Alina Emil Chertock
Also known as: Alina E Chertock
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.
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.
author keywords: Chemotaxis; Navier-Stokes equations; bioconvection; diffuse-domain approach; finite-volume method; finite-difference method
arxiv.org (repository)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
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.
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.
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.
Source: ORCID
Added: September 19, 2023
2023 journal article
Local characteristic decomposition based central-upwind scheme
JOURNAL OF COMPUTATIONAL PHYSICS, 473.
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.
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.
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).
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).
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.
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.
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.
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.
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.
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
3. Good Health and Well-being
(Web of Science)
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.
author keywords: Chemotaxis; kinetic equations; multiscale models; asymptotic preserving (AP) methods; operator splitting
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
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.
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.
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)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
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.
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
3. Good Health and Well-being
(Web of Science)
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.
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.
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.
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.
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.
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.
author keywords: Kinetic models; singular limit; asymptotic-preserving schemes; velocity scaling; aggregation equation; flocking phenomena
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
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.
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
3. Good Health and Well-being
(Web of Science)
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).
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.
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.
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).
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).
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.
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.
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.
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.
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)
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
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.
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.
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.
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.
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.
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.
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.
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)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
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.
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.
Contributors: 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).
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.
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.
Contributors: 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
3. Good Health and Well-being
(Web of Science)
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.
Contributors: n , K. Fellner *, A. Kurganov *, A. Lorz* & P. Markowich*
author keywords: bioconvection; computational methods; micro-organism dynamics
UN Sustainable Development Goal Categories
3. Good Health and Well-being
(Web of Science)
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).
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.
Contributors: 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.
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.
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
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.
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.
Contributors: 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.
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.
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.
Contributors: 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
3. Good Health and Well-being
(Web of Science)
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.
Contributors: 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.
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)
UN Sustainable Development Goal Categories
11. Sustainable Cities and Communities
(Web of Science)
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).
Contributors: S. BenzoniGavage, 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.
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.
Contributors: 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.
Contributors: 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.
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.
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.
Contributors: 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.
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.
Contributors: 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.
Contributors: 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.
Contributors: * & 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.
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.
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.
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.
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.
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.
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.
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.
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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