Nonlinear resonance in systems of conservation laws
SIAM Journal on Applied Mathematics
A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
A multiphase Godunov method for compressbile multifluid and multiphase flows
Journal of Computational Physics
Construction of second-order TVD schemes for nonhomogeneous hyperbolic conservation laws
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Two-phase shock-tube problems and numerical methods of solution
Journal of Computational Physics
Numerical methods for nonconservative hyperbolic systems: a theoretical framework.
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
High-Resolution Finite Volume Methods for Dusty Gas Jets and Plumes
SIAM Journal on Scientific Computing
An exact Riemann solver for compressible two-phase flow models containing non-conservative products
Journal of Computational Physics
Two-dimensional computation of gas flow in a porous bed characterized by a porosity jump
Journal of Computational Physics
A well-balanced approximate Riemann solver for compressible flows in variable cross-section ducts
Journal of Computational and Applied Mathematics
Hi-index | 31.45 |
Gas flow in porous media with a nonconstant porosity function provides a nonconservative Euler system. We propose a new class of schemes for such a system for the one-dimensional situations based on nonconservative fluxes preserving the steady-state solutions. We derive a second-order scheme using a splitting of the porosity function into a discontinuous and a regular part where the regular part is treated as a source term while the discontinuous part is treated with the nonconservative fluxes. We then present a classification of all the configurations for the Riemann problem solutions. In particularly, we carefully study the resonant situations when two eigenvalues are superposed. Based on the classification, we deal with the inverse Riemann problem and present algorithms to compute the exact solutions. We finally propose new Sod problems to test the schemes for the resonant situations where numerical simulations are performed to compare with the theoretical solutions. The schemes accuracy (first- and second-order) is evaluated comparing with a nontrivial steady-state solution with the numerical approximation and convergence curves are established.