A Two-dimensional HLLC Riemann Solver for Conservation Laws : Application to Euler and MHD Flows
arXiv:1110.0750 · doi:10.1016/j.jcp.2011.12.025
Abstract
In this paper we present a genuinely two-dimensional HLLC Riemann solver. On logically rectangular meshes, it accepts four input states that come together at an edge and outputs the multi-dimensionally upwinded fluxes in both directions. This work builds on, and improves, our prior work on two-dimensional HLL Riemann solvers. The HLL Riemann solver presented here achieves its stabilization by introducing a constant state in the region of strong interaction, where four one-dimensional Riemann problems interact vigorously with one another. A robust version of the HLL Riemann solver is presented here along with a strategy for introducing sub-structure in the strongly-interacting state. Introducing sub-structure turns the two-dimensional HLL Riemann solver into a two-dimensional HLLC Riemann solver. The sub-structure that we introduce represents a contact discontinuity which can be oriented in any direction relative to the mesh. The Riemann solver presented here is general and can work with any system of conservation laws. We also present a second order accurate Godunov scheme that works in three dimensions and is entirely based on the present multidimensional HLLC Riemann solver technology. The methods presented are cost-competitive with traditional higher order Godunov schemes.
References in corpus (2)
Cited by in corpus (43)
- A Posteriori Subcell Limiting of the Discontinuous Galerkin Finite Element Method for Hyperbolic Conservation Laws
- A Solution Accurate, Efficient and Stable Unsplit Staggered Mesh Scheme for Three Dimensional Magnetohydrodynamics
- Space-time adaptive ADER discontinuous Galerkin finite element schemes with a posteriori sub-cell finite volume limiting
- High order ADER schemes for a unified first order hyperbolic formulation of Newtonian continuum mechanics coupled with electro-dynamics
- Lagrangian ADER-WENO Finite Volume Schemes on Unstructured Triangular Meshes Based On Genuinely Multidimensional HLL Riemann Solvers
- A fourth-order accurate finite volume method for ideal MHD via upwind constrained transport
- High Order Lagrangian ADER-WENO Schemes on Unstructured Meshes - Application of Several Node Solvers to Hydrodynamics and Magnetohydrodynamics
- Space-time adaptive ADER-DG schemes for dissipative flows: compressible Navier-Stokes and resistive MHD equations
- A divergence-free semi-implicit finite volume scheme for ideal, viscous and resistive magnetohydrodynamics
- Using the PPML approach for constructing a low-dissipation, operator-splitting scheme for numerical simulations of hydrodynamic flows
- Direct Arbitrary-Lagrangian-Eulerian finite volume schemes on moving nonconforming unstructured meshes
- A High-Order Relativistic Two-Fluid Electrodynamic Scheme with Consistent Reconstruction of Electromagnetic Fields and a Multidimensional Riemann Solver for Electromagnetism
- On GLM curl cleaning for a first order reduction of the CCZ4 formulation of the Einstein field equations
- Alfvenic Turbulence Beyond the Ambipolar Diffusion Scale
- A Subluminal Relativistic Magnetohydrodynamics Scheme with ADER-WENO Predictor and Multidimensional Riemann Solver-Based Corrector
- Systematic construction of upwind constrained transport schemes for MHD
- High Order Cell-Centered Lagrangian-Type Finite Volume Schemes with Time-Accurate Local Time Stepping on Unstructured Triangular Meshes
- MHD modeling on geodesic grids
- A novel structure preserving semi-implicit finite volume method for viscous and resistive magnetohydrodynamics
- von Neumann Stability Analysis of Globally Constraint-Preserving DGTD and PNPM Schemes for the Maxwell Equations using Multidimensional Riemann Solvers
- Globally constraint-preserving FR/DG scheme for Maxwell's equations at all orders
- Divergence-free Approximate Riemann Solver for the Quasi-neutral Two-fluid Plasma Model
- On a class of two-dimensional incomplete Riemann solvers
- A high-order weighted finite difference scheme with a multi-state approximate Riemann solver for divergence-free magnetohydrodynamic simulations
- The Piecewise Cubic Method (PCM) for Computational Fluid Dynamics
- A Multistate Low-dissipation Advection Upstream Splitting Method for Ideal Magnetohydrodynamics
- Riemann solver with internal reconstruction (RSIR) for compressible single-phase and non-equilibrium two-phase flows
- Efficient, Divergence-Free, High Order MHD on 3D Spherical Meshes with Optimal Geodesic Meshing
- A well-balanced and exactly divergence-free staggered semi-implicit hybrid finite volume/finite element scheme for the incompressible MHD equations
- Turbulent dynamo in a weakly ionized medium
- Computational and in vitro studies of blast-induced blood-brain barrier disruption
- Technologies for supporting high-order geodesic mesh frameworks for computational astrophysics and space sciences
- Multidimensional upwind hydrodynamics on unstructured meshes using Graphics Processing Units I. Two-dimensional uniform meshes
- Divergence-Free Magnetohydrodynamics on Conformally Moving, Adaptive Meshes Using a Vector Potential Method
- Going Beyond the MHD Approximation: Physics-Based Numerical Solution of the CGL Equations
- An exactly curl-free finite-volume scheme for a hyperbolic compressible barotropic two-phase model
- Physical Constraint Preserving Higher Order Finite Volume Schemes for Divergence-Free Astrophysical MHD and RMHD
- Resolving vortices with an isothermal HLLC Riemann solver
- An Alternative Finite Difference WENO-like Scheme with Physical Constraint Preservation for Divergence-Preserving Hyperbolic Systems
- Techniques, Tricks and Algorithms for Efficient GPU-Based Processing of Higher Order Hyperbolic PDEs
- An accurate and robust genuinely multidimensional Riemann solver for Euler equations based on TV flux splitting
- A global divergence conforming DG method for hyperbolic conservation laws with divergence constraint
- A simplified Cauchy-Kowalewskaya procedure for the implicit solution of generalized Riemann problems of hyperbolic balance laws