF SCIENTIFIC COMPUTING, Vol. 27, pp. 189–199.

By: A. Chertock n, A. Kurganov* & G. Petrova*

Contributors: A. Chertock n, A. Kurganov* & G. Petrova*

author keywords: Saint-Venant system of shallow water equations; transport of pollutant; finite-volume schemes; particle methods; central-upwind schemes; balance laws
TL;DR: The idea behind the new finite- volume-particle (FVP) method is to use different schemes for the flow and the pollution computations: the shallow water equations are numerically integrated using a finite-volume scheme, while the transport equation is solved by a particle method. (via Semantic Scholar)
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation (OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2006 article

On a practical implementation of particle methods

APPLIED NUMERICAL MATHEMATICS, Vol. 56, pp. 1418–1431.

By: A. Chertock n & A. Kurganov*

Contributors: A. Chertock n & A. Kurganov*

author keywords: linear transport equations with discontinuous coefficients; deterministic particle method; method of characteristics; finite-volume methods; reactive Euler equations of gas dynamics
TL;DR: It is demonstrated that some of known recovering procedures, suitable for smooth functions, may fail to produce reasonable results in the nonsmooth case, and several successful strategies which may be useful in practice are discussed. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2005 chapter

Conservative locally moving mesh method for multifluid flows

In Finite Volumes for Complex Applications IV (pp. 273–284). ISTE, London.

By: A. Chertock & A. Kurganov

Sources: NC State University Libraries, ORCID
Added: July 28, 2019

2005 chapter

Fast explicit operator splitting method. Application to the polymer system

In Finite Volumes for Complex Applications IV: Vol. IV (pp. 63–72). ISTE, London.

By: A. Chertock, A. Kurganov & G. Petrova

Sources: NC State University Libraries, ORCID
Added: July 28, 2019

2005 journal article

On degenerate saturated-diffusion equations with convection

NONLINEARITY, 18(2), 609–630.

By: A. Chertock n, A. Kurganov* & P. Rosenau*

Contributors: A. Chertock n, A. Kurganov* & P. Rosenau*

Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2005 journal article

On wavelet-based numerical homogenization

MULTISCALE MODELING & SIMULATION, 3(1), 65–88.

By: A. Chertock n & D. Levy

Contributors: A. Chertock n & D. Levy

author keywords: numerical homogenization; wavelets; Helmholtz equation
TL;DR: This work shows how to improve the efficiency of this numerical homogenization method by choosing a different compact representation of the homogenized operator, and suggests an approach for obtaining a sparse representation that is significantly simpler than the alternative sparse representations. (via Semantic Scholar)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2004 journal article

On a hybrid finite-volume-particle method

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 38(6), 1071–1091.

By: A. Chertock n & A. Kurganov*

Contributors: A. Chertock n & A. Kurganov*

author keywords: shallow water equations; transport of passive pollutant; finite-volume schemes; particle method
TL;DR: A hybrid finite-volume-particle numerical method for computing the transport of a passive pollutant by a flow using the one- and two-dimensional Saint-Venant system of shallow water equations and a particle method. (via Semantic Scholar)
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation (OpenAlex)
Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2003 journal article

Formation of discontinuities in flux-saturated degenerate parabolic equations

NONLINEARITY, 16(6), 1875–1898.

By: A. Chertock n, A. Kurganov* & P. Rosenau*

Contributors: A. Chertock n, A. Kurganov* & P. Rosenau*

Sources: Web Of Science, ORCID, NC State University Libraries
Added: August 6, 2018

2002 journal article

A Particle Method for the KdV Equation

Journal of Scientific Computing, 17(1-4), 491–499.

By: A. Chertock* & D. Levy*

Contributors: A. Chertock* & D. Levy*

author keywords: Particle methods; dispersion-velocity method; KdV equation
TL;DR: The dispersion-velocity particle method is extended to advection models in which the velocity does not depend linearly on the solution or its derivatives and is demonstrated numerically how it captures soliton–soliton interactions. (via Semantic Scholar)
Source: ORCID
Added: August 27, 2019

2002 journal article

On the stability of a class of self-similar solutions to the filtration-absorption equation

European Journal of Applied Mathematics, 13(2), 179–194.

By: A. Chertock*

Contributors: A. Chertock*

Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019

2002 journal article

Particle methods for the KdV equation

Journal of Scientific Computing, 17, 491–499.

By: A. Chertock & D. Levy

Source: NC State University Libraries
Added: July 10, 2019

2001 journal article

Particle Methods for Dispersive Equations

Journal of Computational Physics, 171(2), 708–730.

By: A. Chertock* & D. Levy

Contributors: A. Chertock* & D. Levy

author keywords: particle methods; dispersive equations; diffusion-velocity; dispersion-velocity; compacton equations
TL;DR: A new dispersion-velocity particle method is introduced for approximating solutions of linear and nonlinear dispersive equations for the first time in which particle methods are being used for solving such equations. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019

2000 journal article

Self-similar intermediate asymptotics for a degenerate parabolic filtration-absorption equation

Proceedings of the National Academy of Sciences, 97(18), 9844–9848.

