Refereed Publications (in the reversed chronological order)
Recent Preprints
Saeed Mohammadian, Zuduo Zheng, Shaoshuai Chu & A. Kurganov (2024)
Path-Conservative Central-Upwind Schemes for the Non-Conservative NET-RAT Traffic Flow Model
submitted to Computers and Fluids.
Alina Chertock, Shumo Cui, A. Kurganov & Chenxi Wang (2024)
A Hybrid Finite-Difference-Particle Method for Chemotaxis Models
submitted to Numerische Mathematik.
Alina Chertock, Arsen S. Iskhakov, Safa Janajra & A. Kurganov (2024)
submitted to proceedings of ENUMATH2023 conference.
Shumo Cui, A. Kurganov and Kailiang Wu (2023)
Bound-Preserving Framework for Central-Upwind Schemes for General Hyperbolic Conservation Laws
submitted to SIAM Journal on Scientific Computing.
Shaoshuai Chu, A. Kurganov and Ruixiao Xin (2023)
A Well-Balanced Fifth-Order A-WENO Scheme Based on Flux Globalization
submitted to Beijing Journal of Pure and Applied Mathematics.
Shaoshuai Chu, A. Kurganov and Ruixiao Xin (2023)
New More Efficient A-WENO Schemes
submitted to Journal of Scientific Computing.
Alina Chertock, Michael Herty, Arsen S. Iskhakov, Safa Janajra, A. Kurganov & Mária Lukáčová-Medvid’ová (2023)
New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties
submitted to Communications on Applied Mathematics and Computation.
Qingcheng Fu, A. Kurganov, Mingye Na & Vladimir Zeitlin (2023)
Emergence, Interactions, and Evolution over Topography of Solitons in the Serre-GreenNaghdi Model
submitted to Journal of Fluid Mechanics.
Alina Chertock, A. Kurganov, Michael Redle & Vladimir Zeitlin (2023)
submitted to Journal of Computational Physics.
Yangyang Cao, A. Kurganov, Yongle Liu & Vladimir Zeitlin (2023)
submitted to Journal of Computational Physics.
Shaoshuai Chu, A. Kurganov and Ruixiao Xin (2023)
Low-Dissipation Central-Upwind Schemes for Compressible Multifluids
submitted to Journal of Computational Physics.
Shaoshuai Chu and A. Kurganov (2023)
New Adaptive Low-Dissipation Central-Upwind Schemes
submitted to ESAIM Mathematical Modelling and Numerical Analysis.
A. Kurganov and Mingye Na (2023)
submitted to SMAI Journal of Computational Mathematics.
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.
Alina Chertock, A. Kurganov, Michael Redle & Kailiang Wu (2023)
To appear in SIAM Journal on Scientific Computing.
Alina Chertock, Shaoshuai Chu & A. Kurganov
Accurate Deterministic Projection Methods for Stiff Detonation Waves
to appear in Communications in Mathematics Sciences.
Shaoshuai Chu, A. Kurganov & Ruixiao Xin (2023)
A Fifth-Order A-WENO Scheme Based on the Low-Dissipation Central-Upwind Fluxes
to appear in Proceedings of the XVIII International Conference on Hyperbolic Problems: Theory, Numerics, Applications.
2023
Yangyang Cao, A. Kurganov & Yongle Liu
Communications in Computational Physics, 34 (2023), pp. 993–1042.
Shaoshuai Chu & A. Kurganov
Local Characteristic Decomposition Based Central-Upwind Scheme for Compressible Multifluids
in Finite Volumes for Complex Applications X–Volume 2, Hyperbolic and Related Problems,
Springer Proc. Math. Stat., Vol. 433 (2023), pp. 73–81, Springer, Cham
Vadim A. Kolotilov, A. A. Kurganov, Vladimir V. Ostapenko, Nadezhda A. Khandeeva & Shaoshuai Chu
On the Accuracy of Shock-Capturing Schemes Calculating Gas-Dynamic Shock Waves
Computational Mathematics and Mathematical Physics, 63 (2023), pp. 1341–1349.
Shaoshuai Chu, Olyana A. Kovyrkina, A. Kurganov & Vladimir V. Ostapenko
Numerical Methods for Partial Differential Equations, 39 (2023), pp. 4317–4346.
A. Kurganov & Ruixiao Xin
New Low-Dissipation Central-Upwind Schemes
Journal of Scientific Computing, 96 (2023), Paper No. 56, 33 pp.
Xi Chen & A. Kurganov
A Well-Balanced Partial Relaxation Scheme for the Two-Dimensional Saint-Venant System
Communications in Computational Physics, 33 (2023), pp. 1432-1465.
Alina Chertock, Shaoshuai Chu & A. Kurganov
Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator
East Asian Journal on Applied Mathematics, 13 (2023), pp. 576–609.
Shaoshuai Chu, A. Kurganov, Saeed, Mohammadian & Zuduo Zheng
Fifth-Order A-WENO Path-Conservative Central-Upwind Scheme for Behavioral Non-Equilibrium Traffic Models
Communications in Computational Physics, 33 (2023), pp. 692–732.
Xi Chen, A. Kurganov & Yongle Liu
Journal of Scientific Computing, 95 (2023), Paper No. 95, 38 pp.
