KURGANOV Alexander

Chair Professor

- Brief Biography
- Research
- Teaching
- Published Works

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:

2016 – present Professor, Department of Mathematics, Southern University of Science and Technology, China

2010 – 2015 Professor, Mathematics Department, Tulane University, USA

Summer 2012 Visiting Professor, Institute of Natural Sciences, Shanghai Jiao Tong University, China

May 2012 Visiting Professor, Institute of Mathematics, Univeristy of Bordeaux I, France

Summer 2011 Mercator Guest Professor, Institute of Mathematics, Johannes Gutenberg University, Mainz, Germany

2004 – 2010 Associate Professor, Mathematics Department, Tulane University, USA

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

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:

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

LIST OF PUBLICATIONS (in the reversed chronological order)

[78] X. Liu, A. Mohammadian, J. A. I. Sedano and A. Kurganov,

Three-Dimensional Shallow Water System: A Relaxation Approach

to appear in Journal of Computational Physics

[77] A. Kurganov

Central Schemes: a Powerful Black-Box Solver for Nonlinear Hyperbolic PDEs

to appear in Handbook of Numerical Methods for Hyperbolic Problems: Part A

[76] Y. Cheng and A. Kurganov

Moving-Water Equilibria Preserving Central-Upwind Schemes for the Shallow Water Equations

Communications in Mathematical Sciences, 14 (2016), pp. 1643–1663

[75] A. Beljadid, A. Mohammadian and A. Kurganov

Well-Balanced Positivity Preserving Cell-Vertex Central-Upwind Scheme for Shallow Water Flows

Computers and Fluids, 136 (2016), pp. 193–206

[74] A. Bernstein, A. Chertock and A. Kurganov

Central-Upwind Scheme for Shallow Water Equations with Discontinuous Bottom Topography

Bulletin of the Brazilian Mathematical Society. New Series, 47 (2016), pp. 91–103

[73] H. Shirkhani, A. Mohammadian, O. Seidou and A. Kurganov

A Well-Balanced Positivity-Preserving Central-Upwind Scheme for Shallow Water Equations on Unstructured Quadrilateral Grids

Computers and Fluids, 126 (2016), pp. 25–40

[72] Y. Cheng, A. Kurganov, Z. Qu and T. Tang

Fast and Stable Explicit Operator Splitting Methods for Phase-Field Models

Journal of Computational Physics, 303 (2015), pp. 45–65

[71] X. Liu, A. Mohammadian, A. Kurganov and J. A. I. Sedano

Well-Balanced Central-Upwind Scheme for a Fully Coupled Shallow Water System Modeling Flows over Erodible Bed

Journal of Computational Physics, 300 (2015), pp. 202–218

[70] J. Dewar, A. Kurganov and M. Leopold

Pressure-Based Adaption Indicator for Compressible Euler Equations

Numerical Methods for Partial Differential Equations, 31 (2015), pp. 1844–1874

[69] A. Chertock, S. Cui, A. Kurganov and T. Wu

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

SIAM Journal on Numerical Analysis, 53 (2015), pp. 2008–2029

[68] C.-Y. Kao, A. Kurganov, Z. Qu and Y. Wang

A Fast Explicit Operator Splitting Method for Modified Buckley-Leverett Equations

Journal of Scientific Computing, 64 (2015), pp. 837–857

[67] A. Chertock, S. Cui, A. Kurganov and T. 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), pp. 355–383

[66] S. Yang, A. Kurganov and Y. 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), pp. 678–698

[65] S. Cui, A. Kurganov and A. Medovikov

Particle Methods for PDEs Arising in Financial Modeling

Applied Numerical Mathematics, 93 (2015), pp. 123–139

[64] M. Herty, A. Kurganov and D. Kurochkin

Numerical Method for Optimal Control Problems Governed by Nonlinear Hyperbolic Systems of PDEs

Communications in Mathematical Sciences, 13 (2015), pp. 15–48

[63] M. J. Castro Diaz, Y. Cheng, A. Chertock and A. Kurganov

Solving Two-Mode Shallow Water Equations Using Finite Volume Methods

Communications in Computational Physics, 16 (2014), pp. 1323–1354

[62] A. Chertock, M. Herty and A. Kurganov

An Eulerian-Lagrangian Method for Optimization Problems Governed by Multidimensional Nonlinear Hyperbolic PDEs

