Professor Alexander Kurganov graduated from the Moscow State
University in 1989. He then earned his PhD degree from Tel Aviv
University in 1998. After holding a three-year Assistant Professor
position at the University of Michigan, he moved to Tulane
University, where he worked as an Assistant, Associate and Full
Professor of Mathematics from 2001 to 2019. In 2016, Alexander
Kurganov arrived at SUSTech as a Full Professor and in 2019 he was
promoted to the Chair Professor.
Prof. Kurganov research is focused on numerical methods for
hyperbolic PDEs and related problems. His particular area of
expertise is finite-volume, particle and operator splitting methods
with applications to a wide variety shallow water models,
compressible gas dynamics equations, multi-component and
multi-phase fluids, PDE based models of chemotaxis, pedestrian and
traffic flows, financial mathematics, and several other areas.
Research interests:
◆ Scientific computing
◆ Numerical Methods for Time-Dependent PDEs
◆ Finite-Volume Methods
◆ Numerical Methods for Geophysical Fluid Dynamics
◆ Nonlinear PDEs
Education:
◆ PhD in Applied Mathematics, Tel Aviv University, Israel, 1998
◆ MS (Diploma of Higher Education) in Mathematics, Moscow State University, USSR, 1989
Professional Appointments:
2019–present Chair Professor, Department of Mathematics, Southern University of Science and Technology, China
2016 – 2019 Professor, Department of Mathematics, Southern University of Science and Technology, China
2010 – 2015 Professor, Mathematics Department, Tulane University, USA
2004 – 2010 Associate Professor, Mathematics Department, Tulane University, USA
2001 – 2004 Assistant Professor, Mathematics Department, Tulane University, USA
1998 – 2001 Assistant Professor, Department of Mathematics, University of Michigan, USA
Spring 1998 Postdoctoral Fellow, Institute of Applied & Computational Mathematics Foundation for Research and Technology, Heraklion, Greece
Fall 1997 Postdoctoral Fellow, Mittag-Leffler Institute, The Royal Academy of Sciences, Djursholm, Sweden
Honors & Awards:
2018–2021 NSFC Research Grant, PI, Southern University of Science and Technology, China
2018–2019 NSF Research Grant, PI, Tulane University, USA
2015–2019 NSF Research Grant, PI, Tulane University, USA
2015–2018 NSF Research Grant, PI, Tulane University
2012–2015 NSF Research Grant, PI, Tulane University
2012–2015 ONR Research Grant, PI, Tulane University
2011–2014 NSF Research Grant, PI, Tulane University
2011 German Research Foundation (DFG) Grant, Johannes Gutenberg University, Mainz
2006–2009 NSF Research Grant, PI, Tulane University
2003–2006 NSF Research Grant, PI, Tulane University
2000–2003 NSF Research Grant , PI , University of Michigan/Tulane University
1999 Rackham Graduate School Faculty Fellowship for Research , University of Michigan
1997 The Rosset Prize (for excellence in mathematics), School of Mathematical Sciences, Tel Aviv University,
Israel
Professional Activities
2017–present Associate editor of Applied Numerical Mathematics
2016–present Associate editor of the Computational Physics (specialty section of Frontiers in Physics)
2013–present Associate editor of the Advances and Applications in Fluid Mechanics
2008–present Associate editor of the International Journal of Differential Equations
2006–present Associate editor of the Mathematical Modelling and Applied Computing
2006–present Associate editor of the International Journal of Computing Science and Mathematics
List of Publications
Please see the column 'Published Works' in this page for more information
2019–present Chair Professor, Department of Mathematics, Southern University of Science and Technology, China
Courses: Scientific Computing
2016–2019 Professor, Department of Mathematics, Southern University of Science and Technology, China
Courses: Calculus, Numerical Methods for PDEs, Scientific Computing
2010–2019 Professor, Mathematics Department, Tulane University, USA
Courses: Calculus, Numerical Analysis, Numerical Linear Algebra,
Numerical Methods for ODEs and PDEs,