Olyana A. Kovyrkina, A. A. Kurganov & Vladimir V. Ostapenko,
Comparative Analysis of the Accuracy of Three Different Schemes in the Calculation of Shock Waves,
Mathematical Models and Computer Simulations, 15 (2023), pp. 401–414; Russian text
published in Matematicheskoe Modelirovanie, 34 (2022), pp. 43–64.
Yiming Chen, A. Kurganov & Mingye Na
A Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Scheme for the Shallow Water Flows in Channels
ESAIM Mathematical Modelling and Numerical Analysis, 57 (2023), pp. 1087–1110.
Chenxi Wang, Alina Chertock, Shumo Cui, A. Kurganov & Zhen Zhang
A Diffuse-Domain Based Numerical Method for a Chemotaxis-Fluid Model
Mathematical Models and Methods in Applied Sciences, 33 (2023), pp. 341–375.
Alina Chertock, A. Kurganov, M. Luk´aˇcov´a-Medvid’ov´a, P. Spichtinger & B. Wiebe
Stochastic Galerkin Method for Cloud Simulation. Part II: a Fully Random Navier-StokesCloud Model
Journal of Computational Physics, 479 (2023), Paper No. 111987, 24 pp.
Bao-Shan Wang, Wai Sun Don, A. Kurganov & Yongle Liu
Fifth-Order A-WENO Schemes Based on the Adaptive Diffusion Central-Upwind Rankine-Hugoniot Fluxes
Communications on Applied Mathematics and Computation, 5 (2023), pp. 295–314.
Yangyang Cao, A. Kurganov, Yongle Liu & Vladimir Zeitlin
Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Scheme for Two-Layer Thermal Rotating Shallow Water Equations
Journal of Computational Physics, 474 (2023), Paper No. 111790, 29 pp.
Shaoshuai Chu & A. Kurganov
Flux Globalization Based Well-Balanced Central-Upwind Scheme for One-Dimensional Blood Flow Models
Calcolo, 60 (2023), Paper No. 2, 35 pp.
A. Kurganov, Yongle Liu & Ruixiao Xin
Well-Balanced Path-Conservative Central-Upwind Schemes Based on Flux Globalization
Journal of Computational Physics, 474 (2023), Paper No. 111773, 32 pp.
Alina Chertock, Shaoshuai Chu, Michael Herty, A. Kurganov & Maria Lukacova-Medvidova
Local Characteristic Decomposition Based Central-Upwind Scheme
Journal of Computational Physics, 473 (2023), Paper No. 111718, 24 pp.
Alina Chertock, A. Kurganov, Tong Wu & Jun Yan
Well-Balanced Numerical Method for Atmospheric Flow Equations with Gravity
Applied Mathematics and Computation, 439 (2023), Paper No. 127587, 13 pp.
2022
Olyana Kovyrkina, A. Kurganov & Vladimir Ostapenko
Mathematical Models and Computer Simulations, 34 (2022), pp. 43–64.
Shaoshuai Chu, A. Kurganov & Mingye Na
Fifth-Order A-WENO Schemes Based on the Path-Conservative Central-Upwind Method
Journal of Computational Physics, 469 (2022), Paper No. 111508, 22 pp.
Yangyang Cao, A. Kurganov, Yongle Liu & Ruixiao Xin
Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Models
Journal of Scientific Computing, 92 (2022), Paper No. 69, 31 pp.
A. Kurganov, Zhuolin Qu & Tong Wu
ESAIM Mathematical Modelling and Numerical Analysis, 56 (2022), 1327–1360.
A. Kurganov, Yongle Liu & Maria Lukacova-Medvidova
A Well-Balanced Asymptotic Preserving Scheme for the Two-Dimensional Rotating Shallow Water Equations with Nonflat Bottom Topography
SIAM Journal on Scientific Computing, 44 (2022), A1655–A1680
A supplement is available here.
Alina Chertock, A. Kurganov, Xin Liu, Yongle Liu & Tong Wu
Well-Balancing Via Flux Globalization: Applications to Shallow Water Equations with Wet/Dry Fronts
Journal of Scientific Computing, 90 (2022), Paper No. 9, 21 pp.
2021
A. Kurganov, Yongle Liu & Vladimir Zeitlin
Physics of Fluids, 33 (2021), 106606.
Alina Chertock, Shaoshuai Chu & A. Kurganov
Hybrid Multifluid Algorithms Based on the Path-Conservative Central-Upwind Scheme
Journal of Scientific Computing, 89 (2021), Paper No. 48, 24 pp.
A. Kurganov, Zhuolin Qu, Olga S. Rozanova & Tong Wu
Adaptive Moving Mesh Central-Upwind Schemes for Hyperbolic System of PDEs. Applications to Compressible Euler Equations and Granular Hydrodynamics
Communications on Applied Mathematics and Computation, 3 (2021), 445-479.
A. Kurganov, Yongle Liu & Vladimir Zeitlin
Numerical Dissipation Switch for Two-Dimensional Central-Upwind Schemes
ESAIM Mathematical Modelling and Numerical Analysis, 55 (2021), 713-734.
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(2021), 125-154.
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.
2020
Alina Chertock, A. Kurganov, Jason Miller & Jun Yan
Central-Upwind Scheme for a Non-Hydrostatic Saint-Venant System
Proceedings of the XVII International Conference on Hyperbolic Problems: Theory, Numerics, Applications, pp. 25-41, AIMS Series on Applied Mathematics, 10, Springfield, MO, 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, Tong Wu & 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, 81 (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
Computing 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 here, 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.