Computational Optimization and Applications, 59 (2014), pp. 689–724

[61] A. Kurganov and J. Miller

Central-Upwind Scheme for Savage-Hutter Type Model of Submarine Landslides and Generated Tsunami Waves

Computational Methods in Applied Mathematics, 14 (2014), pp. 177–201

[60] A. Chertock, A. Kurganov and Y. Liu

Central-Upwind Schemes for the System of Shallow Water Equations with Horizontal Temperature Gradients

Numerische Mathematik, 127 (2014), pp. 595–639

[59] A. Kurganov and M. Lukacova-Medvidova

Numerical Study of Two-Species Chemotaxis Models

Discrete and Continuous Dynamical Systems. Series B. A Journal Bridging Mathematics and Sciences, 19 (2014), pp. 131–152

[58] A. Chertock, A. Kurganov, A. Polizzi and I. Timofeyev

Pedestrian Flow Models with Slowdown Interactions

Mathematical Models and Methods in Applied Sciences, 24 (2014), pp. 249–275

[57] A. Chertock, A. Kurganov, Z. Qu and T. Wu

On a Three-Layer Approximation of Two-Layer Shallow Water Equations

Mathematical Modelling and Analysis, 18 (2013), pp. 675–693

[56] A. Bollermann, G. Chen, A. Kurganov and S. Noelle

A Well-Balanced Reconstruction for Wet/Dry Fronts

Journal of Scientific Computing, 56 (2013), pp. 267–290

[55] Y. Chen, A. Kurganov, M. Lei and Y. 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

[54] A. Kurganov and Y. Liu

New Adaptive Artificial Viscosity Method for Hyperbolic Systems of Conservation Laws

Journal of Computational Physics, 231 (2012), pp. 8114–8132

[53] A. Chertock, K. Fellner, A. Kurganov, A. Lorz and P.A. Markowich

Sinking, Merging and Stationary Plumes in a Coupled Chemotaxis-Fluid Model: a High-Resolution Numerical Approach

Journal of Fluid Mechanics, 694 (2012), pp. 155–190

[52] A. Chertock, A. Kurganov, X. Wang and Y. Wu

On a Chemotaxis Model with Saturated Chemotactic Flux

Kinetic and Related Models, 5 (2012), pp. 51–95

[51] S. Bryson, Y. Epshteyn, A. Kurganov and G. Petrova

Well-Balanced Positivity Preserving Central-Upwind Scheme on Triangular Grids for the Saint-Venant System

Mathematical Modelling and Numerical Analysis, 45 (2011), pp. 423–446

[50] A. Chertock, C.I. Christov and 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

[49] A. Chertock, C.R. Doering, E. Kashdan and A. Kurganov

A Fast Explicit Operator Splitting Method for Passive Scalar Advection

Journal of Scientific Computing, 45 (2010), pp. 200–214

[48] A. Chertock and A. Kurganov

On Splitting-Based Numerical Methods for Convection-Diffusion Equations

Quaderni di Matematica, 24 (2009), pp. 303–343

[47] A. Kurganov and J. 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, pp. 155–159

[46] A. Kurganov and A. Polizzi

Non-Oscillatory Central Schemes for Traffic Flow Models with Arrhenius Look-Ahead Dynamics

Networks and Heterogeneous Media, 4 (2009), pp. 431–451

[45] I. Kliakhandler and A. Kurganov

Quasi-Lagrangian Acceleration of Eulerian Methods

Communications in Computational Physics, 6 (2009), pp. 743–757

[44] A. Kurganov and G. Petrova

Central-Upwind Schemes for Two-Layer Shallow Water Equations

SIAM Journal on Scientific Computing, 31 (2009), pp. 1742–1773

[43] A. Chertock, A. Kurganov and G. Petrova

Fast Explicit Operator Splitting Method for Convection-Diffusion Equations

International Journal for Numerical Methods in Fluids, 59 (2009), pp. 309–332

[42] A. Chertock and A. Kurganov

Computing Multivalued Solutions of Pressureless Gas Dynamics by Deterministic Particle Methods

Communications in Computational Physics, 5 (2009), pp. 565–581

[41] Y. Epshteyn and A. Kurganov

New Interior Penalty Discontinuous Galerkin Methods for the Keller-Segel Chemotaxis Model

SIAM Journal on Numerical Analysis, 47 (2008), pp. 386–408

[40] A. Chertock and A. Kurganov

A Simple Eulerian Finite-Volume Method for Compressible Fluids in Domains with Moving Boundaries