Applied Mathematics, ODEs, Numerical Methods for Geophysical Fluid Dynamics
2009–2012 Mathematics Department Graduate Coordinator, Tulane University, USA
Summer 2012 Visiting Professor, Institute of Natural Sciences, Shanghai Jiao Tong University, China
Course: Numerical Methods for Nonlinear Time-Dependent PDEs
May 2012 Visiting Professor, Institute of Mathematics, 2 Univeristy of Bordeaux I, France
Summer 2011 Mercator Guest Professor, Institute of Mathematics, Johannes Gutenberg University, Mainz, Germany
Course: Numerical Methods for Nonlinear Time-Dependent PDEs
2004–2010 Associate Professor, Mathematics Department, Tulane University, USA
Courses: Calculus, ODEs, PDEs, Numerical Analysis, Numerical Linear Algebra,
Numerical Methods for ODEs and PDEs,
Numerical Methods for Nonlinear Time-Dependent PDEs
Summer 2009 Visiting Associate Professor, Institute of Mathematics, Paul Sabatier University, Toulouse, France
Fall 2005 Visiting Associate Professor, Department of Mathematics, University of Michigan, USA
Course: Numerical Methods for Hyperbolic Conservation Laws
2001–2004 Assistant Professor, Mathematics Department, Tulane University, USA
Courses: Calculus, ODEs, Introduction to Numerical Analysis,
Numerical Methods for Geophysical Fluid Dynamics,
Numerical Methods for Hyperbolic Conservation Laws
1998–2001 Assistant Professor, Department of Mathematics, University of Michigan, USA
Courses: Applied Honors Calculus, Numerical Linear Algebra, Introduction to Numerical Methods
Refereed Publications (in the reversed chronological order)
Recent Preprints
A. Kurganov, Yongle Liu & Maria Lukacova-Medvidova (2021)
A Well-Balanced Asymptotic Preserving Scheme for the Two-Dimensional Rotating Shallow Water Equations with Nonflat Bottom Topography
submitted to SIAM Journal on Scientific Computing
Alina Chertock, Shaoshuai Chu & A. Kurganov (2021)
An Accurate Deterministic Projection Method for Stiff Detonation Waves
submitted to Journal of Computational Physics
Alina Chertock, Shaoshuai Chu & A. Kurganov (2021)
Hybrid Multifluid Algorithms Based on the Path-Conservative Central-Upwind Scheme
submitted to Journal of Scientific Computing
Bao-Shan Wang, Wai Sun Don, A. Kurganov & Yongle Liu (2021)
Fifth-Order A-WENO Finite-Difference Schemes Based on the Central-Upwind Rankine-Hugoniot Fluxes
submitted to Communications on Applied Mathematics and Computation
Alina Chertock, A. Kurganov, Tong Wu & Jun Yan (2021)
Well-Balanced Numerical Method for Atmospheric Flow Equations with Gravity
submitted to Communications in Computational Physics
Alina Chertock, Shaoshuai Chu & A. Kurganov (2020)
An Accurate Deterministic Projection Method for Two-Dimensional Stiff Detonation Waves
submitted to Applied Mathematics and Computation.
Alina Chertock, Shi Jin & A. Kurganov (2015)
A Well-Balanced Operator Splitting Based Stochastic Galerkin Method for the One-Dimensional Saint-Venant System with Uncertainty
submitted to Communications in Computational Physics.
Alina Chertock, Shi Jin & A. Kurganov (2015)
An Operator Splitting Based Stochastic Galerkin Method for the One-Dimensional Compressible Euler Equations with Uncertainty
submitted to SIAM/ASA Journal on Uncertainty Quantification.
A. Kurganov & Michael Pollack (2013)
Semi-Discrete Central-Upwind Schemes for Elasticity in Heterogeneous Media
submitted to IMA Journal of Numerical Analysis.
A. Kurganov, Yongle Liu & Vladimir Zeitlin (2020)
Numerical Dissipation Switch for Two-Dimensional Central-Upwind Schemes
to appear in Mathematical Modelling and Numerical Analysis.
A. Kurganov, Zhuolin Qu, Olga S. Rozanova & Tong Wu (2020)
Adaptive Moving Mesh Central-Upwind Schemes for Hyperbolic System of PDEs. Applications to Compressible Euler Equations and Granular Hydrodynamics
to appear in Communications on Applied Mathematics and Computation.
Alina Chertock, A. Kurganov, Jason Miller & Jun Yan (2019)
Central-Upwind Scheme for a Non-Hydrostatic Saint-Venant System
to appear in Proceedings of the XVII International Conference on Hyperbolic Problems: Theory, Numerics, Applications (University Park, 2018).