By: G. Barenblatt, M. Bertsch*, A. Chertock* & V. Prostokishin*

Contributors: G. Barenblatt, M. Bertsch*, A. Chertock* & V. Prostokishin*

MeSH headings : Geological Phenomena; Geology; Models, Biological; Models, Statistical; Models, Theoretical; Water
TL;DR: Numerical experiments indicate that the self-similar solutions obtained represent intermediate asymptotics of a wider class of solutions when the influence of details of the initial conditions disappears but the solution is still far from the ultimate state: identical zero. (via Semantic Scholar)
UN Sustainable Development Goal Categories
6. Clean Water and Sanitation (OpenAlex)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 27, 2019

2000 journal article

Strict Stability of High-Order Compact Implicit Finite-Difference Schemes: The Role of Boundary Conditions for Hyperbolic PDEs, I

Journal of Computational Physics, 160(1), 42–66.

By: S. Abarbanel & A. Chertock*

Contributors: S. Abarbanel & A. Chertock*

author keywords: hyperbolic PDEs; boundary conditions; stability; accuracy; error bounds
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019

2000 journal article

Strict Stability of High-Order Compact Implicit Finite-Difference Schemes: The Role of Boundary Conditions for Hyperbolic PDEs, II

Journal of Computational Physics, 160(1), 67–87.

By: S. Abarbanel*, A. Chertock* & A. Yefet*

Contributors: S. Abarbanel*, A. Chertock* & A. Yefet*

author keywords: hyperbolic PDEs; boundary conditions; stability; accuracy; error bounds
TL;DR: This paper deals with the problem of systems of hyperbolic PDEs in one and two space dimensions, using the theory of part I of Part I of theorems on ellipsoidal topographies. (via Semantic Scholar)
Sources: Crossref, ORCID, NC State University Libraries
Added: July 20, 2019

1991 journal article

An algorithm for the numerical solution of equations describing processes in photoreceivers

Mat. Model., 3(10), 95–103.

By: Y. Karamzin, V. Trofimov & A. Chertok

Source: ORCID
Added: September 8, 2019

1991 journal article

On a numerical algorithm for nonlinear differential equations describing some processes in photoreceivers

Journal of Mathematical Modeling, 3, 95–103.

By: A. Chertock, Y. Karamzin & V. Trofimov

Source: NC State University Libraries
Added: July 28, 2019

Employment

Updated: November 2nd, 2021 17:58

2021 - present

North Carolina State University Raleigh, NC, US
LeRoy B. Martin, Jr. Distinguished Professor Department of Mathematics

2015 - present

North Carolina State University Raleigh, NC, US
Associate Director Center for Research in Scientific Computation

2015 - present

North Carolina State University Raleigh, NC, US
Head Department of Mathematics

2013 - present

North Carolina State University Raleigh, NC, US
Professor Department of Mathematics

2007 - 2013

North Carolina State University Raleigh, NC, US
Associate Professor Department of Mathematics

2002 - 2007

North Carolina State University Raleigh, NC, US
Assistant Professor Department of Mathematics

2001 - 2002

University of California Berkeley, CA, US
Visiting Assistant Professor Department of Mathematics

1999 - 2002

University of California and Lawrenece Berkeley National Laboratory Berkeley, CA, US
Postdoctoral Fellow Department of Mathematics

1996 - 1999

Tel Aviv University and Academic College of Tel-Aviv-Yaffo Tel Aviv, IL
Instructor School of Mathematical Sciences

1991 - 1996

Tel Aviv University Tel Aviv, IL
Teaching Assistant School of Mathematical Sciences

Education

Updated: November 2nd, 2021 15:49

1999 - 2001

University of California Berkeley Berkeley, CA, US
Postdoctoral Fellow Mathematics

1991 - 1999

Tel Aviv University Tel Aviv, IL
Ph.D. School of Mathematical Sciences

1984 - 1989

Lomonosov Moscow State University Moscow, RU
M.Sc. (Diploma of Higher Education) Faculty of Computational Mathematics and Cybernetics

Funding History

Funding history based on the linked ORCID record. Updated: August 9th, 2023 22:00

grant September 1, 2022 - September 1, 2025
Development and Application of Modern Numerical Methods for Nonlinear Hyperbolic Systems of Partial Differential Equations
National Science Foundation
grant September 1, 2018 - August 31, 2022
Collaborative Research: Structure Preserving Numerical Methods for Hyperbolic Balance Laws with Applications to Shallow Water and Atmospheric Models
Directorate for Mathematical & Physical Sciences
grant September 1, 2015 - August 31, 2019
Collaborative Research: Numerical Methods for Partial Differential Equations Arising in Shallow Water Modeling
Directorate for Mathematical & Physical Sciences
grant September 1, 2012 - August 31, 2016
Collaborative Research: Numerical Methods for Shallow Water Equations and Related Models
Directorate for Mathematical & Physical Sciences
grant January 1, 2012 - January 1, 2015
Numerical Methods for Shallow Water Equations and Related Models
Office of Naval Research
grant October 1, 2011 - September 30, 2015
Collaborative Research: Development of High-Resolution Finite-Volume Methods for Systems of Nonlinear Time-Dependent PDEs
Directorate for Mathematical & Physical Sciences
grant September 1, 2007 - August 31, 2011
Innovative Numerical Methods for Nonlinear Time-Dependent PDEs
Directorate for Mathematical & Physical Sciences
grant September 1, 2004 - February 29, 2008
Particle Methods for Nonlinear Time-Dependent PDEs
Directorate for Mathematical & Physical Sciences

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