Communications in Mathematical Sciences, 6 (2008), pp. 531–556

[39] A. Chertock and A. Kurganov

A Second-Order Positivity Preserving Central-Upwind Scheme for Chemotaxis and Haptotaxis Models

Numerische Mathematik, 111 (2008), pp. 169–205

[38] A. Chertock, S. Karni and A. Kurganov

Interface Tracking Method for Compressible Multifluids

Mathematical Modelling and Numerical Analysis, 42 (2008), pp. 991–1019

[37] A. Kurganov and G. Petrova

A Central-Upwind Scheme for Nonlinear Water Waves Generated by Submarine Landslides

Hyperbolic Problems: Theory, Numerics, Applications (Lyon 2006), pp. 635–642, Springer, 2008

[36] A. Chertock, E. Kashdan and A. Kurganov

Propagation of Diffusing Pollutant by a Hybrid Eulerian-Lagrangian Method

Hyperbolic Problems: Theory, Numerics, Applications (Lyon 2006), pp. 371–380, Springer, 2008

[35] A. Chertock, A. Kurganov and Yu. G. Rykov

A New Sticky Particle Method for Pressureless Gas Dynamics

SIAM Journal on Numerical Analysis, 45 (2007), pp. 2408–2441

[34] A. Kurganov, G. Petrova and B. Popov

Adaptive Semi-Discrete Central-Upwind Schemes for Nonconvex Hyperbolic Conservation Laws

SIAM Journal on Scientific Computing, 29 (2007), pp. 2381–2401

[33] A. Kurganov and G. Petrova

A Second-Order Well-Balanced Positivity Preserving Central-Upwind Scheme for the Saint-Venant System

Communications in Mathematical Sciences, 5 (2007), pp. 133–160

[32] A. Kurganov and C.-T. Lin

On the Reduction of Numerical Dissipation in Central-Upwind Schemes

Communications in Computational Physics, 2 (2007), pp. 141–163

[31] L.A. Constantin and A. Kurganov

Adaptive Central-Upwind Schemes for Hyperbolic Systems of Conservation Laws

Hyperbolic Problems: Theory, Numerics and Applications (Osaka, 2004), pp. 95–103, Yokohama Publishers, 2006

[30] A. Kurganov

Well-Balanced Central-Upwind Scheme for Compressible Two-Phase Flows

Proceedings of the European Conference on Computational Fluid Dynamics ECCOMAS CFD 2006

[29] A. Chertock and A. Kurganov

On a Practical Implementation of Particle Methods

Applied Numerical Mathematics, 56 (2006), pp. 1418–1431

[28] A. Kurganov and G. Petrova

Adaptive Central-Upwind Schemes for Hamilton-Jacobi Equations with Nonconvex Hamiltonians

Journal of Scientific Computing, 27 (2006), pp. 323–333

[27] A. Chertock, A. Kurganov and G. Petrova

Finite-Volume-Particle Methods for Models of Transport of Pollutant in Shallow Water

Journal of Scientific Computing, 27 (2006), pp. 189–199

[26] A. Kurganov and P. Rosenau

On Reaction Processes with Saturating Diffusion

Nonlinearity, 19 (2006), pp. 171–193

[25] A. Chertock and A. Kurganov

Conservative Locally Moving Mesh Method for Multifluid Flows

Finite Volumes for Complex Applications, IV (Marrakech, 2005), pp. 273–284, Hermes Sci. Publ., 2005

[24] A. Chertock, A. Kurganov and G. Petrova

Fast Explicit Operator Splitting Method. Application to the Polymer System

Finite Volumes for Complex Applications, IV (Marrakech, 2005), pp. 63–72, Hermes Sci. Publ., 2005

[23] A. Kurganov and G. Petrova

Central-Upwind Schemes on Triangular Grids for Hyperbolic Systems of Conservation Laws

Numerical Methods for Partial Differential Equations, 21 (2005), pp. 536–552

[22] A. Chertock, A. Kurganov and P. Rosenau

On Degenerate Saturated-Diffusion Equations with Convection

Nonlinearity, 18 (2005), pp. 609–630

[21] S. Bryson, A. Kurganov, D. Levy and G. Petrova

Semi-Discrete Central-Upwind Schemes with Reduced Dissipation for Hamilton-Jacobi Equations