2021
Naveen Kumar Garg, A. Kurganov & Yongle Liu
Semi-Discrete Central-Upwind Rankine-Hugoniot Schemes for Hyperbolic Systems of Conservation Laws
Journal of Computational Physics, 428 (2021), 110078
A. Kurganov, Yongle Liu & Vladimir Zeitlin
Thermal vs Isothermal Rotating Shallow Water Equations: Comparison of Dynamical Processes in Two Models by Simulations with a Novel Well-Balanced Central-Upwind Scheme
Geophysical and Astrophysical Fluid Dynamics, 115 (2020), 125-154
2020
A. Kurganov & Petr N. Vabishchevich
Monotonization of a Family of Implicit Schemes for the Burgers Equation
Modeling, Simulation and Optimization of Complex Processes HPSC 2018, pp. 247--256, Springer, 2020.
Bao-Shan Wang, Wai Sun Don, Naveen Kumar Garg & A. Kurganov
Fifth-Order A-WENO Finite-Difference Schemes Based on a New Adaptive Diffusion Central Numerical Flux
SIAM Journal on Scientific Computing, 42 (2020), A3932-A3956.
Alina Chertock, A. Kurganov & Tong Wu
Operator Splitting Based Central-Upwind Schemes for Shallow Water Equations with Moving Bottom Topography
Communications in Mathematical Sciences, 18 (2020), 2149-2168.
Christian Klingenberg, A. Kurganov, Yongle Liu & Markus Zenk
Moving-Water Equilibria Preserving HLL-Type Schemes for the Shallow Water Equations
Communications in Mathematical Research, 36 (2020), 247-271.
Xin Liu, Xi Chen, Shi Jin, A. Kurganov & Hui Yu
Moving-Water Equilibria Preserving Partial Relaxation Scheme for the Saint-Venant System
SIAM Journal on Scientific Computing, 42 (2020), A2206-A2229.
Mohammad A. Ghazizadeh, Abdolmajid Mohammadian & A. Kurganov
An Adaptive Well-Balanced Positivity Preserving Scheme on Quadtree Grids for Shallow Water Equations
Computers and Fluids, 208 (2020), 104633
A. Kurganov, Yongle Liu & Vladimir Zeitlin
Moist-Convective Thermal Rotating Shallow Water Model
Physics of Fluids, 32 (2020), 066601
A. Kurganov, Yongle Liu & Vladimir Zeitlin
A Well-Balanced Central-Upwind Scheme for the Thermal Rotating Shallow Water Equations
Journal of Computational Physics, 411 (2020), 109414.
Alina Chertock, A. Kurganov & Yongle Liu
Finite-Volume-Particle Methods for the Two-Component Camassa-Holm System
Communications in Computational Physics, 27(2020), 480-502
2019
Xin Liu, Alina Chertock, A. Kurganov & Karlan Wolfkill
One-Dimensional/Two-Dimensional Coupling Approach with Quadrilateral Confluence Region for Modeling River Systems
Journal of Scientific Computing, 5 (2019), 1297-1328
Alina Chertock, A. Kurganov, Maria Lukacova-Medvidova, Peter Spichtinger & Bettina Wiebe
Stochastic Galerkin Method for Cloud Simulation
Mathematics of Climate and Weather Forecasting. 5(2019), 65-106
Alina Chertock & A. Kurganov
High-Resolution Positivity and Asymptotic Preserving Numerical Methods for Chemotaxis and Related Models
Active Particles. Vol. 2. Modeling and Simulation in Science, Springer International Publishing, Birkhauser (2019), 109-148..
Manuel Jesus Castro Diaz, A. Kurganov and Tomas Morales de Luna
Path-Conservative Central-Upwind Schemes for Nonconservative Hyperbolic Systems
Mathematical Modelling and Numerical Analysis, 53 (2019), 959-985.
Yuanzhen Cheng, Alina Chertock, Michael Herty, A. Kurganov & Tong Wu
A New Approach for Designing Moving-Water Equilibria Preserving Schemes for the Shallow Water Equations
Journal of Scientific Computing, 80 (2019), 538-554.
Xin Liu, Alina Chertock & A. Kurganov
An Asymptotic Preserving Scheme for the Two-Dimensional Shallow Water Equations with Coriolis Forces
Journal of Computational Physics, 391 (2019), 259-279.
