Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
SIAM Journal on Mathematical Analysis
On Godunov-type methods near low densities
Journal of Computational Physics
Numerical solution of the Riemann problem for two-dimensional gas dynamics
SIAM Journal on Scientific Computing
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
On the Choice of Wavespeeds for the HLLC Riemann Solver
SIAM Journal on Scientific Computing
The Runge-Kutta discontinuous Galerkin method for conservation laws V multidimensional systems
Journal of Computational Physics
Solution of Two-Dimensional Riemann Problems of Gas Dynamics by Positive Schemes
SIAM Journal on Scientific Computing
Weighted essentially non-oscillatory schemes on triangular meshes
Journal of Computational Physics
Compact Central WENO Schemes for Multidimensional Conservation Laws
SIAM Journal on Scientific Computing
Journal of Computational Physics
An HLLC Riemann solver for magneto-hydrodynamics
Journal of Computational Physics
Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
Journal of Computational Physics
Numerical comparison of Riemann solvers for astrophysical hydrodynamics
Journal of Computational Physics
A central WENO scheme for solving hyperbolic conservation laws on non-uniform meshes
Journal of Computational Physics
FORCE schemes on unstructured meshes I: Conservative hyperbolic systems
Journal of Computational Physics
HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow
Journal of Computational Physics
A HLL-Rankine-Hugoniot Riemann solver for complex non-linear hyperbolic problems
Journal of Computational Physics
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This article presents a numerical model that enables to solve on unstructured triangular meshes and with a high-order of accuracy, a multi-dimensional Riemann problem that appears when solving hyperbolic problems. For this purpose, we use a MUSCL-like procedure in a ''cell-vertex'' finite-volume framework. In the first part of this procedure, we devise a four-state bi-dimensional HLL solver (HLL-2D). This solver is based upon the Riemann problem generated at the centre of gravity of a triangular cell, from surrounding cell-averages. A new three-wave model makes it possible to solve this problem, approximately. A first-order version of the bi-dimensional Riemann solver is then generated for discretizing the full compressible Euler equations. In the second part of the MUSCL procedure, we develop a polynomial reconstruction that uses all the surrounding numerical data of a given point, to give at best third-order accuracy. The resulting over determined system is solved by using a least-square methodology. To enforce monotonicity conditions into the polynomial interpolation, we develop a simplified central WENO (CWENO) procedure. Numerical tests and comparisons with competing numerical methods enable to identify the salient features of the whole model.