Semi-Godunov schemes for multiphase flows in porous media

DOI10.1016/j.apnum.2008.12.019zbMath1191.35022OpenAlexW2007475630MaRDI QIDQ1030794

Nils Henrik Risebro, Siddhartha Mishra, Kenneth Hvistendahl Karlsen

Publication date: 2 July 2009

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2008.12.019

zbMATH Keywords

finite volume schemesdiscontinuous flux

Mathematics Subject Classification ID

Flows in porous media; filtration; seepage (76S05) Hyperbolic conservation laws (35L65) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Theoretical approximation in context of PDEs (35A35) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Initial value problems for first-order hyperbolic systems (35L45)

Related Items

Godunov-type numerical methods for a model of granular flow ⋮ A finite volume method for a two-phase multicomponent polymer flooding ⋮ Simulation of multiphase flows in porous media with gravitational effects using dominant wave method ⋮ High-order well-balanced finite volume schemes for simulating wave propagation in stratified magnetic atmospheres ⋮ Splitting-Based Structure Preserving Discretizations for Magnetohydrodynamics

Cites Work

• Unnamed Item
• Unnamed Item
• Convergence of finite volume schemes for triangular systems of conservation laws
• Well-posedness in \(BV_t\) and convergence of a difference scheme for continuous sedimentation in ideal clarifier-thickener units
• Existence and stability of entropy solutions for a conservation law with discontinuous non-convex fluxes
• Semi-Godunov schemes for general triangular systems of conservation laws
• Strong Stability-Preserving High-Order Time Discretization Methods
• OPTIMAL ENTROPY SOLUTIONS FOR CONSERVATION LAWS WITH DISCONTINUOUS FLUX-FUNCTIONS
• On the Strict Hyperbolicity of the Buckley–Leverett Equations for Three-Phase Flow in a Porous Medium
• Riemann Problems for Nonstrictly Hyperbolic 2 × 2 Systems of Conservation Laws
• Solution of the Cauchy Problem for a Conservation Law with a Discontinuous Flux Function
• Convergence of a Difference Scheme for Conservation Laws with a Discontinuous Flux
• A Difference Scheme for Conservation Laws with a Discontinuous Flux: The Nonconvex Case
• Finite Volume Methods for Hyperbolic Problems
• Upwind difference approximations for degenerate parabolic convection-diffusion equations with a discontinuous coefficient