Alina Chertock, A. Kurganov, Mario Ricchiuto & Tong Wu
Adaptive Moving Mesh Upwind Scheme for the Two-Species Chemotaxis Model
Computers and Mathematics with Applications, 77 (2019), 3172-3185.
Alina Chertock, A. Kurganov, Maria Lukacova-Medvidova & Seyma Nur Ozcan
An Asymptotic Preserving Scheme for Kinetic Chemotaxis Models in Two Space Dimensions
Kinetic and Related Models, 12 (2019), 195-216.
2018
Xin Liu, Jason Albright, Yekaterina Epshteyn & A. Kurganov
Well-Balanced Positivity Preserving Central-Upwind Scheme with a Novel Wet/Dry Reconstruction on Triangular Grids for the Saint-Venant System
Journal of Computational Physics, 374 (2018), 213-236.
Michael Herty, A. Kurganov & Dmitry Kurochkin
On Convergence of Numerical Methods for Optimization Problems Governed by Scalar Hyperbolic Conservation Laws
in Theory, Numerics and Applications of Hyperbolic Problems I. HYP 2016, Springer Proc. Math. Stat., Vol 236 (2018), 691-706, Springer, Cham.
A. Kurganov
Finite-Volume Schemes for Shallow-Water Equations
Acta Numerica (2018), 289-351.
Alina Chertock, Michael Dudzinski, A. Kurganov & Maria Lukacova-Medvidova
Well-Balanced Schemes for the Shallow Water Equations with Coriolis Forces
Numerische Mathematik, 138 (2018), 939-973.
Alina Chertock, Yekaterina Epshteyn, Hengrui Hu & A. Kurganov
High-Order Positivity-Preserving Hybrid Finite-Volume-Finite-Difference Methods for Chemotaxis Systems
Advances in Computational Mathematics, 44 (2018), 327-350.
Alina Chertock, Shumo Cui, A. Kurganov, Seyma Nur Ozcan & Eitan Tadmor
Well-Balanced Schemes for the Euler Equations with Gravitation: Conservative Formulation Using Global Fluxes
Journal of Computational Physics, 358 (2018), 36-52.
Alina Chertock, Armando Coco, A. Kurganov & Giovanni Russo
A Second-Order Finite-Difference Method for Compressible Fluids in Domains with Moving Boundaries
Communications in Computational Physics, 23 (2018), 230-263.
2017
Alina Chertock, Shumo Cui & A. Kurganov
Hybrid Finite-Volume-Particle Method for Dusty Gas Flows
SMAI Journal of Computational Mathematics, 3 (2017), 139-180.
Yuanzhen Cheng, Alina Chertock & A. Kurganov
A Simple Finite-Volume Method on a Cartesian Mesh for Pedestrian Flows with Obstacles
Finite Volumes for Complex Applications, VIII---methods and theoretical aspects (Lille, 2017), pp. 43-55, Springer Proc. Math. Stat., 199, 2017.
A. Kurganov, Martina Prugger & Tong Wu
Second-Order Fully Discrete Central-Upwind Scheme for Two-Dimensional Hyperbolic Systems of Conservation Laws
SIAM Journal on Scientific Computing, 39 (2017), A947-A965.
Xin Liu, Abdolmajid Mohammadian, Julio Angel Infante Sedano & A. Kurganov
Three-Dimensional Shallow Water System: A Relaxation Approach
Journal of Computational Physics, 333 (2017), 160-179.
2016
A. Kurganov
Central Schemes: a Powerful Black-Box Solver for Nonlinear Hyperbolic PDEs
Handbook of Numerical Methods for Hyperbolic Problems, pp. 525-548, Handb. Numer. Anal., 17, Elsevier/North-Holland, Amsterdam, 2016.
Yuanzhen Cheng & A. Kurganov
Moving-Water Equilibria Preserving Central-Upwind Schemes for the Shallow Water Equations
Communications in Mathematical Sciences, 14 (2016), 1643-1663.
Abdelaziz Beljadid, Abdolmajid Mohammadian & A. Kurganov
Well-Balanced Positivity Preserving Cell-Vertex Central-Upwind Scheme for Shallow Water Flows
Computers and Fluids, 136 (2016), 193-206.
Andrew Bernstein, Alina Chertock & A. Kurganov
Central-Upwind Scheme for Shallow Water Equations with Discontinuous Bottom Topography
Bulletin of the Brazilian Mathematical Society. New Series, 47 (2016), 91-103.
