Nonlinear resonance in systems of conservation laws
SIAM Journal on Applied Mathematics
Journal of Computational Physics
Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
A multiphase Godunov method for compressbile multifluid and multiphase flows
Journal of Computational Physics
Representation of weak limits and definition of nonconservative products
SIAM Journal on Mathematical Analysis
A high-resolution numerical method for a two-phase model of deflagration-to-detonation transition
Journal of Computational Physics
Mathematical and numerical modeling of two-phase compressible flows with micro-inertia
Journal of Computational Physics
The Riemann problem for the Baer-Nunziato two-phase flow model
Journal of Computational Physics
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
First- and second-order finite volume methods for the one-dimensional nonconservative Euler system
Journal of Computational Physics
HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow
Journal of Computational Physics
A Simple Extension of the Osher Riemann Solver to Non-conservative Hyperbolic Systems
Journal of Scientific Computing
Journal of Computational Physics
A gas kinetic scheme for the Baer-Nunziato two-phase flow model
Journal of Computational Physics
Hi-index | 31.47 |
In this article we present a new numerical procedure for solving exactly the Riemann problem of compressible two-phase flow models containing non-conservative products. These products appear in the expressions for the interactions between the two phases. Thus, in the compressible limit, the governing equations are hyperbolic but can not be written as conservation laws, i.e. in divergence form. In general, the solution to the Riemann problem of these models contains six distinct centered waves. According to the relative position of these waves in the x-t plane, the possible solutions can be classified into four principal configurations. The Riemann solver we propose herein investigates sequentially each of these configurations until an admissible solution is calculated. Special configurations, corresponding to coalescence of waves, are also analyzed and included in the solver. Further, we examine the accuracy and robustness of three known methods for the integration of the non-conservative products, via a series of numerical tests. Finally, the issue of existence and uniqueness of solutions to the Riemann problem is discussed.