IMA Journal of Numerical Analysis, 25 (2005), pp. 113–138

[20] S. Karni and A. Kurganov

Local Error Analysis for Approximate Solutions of Hyperbolic Conservation Laws

Advances in Computational Mathematics, 22 (2005), pp. 79–99

[19] A. Chertock and A. Kurganov

On a Hybrid Finite-Volume-Particle Method

Mathematical Modelling and Numerical Analysis, 38 (2004), pp. 1071–1091

[18] S. Karni, E. Kirr, A. Kurganov and G. Petrova

Compressible Two-Phase Flows by Central and Upwind Schemes

Mathematical Modelling and Numerical Analysis, 38 (2004), pp. 477–494

[17] J. Otero, L.A. Dontcheva, H. Johnston, R.A. Worthing, A. Kurganov, G. Petrova and C.R. Doering

High Raleigh Number Convection in a Fluid Saturated Porous Layer

Journal of Fluid Mechanics, 500 (2004), pp. 263–281

[16] A. Kurganov

An Accurate Deterministic Projection Method for Hyperbolic Systems with Stiff Source Term

Hyperbolic Problems: Theory, Numerics, Applications (Pasadena, 2002), pp. 665–674, Springer-Verlag, 2003

[15] A. Chertock, A. Kurganov and P. Rosenau

Formation of Discontinuities in Flux-Saturated Degenerate Parabolic Equations

Nonlinearity, 16 (2003), pp. 1875–1898

[14] A. Kurganov

Central-Upwind Schemes for Balance Laws. Application to the Broadwell Model

Finite Volumes for Complex Applications, III (Porquerolles, 2002), pp. 351–358, Hermes Sci. Publ., Paris, 2002

[13] A. Kurganov and D. Levy

Central-Upwind Schemes for the Saint-Venant System

Mathematical Modelling and Numerical Analysis, 36 (2002), pp. 397–425

[12] A. Kurganov and E. Tadmor

Solution of Two-Dimensional Riemann Problems for Gas Dynamics without Riemann Problem Solvers

Numerical Methods for Partial Differential Equations, 18 (2002), pp. 584–608

[11] S. Karni, A. Kurganov and G. Petrova

A Smoothness Indicator for Adaptive Algorithms for Hyperbolic Systems

Journal of Computational Physics, 178 (2002), pp. 323–341

[10] A. Kurganov, S. Noelle and G. Petrova

Semi-Discrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton-Jacobi Equations

SIAM Journal on Scientific Computing, 23 (2001), pp. 707–740

[9] A. Kurganov and G. Petrova

A Third-Order Semi-Discrete Genuinely Multidimensional Central Scheme for Hyperbolic Conservation Laws and Related Problems

Numerische Mathematik, 88 (2001), pp. 683–729

[8] A. Kurganov and D. Levy

A Third-Order Semi-Discrete Central Scheme for Conservation Laws and Convection-Diffusion Equations

SIAM Journal on Scientific Computing, 22 (2000), pp. 1461–1488

[7] A. Kurganov and G. Petrova

Central Schemes and Contact Discontinuities

Mathematical Modelling and Numerical Analysis, 34 (2000), pp. 1259–1275

[6] A. Kurganov and E. Tadmor

New High-Resolution Semi-Discrete Central Schemes for Hamilton-Jacobi Equations

Journal of Computational Physics, 160 (2000), pp. 720–742

[5] A. Kurganov and E. Tadmor

New High Resolution Central Schemes for Nonlinear Conservation Laws and Convection-Diffusion Equations

Journal of Computational Physics, 160 (2000), pp. 241–282

[4] J. Goodman, A. Kurganov and P. Rosenau

Breakdown of Burgers-type Equations with Saturating Dissipation Fluxes

Nonlinearity, 12 (1999), pp. 247–268

[3] A. Kurganov, D. Levy and P. Rosenau

On Burgers-type Equations with Non-monotonic Dissipative Fluxes

Communications on Pure and Applied Mathematics, 51 (1998), pp. 443–473

[2] A. Kurganov and E. Tadmor

Stiff Systems of Hyperbolic Conservation Laws. Convergence and Error Estimates

SIAM Journal on Mathematical Analysis, 28 (1997), pp. 1446–1456

[1] A. Kurganov and P. Rosenau

The Effect of a Saturating Dissipation in Burgers-type Equations

Communications on Pure and Applied Mathematics, 50 (1997), pp. 753–771