Hamidreza Shirkhani, Abdolmajid Mohammadian, Ousmane Seidou & A. Kurganov
A Well-Balanced Positivity-Preserving Central-Upwind Scheme for Shallow Water Equations on Unstructured Quadrilateral Grids
Computers and Fluids, 126 (2016), 25-40.
2015
Yuanzhen Cheng, A. Kurganov, Zhuolin Qu & Tao Tang
Fast and Stable Explicit Operator Splitting Methods for Phase-Field Models
Journal of Computational Physics, 303 (2015), 45-65.
Xin Liu, Abdolmajid Mohammadian, A. Kurganov & Julio Angel Infante Sedano
Well-Balanced Central-Upwind Scheme for a Fully Coupled Shallow Water System Modeling Flows over Erodible Bed
Journal of Computational Physics, 300 (2015), 202-218.
Jeremy Dewar, A. Kurganov & Maren Leopold
Pressure-Based Adaption Indicator for Compressible Euler Equations
Numerical Methods for Partial Differential Equations, 31 (2015), 1844-1874.
Alina Chertock, Shumo Cui, A. Kurganov & Tong Wu
Steady State and Sign Preserving Semi-Implicit Runge-Kutta Methods for ODEs with Stiff Damping Term
SIAM Journal on Numerical Analysis, 53 (2015), 2008-2029.
Chiu-Yen Kao, A. Kurganov, Zhuolin Qu & Ying Wang
A Fast Explicit Operator Splitting Method for Modified Buckley-Leverett Equations
Journal of Scientific Computing, 64 (2015), 837-857.
Alina Chertock, Shumo Cui, A. Kurganov & Tong Wu
Well-Balanced Positivity Preserving Central-Upwind Scheme for the Shallow Water System with Friction Terms
International Journal for Numerical Methods in Fluids, 78 (2015), 355-383.
Suo Yang, A. Kurganov & Yingjie Liu
Well-Balanced Central Schemes on Overlapping Cells with Constant Subtraction Techniques for the Saint-Venant Shallow Water System
Journal of Scientific Computing, 63 (2015), 678-698.
Shumo Cui, A. Kurganov & Alexei Medovikov
Particle Methods for PDEs Arising in Financial Modeling
Applied Numerical Mathematics, 93 (2015), 123-139.
Michael Herty, A. Kurganov & Dmitry Kurochkin
Numerical Method for Optimal Control Problems Governed by Nonlinear Hyperbolic Systems of PDEs
Communications in Mathematical Sciences, 13 (2015), 15-48.
2014
Manuel Jesus Castro Diaz, Yuanzhen Cheng, Alina Chertock & A. Kurganov
Solving Two-Mode Shallow Water Equations Using Finite Volume Methods
Communications in Computational Physics, 16 (2014), 1323-1354.
Alina Chertock, Michael Herty & A. Kurganov
An Eulerian-Lagrangian Method for Optimization Problems Governed by Multidimensional Nonlinear Hyperbolic PDEs
Computational Optimization and Applications, 59 (2014), 689-724.
A. Kurganov & Jason Miller
Central-Upwind Scheme for Savage-Hutter Type Model of Submarine Landslides and Generated Tsunami Waves
Computational Methods in Applied Mathematics, 14 (2014), 177-201.
Alina Chertock, A. Kurganov & Yu Liu
Central-Upwind Schemes for the System of Shallow Water Equations with Horizontal Temperature Gradients
Numerische Mathematik, 127 (2014), 595-639.
A. Kurganov & Maria Lukacova-Medvidova
Numerical Study of Two-Species Chemotaxis Models
Discrete and Continuous Dynamical Systems. Series B. A Journal Bridging Mathematics and Sciences, 19 (2014), 131-152.
Alina Chertock, A. Kurganov, Anthony Polizzi & Ilya Timofeyev
Pedestrian Flow Models with Slowdown Interactions
Mathematical Models and Methods in Applied Science, 24 (2014), 249-275.
2013
Alina Chertock, A. Kurganov, Zhuolin Qu & Tong Wu
On a Three-Layer Approximation of Two-Layer Shallow Water Equations
Mathematical Modelling and Analysis, 18 (2013), 675-693.
