A study of numerical methods for hyperbolic conservation laws with stiff source terms
Journal of Computational Physics
Mathematical and numerical modeling of two-phase flows
Proceedings of the 10th international conference on computing methods in applied sciences and engineering on Computing methods in applied sciences and engineering
Finite volume approximation of two phase-fluid flows based on an approximate Roe-type Riemann solver
Journal of Computational Physics
An approximate linearized Riemann solver for a two-fluid model
Journal of Computational Physics
A well-balanced scheme for the numerical processing of source terms in hyperbolic equations
SIAM Journal on Numerical Analysis
Approximate Riemann solvers, parameter vectors, and difference schemes
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
A numerical method using upwind schemes for the resolution of two-phase flows
Journal of Computational Physics
Analysis and Approximation of Conservation Laws with Source Terms
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Journal of Computational Physics
A density perturbation method to study the eigenstructure of two-phase flow equation systems
Journal of Computational Physics
The surface gradient method for the treatment of source terms in the shallow-water equations
Journal of Computational Physics
A technique of treating negative weights in WENO schemes
Journal of Computational Physics
Discrete equations for physical and numerical compressible multiphase mixtures
Journal of Computational Physics
A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
SIAM Journal on Scientific Computing
Journal of Computational Physics
Numerical Solutions to Compressible Flows in a Nozzle with Variable Cross-section
SIAM Journal on Numerical Analysis
Application of mesh-adaptation for pollutant transport by water flow
Mathematics and Computers in Simulation
A simple finite volume method for the shallow water equations
Journal of Computational and Applied Mathematics
Mathematics and Computers in Simulation
Hi-index | 31.45 |
This work is devoted to the analysis of a finite volume method recently proposed for the numerical computation of a class of non-homogenous systems of partial differential equations of interest in fluid dynamics. The stability analysis of the proposed scheme leads to the introduction of the sign matrix of the flux jacobian. It appears that this formulation is equivalent to the VFRoe scheme introduced in the homogeneous case and has a natural extension here to non-homogeneous systems. Comparative numerical experiments for the Shallow Water and Euler equations with source terms, and a model problem of two-phase flow (Ransom faucet) are presented to validate the scheme. The numerical results present a convergence stagnation phenomenon for certain forms of the source term, notably when it is singular. Convergence stagnation has been also shown in the past for other numerical schemes. This issue is addressed in a specific section where an explanation is given with the help of a linear model equation, and a cure is demonstrated.