A matrix stability analysis of the carbuncle phenomenon
Journal of Computational Physics
A fluid-mixture type algorithm for barotropic two-fluid flow problems
Journal of Computational Physics
Journal of Scientific Computing
An HLLC Riemann solver for magneto-hydrodynamics
Journal of Computational Physics
A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics
Journal of Computational Physics
Journal of Scientific Computing
High-order discontinuous Galerkin methods using an hp-multigrid approach
Journal of Computational Physics
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Journal of Computational Physics
Implementation of WENO schemes in compressible multicomponent flow problems
Journal of Computational Physics
3D transient fixed point mesh adaptation for time-dependent problems: Application to CFD simulations
Journal of Computational Physics
HLLC solver for ideal relativistic MHD
Journal of Computational Physics
An HLLC Scheme to Solve The M1 Model of Radiative Transfer in Two Space Dimensions
Journal of Scientific Computing
Space-time discontinuous Galerkin discretization of rotating shallow water equations
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
An HLLC scheme for Ten-Moments approximation coupled with magnetic field
International Journal of Computing Science and Mathematics
Towards a compact high-order method for non-linear hyperbolic systems, II. The Hermite-HLLC scheme
Journal of Computational Physics
On the HLLC Riemann solver for interface interaction in compressible multi-fluid flow
Journal of Computational Physics
Robust HLLC Riemann solver with weighted average flux scheme for strong shock
Journal of Computational Physics
Adjoint-based h-p adaptive discontinuous Galerkin methods for the 2D compressible Euler equations
Journal of Computational Physics
Journal of Computational Physics
High-order sonic boom modeling based on adaptive methods
Journal of Computational Physics
HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow
Journal of Computational Physics
Journal of Computational Physics
A new adaptive mesh refinement data structure with an application to detonation
Journal of Computational Physics
A high-order multi-dimensional HLL-Riemann solver for non-linear Euler equations
Journal of Computational Physics
Journal of Computational Physics
Structural and Multidisciplinary Optimization
A diffuse interface model with immiscibility preservation
Journal of Computational Physics
A HLL-Rankine-Hugoniot Riemann solver for complex non-linear hyperbolic problems
Journal of Computational Physics
Positivity-preserving Lagrangian scheme for multi-material compressible flow
Journal of Computational Physics
A simple GPU-accelerated two-dimensional MUSCL-Hancock solver for ideal magnetohydrodynamics
Journal of Computational Physics
Journal of Computational Physics
GPU computing of compressible flow problems by a meshless method with space-filling curves
Journal of Computational Physics
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This paper considers a class of approximate Riemann solver devised by Harten, Lax, and van Leer (denoted HLL) for the Euler equations of inviscid gas dynamics. In their 1983 paper, Harten, Lax, and van Leer showed how, with a priori knowledge of the signal velocities, a single-state approximate Riemann solver could be constructed so as to automatically satisfy the entropy condition and yield exact resolution of isolated shock waves. Harten, Lax, and van Leer further showed that a two-state approximation could be devised, such that both shock and contact waves would be resolved exactly. However, the full implementation of this two-state approximation was never given. We show that with an appropriate choice of acoustic and contact wave velocities, the two-state so-called HLLC construction of Toro, Spruce, and Speares will yield this exact resolution of isolated shock and contact waves. We further demonstrate that the resulting scheme is positively conservative. This property, which cannot be guaranteed by any linearized approximate Riemann solver, forces the numerical method to preserve initially positive pressures and densities. Numerical examples are given to demonstrate that the solutions generated are comparable to those produced with an exact Riemann solver, only with a stronger enforcement of the entropy condition across expansion waves.