Andreas Bollermann, Guoxian Chen, A. Kurganov & Sebastian Noelle
A Well-Balanced Reconstruction for Wet/Dry Fronts for the Shallow Water Equations
Journal of Scientific Computing, 56 (2013), 267-290.
Yunlong Chen, A. Kurganov, Minlan Lei & Yu Liu
An Adaptive Artificial Viscosity Method for the Saint-Venant System
Lectures Presented at a Workshop at the Mathematical Research Institute Oberwolfach, Germany, Jan 15 - 21, 2012; R. Ansorge et al. (Eds.): Recent Developments in the Numerics of Nonlinear Conservation Laws, Series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Vol. 120, pp. 125-141, Springer-Verlag Berlin Heidelberg 2013.
2012
A. Kurganov & Yu Liu
New Adaptive Artificial Viscosity Method for Hyperbolic Systems of Conservation Laws
Journal of Computational Physics, 231 (2012), 8114-8132.
Alina Chertock, Klemens Fellner, A. Kurganov, Alexander Lorz & Peter A. Markowich
Sinking, Merging and Stationary Plumes in a Coupled Chemotaxis-Fluid Model: a High-Resolution Numerical Approach
Journal of Fluid Mechanics, 694 (2012), 155-190.
Alina Chertock, A. Kurganov, Xuefeng Wang & Yaping Wu
On a Chemotaxis Model with Saturated Chemotactic Flux
Kinetic and Related Models, 5 (2012), 51-95.
2011
Steve Bryson, Yekaterina Epshteyn, A. Kurganov & Guergana Petrova
Well-Balanced Positivity Preserving Central-Upwind Scheme on Triangular Grids for the Saint-Venant System
Mathematical Modelling and Numerical Analysis, 45 (2011), 423-446.
Alina Chertock, Christo Christov & A. Kurganov
Central-Upwind Schemes for the Boussinesq Paradigm Equations
The Proceedings of the Fourth Russian-German Advanced Research Workshop on Computational Science and High Performance Computing, Freiburg, 2009; E. Krause et al. (Eds.): Computational Science and High Performance Computing IV, Series: Notes on Numerical Fluid Mechanics and Multidisciplinary Design, Vol. 115, pp. 267-281, Springer-Verlag Berlin Heidelberg 2011.
2010
Alina Chertock, Charles R. Doering, Eugene Kashdan & A. Kurganov
A Fast Explicit Operator Splitting Method for Passive Scalar Advection
Journal of Scientific Computing, 45 (2010), 200-214.
2009
Alina Chertock & A. Kurganov
On Splitting-Based Numerical Methods for Convection-Diffusion Equations
Quaderni di Matematica, 24 (2009), 303-343.
A. Kurganov & Jeffrey Rauch
The Order of Accuracy of Quadrature Formulae for Periodic Functions
in Advances in phase space analysis of partial differential equations. In honor of Ferruccio Colombini's 60th birthday, A. Bove, D. Del Santo, and M.K.V. Murthy, eds., vol. 78 of Progress in nonlinear differential equations and their applications, Boston, 2009, Birkhauser, 155-159.
A. Kurganov & Anthony Polizzi
Non-Oscillatory Central Schemes for Traffic Flow Models with Arrhenius Look-Ahead Dynamics
Networks and Heterogeneous Media, 4 (2009), 431-451.
Igor Kliakhandler & A. Kurganov
Quasi-Lagrangian Acceleration of Eulerian Methods
Communications in Computational Physics, 6 (2009), 743-757.
A. Kurganov & Guergana Petrova
Central-Upwind Schemes for Two-Layer Shallow Water Equations
SIAM Journal on Scientific Computing, 31 (2009), 1742-1773.
Alina Chertock, A. Kurganov & Guergana Petrova
Fast Explicit Operator Splitting Method for Convection-Diffusion Equation
International Journal for Numerical Methods in Fluids, 59 (2009), 309-332.
Alina Chertock & A. Kurganov
ing Multivalued Solutions of Pressureless Gas Dynamics by Deterministic Particle MethodsComputing Multivalued Solutions of Pressureless Gas Dynamics by Deterministic Particle Methods
Communications in Computational Physics, 5 (2009), 565-581.
2008
Yekaterina Epshteyn & A. Kurganov
New Interior Penalty Discontinuous Galerkin Methods for the Keller-Segel Chemotaxis Model
SIAM Journal on Numerical Analysis, 47 (2008), 386-408.
