Nonlinear resonance in systems of conservation laws
SIAM Journal on Applied Mathematics
Convergence of the 2×2 Godunov method for a general resonant nonlinear balance law
SIAM Journal on Applied Mathematics
A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
SIAM Journal on Numerical Analysis
Analysis and Approximation of Conservation Laws with Source Terms
SIAM Journal on Numerical Analysis
A multiphase Godunov method for compressbile multifluid and multiphase flows
Journal of Computational Physics
A Simple Method for Compressible Multifluid Flows
SIAM Journal on Scientific Computing
Equilibrium schemes for scalar conservation laws with stiff sources
Mathematics of Computation
Journal of Computational Physics
The Riemann problem for the Baer-Nunziato two-phase flow model
Journal of Computational Physics
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
SIAM Journal on Scientific Computing
SIAM Journal on Scientific Computing
Numerical Solutions to Compressible Flows in a Nozzle with Variable Cross-section
SIAM Journal on Numerical Analysis
The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow
Journal of Computational Physics
Journal of Computational Physics
A Hybrid Algorithm for the Baer-Nunziato Model Using the Riemann Invariants
Journal of Scientific Computing
Journal of Computational Physics
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We present a well-balanced numerical scheme for approximating the solution of the Baer-Nunziato model of two-phase flows by balancing the source terms and discretizing the compaction dynamics equation. First, the system is transformed into a new one of three subsystems: the first subsystem consists of the balance laws in the gas phase, the second subsystem consists of the conservation law of the mass in the solid phase and the conservation law of the momentum of the mixture, and the compaction dynamic equation is considered as the third subsystem. In the first subsystem, stationary waves are used to build up a well-balanced scheme which can capture equilibrium states. The second subsystem is of conservative form and thus can be numerically treated in a standard way. For the third subsystem, the fact that the solid velocity is constant across the solid contact suggests us to compose the technique of the Engquist-Osher scheme. We show that our scheme is capable of capturing exactly equilibrium states. Moreover, numerical tests show the convergence of approximate solutions to the exact solution.