Refereed Publications (in the reversed chronological order)

Recent Preprints

• Alina Chertock, Christo Christov, & A. Kurganov (2009)
  Central-Upwind Schemes for the Boussinesq Paradigm Equations
  submitted to the Proceedings of the Fourth Russian-German Advanced Research Workshop on Computational Science and High Performance Computing, Freiburg, 2009.
  
  
• Steve Bryson, Yekaterina Epshteyn, A. Kurganov, & G. Petrova (2008)
  Well-Balanced Positivity Preserving Central-Upwind Scheme on Triangular Grids for the Saint-Venant System
  submitted to Mathematical Modelling and Numerical Analysis.
  
  
• Alina Chertock, Charles R. Doering, Eugene Kashdan, & A. Kurganov (2008)
  A Fast Explicit Operator Splitting Method for Passive Scalar Advection
  submitted to Journal of Scientific Computing.
  
  
• Alina Chertock & A. Kurganov (2008)
  On Splitting-Based Numerical Methods for Convection-Diffusion Equations
  to appear in Quaderni di Matematica.
  
  
• A. Kurganov & Jeffrey Rauch (2006)
  The Order of Accuracy of Quadrature Formulae for Periodic Functions
  to appear in Phase Space Analysis of PDEs 2007, eds. A. Bove, D. Del Santo, M.K.V. Murthy, Progress in nonlinear differential equations and their applications, Birkhauser.
  
  

  2009

• 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 (gzipped .pdf file)
  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 (gzipped pdf file)
  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 (gzipped pdf file)
  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 (gzipped .pdf file)
  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 (gzipped .pdf file)
  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 (gzipped . pdf file)
  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 R elated 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.