An extended version of this paper, available herehere, was published as a Center for Nonlinear Analysis at Carnegie Mellon University scientific report 07-CNA-006
Alina Chertock & A. Kurganov
A Simple Eulerian Finite-Volume Method for Compressible Fluids in Domains with Moving Boundaries
Communications in Mathematical Sciences, 6 (2008), 531-556.
Alina Chertock & A. Kurganov
A Second-Order Positivity Preserving Central-Upwind Scheme for Chemotaxis and Haptotaxis Models
Numerische Mathematik, 111 (2008), 169-205.
Alina Chertock, Smadar Karni & A. Kurganov
Interface Tracking Method for Compressible Multifluids
Mathematical Modelling and Numerical Analysis, 42 (2008), 991-1019.
A. Kurganov & Guergana Petrova
A Central-Upwind Scheme for Nonlinear Water Waves Generated by Submarine Landslides
Hyperbolic Problems: Theory, Numerics, Applications (Lyon, 2006), 635-642, Springer, 2008.
Alina Chertock, Eugene Kashdan & A. Kurganov
Propagation of Diffusing Pollutant by a Hybrid Eulerian-Lagrangian Method
Hyperbolic Problems: Theory, Numerics, Applications (Lyon, 2006), 371-380, Springer, 2008.
2007
Alina Chertock, A. Kurganov & Yurii Rykov
A New Sticky Particle Method for Pressureless Gas Dynamics
SIAM Journal on Numerical Analysis, 45 (2007), 2408-2441.
A. Kurganov, Guergana Petrova & Bojan Popov
Adaptive Semi-Discrete Central-Upwind Schemes for Nonconvex Hyperbolic Conservation Laws
SIAM Journal on Scientific Computing, 29 (2007), 2381-2401.
A. Kurganov & Guergana Petrova
A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System
Communications in Mathematical Sciences, 5 (2007), 133-160.
A. Kurganov & Chi-Tien Lin
On the Reduction of Numerical Dissipation in Central-Upwind Schemes
Communications in Computational Physics, 2 (2007), 141-163.
2006
Lucian A. Constantin & A. Kurganov
Adaptive Central-Upwind Schemes for Hyperbolic Systems of Conservation Laws
Hyperbolic Problems: Theory, Numerics, Applications (Osaka, 2004), 95-103, Yokohama Publishers, 2006.
A. Kurganov
Well-Balanced Central-Upwind Scheme for Compressible Two-Phase Flows
Proceedings of the European Conference on Computational Fluid Dynamics ECCOMAS CFD 2006.
Alina Chertock & A. Kurganov
On a Practical Implementation of Particle Methods
Applied Numerical Mathematics, 56 (2006), 1418-1431.
A. Kurganov & Guergana Petrova
Adaptive Central-Upwind Schemes for Hamilton-Jacobi Equations with Nonconvex Hamiltonians
Journal of Scientific Computing, 27 (2006), 323-333.
Alina Chertock, A. Kurganov & Guergana Petrova
Finite-Volume-Particle Methods for Models of Transport of Pollutant in Shallow Water
Journal of Scientific Computing, 27 (2006), 189-199.
A. Kurganov & Philip Rosenau
On Reaction Processes with Saturating Diffusion
Nonlinearity, 19 (2006), 171-193.
2005
Alina Chertock & A. Kurganov
Conservative Locally Moving Mesh Method for Multifluid Flows
Finite Volumes for Complex Applications, IV, Marrakech, 2005, 273-284, Hermes Sci. Publ.
Alina Chertock, A. Kurganov & Guergana Petrova
Fast Explicit Operator Splitting Method. Application to the Polymer System
Finite Volumes for Complex Applications, IV, Marrakech, 2005, 63-72, Hermes Sci. Publ.
A. Kurganov & Guergana Petrova
Central-Upwind Schemes on Triangular Grids for Hyperbolic Systems of Conservation Laws
Numerical Methods for Partial Differential Equations, 21 (2005), 536-552.
Alina Chertock, A. Kurganov & Philip Rosenau
On Degenerate Saturated-Diffusion Equations with Convection
Nonlinearity, 18 (2005), 609-630.
Steve Bryson, A. Kurganov, Doron Levy & Guergana Petrova
Semi-Discrete Central-Upwind Schemes with Reduced Dissipation for Hamilton-Jacobi Equations
IMA Journal of Numerical Analysis, 25 (2005), 113-138.
