Higher order Godunov methods for general systems of hyperbolic conservation laws
Journal of Computational Physics
Journal of Computational Physics
A multiphase Godunov method for compressbile multifluid and multiphase flows
Journal of Computational Physics
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
Discrete equations for physical and numerical compressible multiphase mixtures
Journal of Computational Physics
An exact Riemann solver for compressible two-phase flow models containing non-conservative products
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 Hybrid Algorithm for the Baer-Nunziato Model Using the Riemann Invariants
Journal of Scientific Computing
Numerical approximation for a Baer-Nunziato model of two-phase flows
Applied Numerical Mathematics
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
Journal of Computational Physics
Hi-index | 31.48 |
This paper considers the Riemann problem and an associated Godunov method for a model of compressible two-phase flow. The model is a reduced form of the well-known Baer-Nunziato model that describes the behavior of granular explosives. In the analysis presented here, we omit source terms representing the exchange of mass, momentum and energy between the phases due to compaction, drag, heat transfer and chemical reaction, but retain the non-conservative nozzling terms that appear naturally in the model. For the Riemann problem the effect of the nozzling terms is confined to the contact discontinuity of the solid phase. Treating the solid contact as a layer of vanishingly small thickness within which the solution is smooth yields jump conditions that connect the states across the contact, as well as a prescription that allows the contribution of the nozzling terms to be computed unambiguously. An iterative method of solution is described for the Riemann problem, that determines the wave structure and the intermediate states of the flow, for given left and right states. A Godunov method based on the solution of the Riemann problem is constructed. It includes non-conservative flux contributions derived from an integral of the nozzling terms over a grid cell. The Godunov method is extended to second-order accuracy using a method of slope limiting, and an adaptive Riemann solver is described and used for computational efficiency. Numerical results are presented, demonstrating the accuracy of the numerical method and in particular, the accurate numerical description of the flow in the vicinity of a solid contact where phases couple and nozzling terms are important. The numerical method is compared with other methods available in the literature and found to give more accurate results for the problems considered.