Works (70)

2022 journal article

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

JOURNAL OF SCIENTIFIC COMPUTING, 1.

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

Sources: Web Of Science, ORCID
Added: November 29, 2021

2021 journal article

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

JOURNAL OF SCIENTIFIC COMPUTING, 11.

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

Sources: Web Of Science, ORCID
Added: October 26, 2021

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

Sources: Web Of Science, ORCID
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, A. Kurganov & T. Wu

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, M. Herty, A. Kurganov & T. Wu

Sources: Web Of Science, ORCID
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

Sources: Web Of Science, Crossref, ORCID
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

Sources: ORCID, Crossref
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 & A. Kurganov

Sources: Web Of Science, ORCID
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 & A. Kurganov

Sources: Web Of Science, ORCID
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, P. Degond, S. Hecht & J. Vincent

Sources: Web Of Science, ORCID
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, 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.

By: A. Chertock

Source: ORCID
Added: September 10, 2019

2019 journal article

Preface to the Special Issue in Memory of Professor Saul Abarbanel

Journal of Scientific Computing.

By: A. Chertock

Source: ORCID
Added: September 15, 2020

2019 journal article

Stochastic Galerkin method for cloud simulation

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

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

Sources: Crossref, ORCID
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

Kinet. Relat. Models, 11(4), 735–756.

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

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

2018 journal article

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

Adv. Comput. Math., 44(1), 327–350.

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

Sources: NC State University Libraries, ORCID
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, M. Herty & Ş. Özcan

Sources: Crossref, ORCID
Added: August 30, 2019

2018 journal article

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

J. Comput. Phys., 358, 36–52.

By: A. Chertock, S. Cui, A. Kurganov, Ş. Özcan & E. Tadmor

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

2018 journal article

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

Numer. Math., 138(4), 939–973.

By: A. Chertock, M. Dudzinski, A. Kurganov & M. Lukáčová-Medviďová

Sources: NC State University Libraries, ORCID
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

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 & A. Kurganov

Sources: Crossref, ORCID
Added: August 6, 2018

2017 journal article

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

J. Comput. Phys., 335, 387–403.

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

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

2016 journal article

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

Bull. Braz. Math. Soc. (N.S.), 47(1), 91–103.

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

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

2015 journal article

A finite-volume method for nonlinear nonlocal equations with a gradient flow structure

Commun. Comput. Phys., 17(1), 233–258.

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

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

2015 journal article

Elastic collisions among peakon solutions for the Camassa-Holm equation

Appl. Numer. Math., 93, 30–46.

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

Sources: NC State University Libraries, ORCID
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

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

2015 journal article

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

Internat. J. Numer. Methods Fluids, 78(6), 355–383.

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

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

2014 journal article

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

Comput. Optim. Appl., 59(3), 689–724.

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

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

2014 journal article

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

Numer. Math., 127(4), 595–639.

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

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

2014 journal article

Solving two-mode shallow water equations using finite volume methods

Commun. Comput. Phys., 16(5), 1323–1354.

By: M. Dı́az, Y. Cheng, A. Chertock & A. Kurganov

Sources: NC State University Libraries, ORCID
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, A. Kurganov, A. Polizzi & I. Timofeyev

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

2013 journal article

Three-layer approximation of two-layer shallow water equations

Math. Model. Anal., 18(5), 675–693.

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

Sources: NC State University Libraries, ORCID
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, J. Liu & T. Pendleton

Sources: NC State University Libraries, ORCID
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, J. Liu & T. Pendleton

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, P. Toit & J. Marsden

Sources: NC State University Libraries, ORCID
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, A. Kurganov, X. Wang & Y. Wu

Sources: NC State University Libraries, ORCID
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, K. Fellner, A. Kurganov, A. Lorz & P. Markowich

Sources: Crossref, ORCID
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, C. Christov & A. Kurganov

Sources: NC State University Libraries, ORCID
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, C. Doering, E. Kashdan & A. Kurganov

Sources: NC State University Libraries, ORCID
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 journal article

Fast explicit operator splitting method for convection-diffusion equations

International Journal For Numerical Methods in Fluids, 59(3), 309–332.

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

Sources: NC State University Libraries, ORCID
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 second-order positivity preserving central-upwind scheme for chemotaxis and haptotaxis models

Numerische Mathematik, 111(2), 169–205.

By: A. Chertock & A. Kurganov

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

2008 journal article

A simple Eulerian finite-volume method for compressible fluids in domains with moving boundaries

Commun. Math. Sci., 6(3), 531–556.

By: A. Chertock & A. Kurganov

Sources: NC State University Libraries, ORCID
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, S. Karni & A. Kurganov

Sources: NC State University Libraries, ORCID
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, D. Gottlieb & A. Solomonoff

Sources: NC State University Libraries, ORCID
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, E. Kashdan, A. Kurganov, S. BenzoniGavage & D. Serre

Sources: Crossref, ORCID
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

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

2006 journal article

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

Journal of Scientific Computing, 27(1-3), 189–199.

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

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

2006 journal article

On a practical implementation of particle methods

Applied Numerical Mathematics, 56(10-11), 1418–1431.

By: A. Chertock & A. Kurganov

Sources: NC State University Libraries, ORCID
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, A. Kurganov & P. Rosenau

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

2005 journal article

On wavelet-based numerical homogenization

Multiscale Modeling & Simulation, 3(1), 65–88.

By: A. Chertock & D. Levy

Sources: 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 & A. Kurganov

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

2003 journal article

Formation of discontinuities in flux-saturated degenerate parabolic equations

Nonlinearity, 16(6), 1875–1898.

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

Sources: NC State University Libraries, ORCID
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

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

Sources: Crossref, ORCID
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

Sources: Crossref, ORCID
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

Sources: Crossref, ORCID
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

Sources: Crossref, ORCID
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

Sources: Crossref, ORCID
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

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

2012 - 2019

Moscow Institute of Physics and Technology Dolgoprudnyy, RU
Adjunct Professor

2016 - 2016

University of Stuttgart Stuttgart, DE
Simons Visiting Professor Institute of Applied Analysis and Numerical Simulation

2014 - 2014

Johannes Gutenberg University of Mainz Mainz, Rheinland-Pfalz, DE
Visiting Professor Institute of Mathematics

2007 - 2013

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

2012 - 2012

Shanghai Jiao Tong University Shanghai, CN
Visiting Professor Department of Mathematics

2010 - 2011

Paul Sabatier University Toulouse, FR
Visiting Professor Institute of mathematics

2007 - 2009

Brown University Providence, RI, US
Visiting Associate Professor Division of Applied 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

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.

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