Smadar Karni & A. Kurganov
Local Error Analysis for Approximate Solutions of Hyperbolic Conservation Laws
Advances in Computational Mathematics, 22 (2005), 79-99.
2004
Alina Chertock & A. Kurganov
On a Hybrid Finite-Volume-Particle Method
Mathematical Modelling and Numerical Analysis, 38 (2004), 1071-1091.
Smadar Karni, Eduard Kirr, A. Kurganov & Guergana Petrova
Compressible Two-Phase Flows by Central and Upwind Schemes
Mathematical Modelling and Numerical Analysis, 38 (2004), 477-493.
Jesse Otero, Lubomira A. Dontcheva, Hans Johnston, Rodney A. Worthing, A. Kurganov, Guergana Petrova & Charles R. Doering
High Raleigh Number Convection in a Fluid Saturated Porous Layer
Journal of Fluid Mechanics, 500 (2004), 263-281.
2003
A. Kurganov
An Accurate Deterministic Projection Method for Hyperbolic Systems with Stiff Source Term
Hyperbolic Problems: Theory, Numerics, Applications (Pasadena, 2002),665-674, Springer-Verlag, 2003.
Alina Chertock, A. Kurganov & Philip Rosenau
Formation of Discontinuities in Flux-Saturated Degenerate Parabolic Equations
Nonlinearity, 16 (2003), 1875-1898.
2002
A. Kurganov
Central-Upwind Schemes for Balance Laws. Application to the Broadwell Model
Finite Volumes for Complex Applications, III, Porquerolles, 2002, 365-372, Hermes Sci. Publ., Paris.
A. Kurganov & Doron Levy
Central-Upwind Schemes for the Saint-Venant System
Mathematical Modelling and Numerical Analysis, 36 (2002), 397-425.
A. Kurganov & Eitan Tadmor
Solution of Two-Dimensional Riemann Problems for Gas Dynamics without Riemann Problem Solvers
Numerical Methods for Partial Differential Equations 18 (2002), 584-608.
Smadar Karni, A. Kurganov & Guergana Petrova
A Smoothness Indicator for Adaptive Algorithms for Hyperbolic Systems
Journal of Computational Physics 178 (2002), 323-341.
2001
A. Kurganov, Sebastian Noelle & Guergana Petrova
Semi-Discrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton-Jacobi Equations
SIAM Journal on Scientific Computing 23 (2001), 707-740.
A. Kurganov & Guergana Petrova
A Third-Order Semi-Discrete Genuinely Multidimensional Central Scheme for Hyperbolic Conservation Laws and Related Problems
Numerische Mathematik 88 (2001), 683-729.
2000
A. Kurganov & Doron Levy
A Third-Order Semi-Discrete Central Scheme for Conservation Laws and Convection-Diffusion Equations
SIAM Journal on Scientific Computing 22 (2000), 1461-1488.
A. Kurganov & Guergana Petrova
Central Schemes and Contact Discontinuities
Mathematical Modelling and Numerical Analysis 34 (2000), 1259-1275.
A. Kurganov & Eitan Tadmor
New High-Resolution Semi-Discrete Central Schemes for Hamilton-Jacobi Equations
Journal of Computational Physics 160 (2000), 720-742.
A. Kurganov & Eitan Tadmor
New High Resolution Central Schemes for Nonlinear Conservation Laws and Convection-Diffusion Equations
Journal of Computational Physics 160 (2000), 241-282.
1999
Jonathan Goodman, A. Kurganov & Philip Rosenau
Breakdown of Burgers-type Equations with Saturating Dissipation Fluxes
Nonlinearity 12 (1999), 247-268.
1998
A. Kurganov, Doron Levy & Philip Rosenau
On Burgers-type Equations with Non-monotonic Dissipative Fluxes
Communications on Pure and Applied Mathematics 51 (1998), 443-473.
1997
A. Kurganov & Eitan Tadmor
Stiff Systems of Hyperbolic Conservation Laws. Convergence and Error Estimates
SIAM Journal on Mathematical Analysis 28 (1997), 1446-1456.
A. Kurganov & Philip Rosenau
The Effect of a Saturating Dissipation in Burgers-type Equations
Communications on Pure and Applied Mathematics 50 (1997), 753-771.
