A new efficient formulation of the HLLEM Riemann solver for general conservative and non-conservative hyperbolic systems

DOI10.1016/j.jcp.2015.10.014zbMath1349.76603OpenAlexW2190293247MaRDI QIDQ2374898

Publication date: 5 December 2016

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2015.10.014

zbMATH Keywords

conservation laws and general hyperbolic PDE with non-conservative terms Euler equations with real equation of state and multiphase flows path-conservative HLLEM Riemann solver resolution of linearly degenerate intermediate waves RMHD/MHD equations and nonlinear elasticity well-balanced scheme for single and two-layer shallow water equations

Mathematics Subject Classification ID

Magnetohydrodynamics and electrohydrodynamics (76W05) Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs (65M25) Multiphase and multicomponent flows (76Txx) Incompressible viscous fluids (76Dxx)

Related Items

A staggered semi-implicit hybrid finite volume / finite element scheme for the shallow water equations at all Froude numbers, A cure for numerical shock instability in HLLC Riemann solver using antidiffusion control, Using piecewise-linear reconstruction to constructing a low-dissipation HLL method for numerical solution of hydrodynamics equation, Space-time adaptive ADER discontinuous Galerkin schemes for nonlinear hyperelasticity with material failure, Systematic construction of upwind constrained transport schemes for MHD, Self-similar structures based genuinely two-dimensional Riemann solvers in curvilinear coordinates, A path-conservative Osher-type scheme for axially symmetric compressible flows in flexible visco-elastic tubes, High order ADER schemes and GLM curl cleaning for a first order hyperbolic formulation of compressible flow with surface tension, An augmented HLLEM ADER numerical model parallel on GPU for the porous shallow water equations, A study of higher-order reconstruction methods for genuinely two-dimensional Riemann solver, A universal centred high-order method based on implicit Taylor series expansion with fast second order evolution of spatial derivatives, Multidimensional approximate Riemann solvers for hyperbolic nonconservative systems. Applications to shallow water systems, The exact Riemann solver for the shallow water equations with a discontinuous bottom, Exploring various flux vector splittings for the magnetohydrodynamic system, High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: viscous heat-conducting fluids and elastic solids, An effective all-speed Riemann solver with self-similar internal structure for Euler system, On a modification of the Rusanov solver for the equations of special relativistic magnetic hydrodynamics, A finite-volume approach for compressible single- and two-phase flows in flexible pipelines with fluid-structure interaction, Тестовые задачи динамики газовзвесей с использованием асимптотически точных решений, Efficient GPU implementation of multidimensional incomplete Riemann solvers for hyperbolic nonconservative systems: applications to shallow water systems with topography and dry areas, Solving two-phase shallow granular flow equations with a well-balanced NOC scheme on multiple GPUs, A well-balanced path conservative SPH scheme for nonconservative hyperbolic systems with applications to shallow water and multi-phase flows, Globally divergence-free DG scheme for ideal compressible MHD, A kinetic approach of the bi-temperature Euler model, A new framework for magnetohydrodynamic simulations with anisotropic pressure, A simplified Cauchy-Kowalewskaya procedure for the local implicit solution of generalized Riemann problems of hyperbolic balance laws, A simple diffuse interface approach for compressible flows around moving solids of arbitrary shape based on a reduced Baer-Nunziato model, A Hybrid Scheme of Level Set and Diffuse Interface Methods for Simulating Multi-Phase Compressible Flows, A study of multidimensional fifth-order WENO method for genuinely two-dimensional Riemann solver, SpECTRE: A task-based discontinuous Galerkin code for relativistic astrophysics, ExaHyPE: an engine for parallel dynamically adaptive simulations of wave problems, Well balancing of the SWE schemes for moving-water steady flows, HLLEPJ and HLLCEPJ Riemann solvers for the wilkins model of elastoplasticity, A comparison of explicit and semi‐implicit finite volume schemes for viscous compressible flows in elastic pipes in fast transient regime, On the numerical solution of nonconservative hyperbolic systems of equations, Multidimensional Riemann problem with self-similar internal structure. Part III: A multidimensional analogue of the HLLI Riemann solver for conservative hyperbolic systems, A flux splitting method for the Baer-Nunziato equations of compressible two-phase flow, Numerical and analytical investigation of shock wave processes in elastoplastic media, Stabilized bi-cubic Hermite Bézier finite element method with application to gas-plasma interactions occurring during massive material injection in tokamaks, On the computation of compressible multiphase flows with heat and mass transfer in elastic pipelines, On numerical instabilities of Godunov-type schemes for strong shocks, Mathematical modeling of wide-range compressible two-phase flows, A new all-speed flux scheme for the Euler equations, A new genuinely two-dimensional Riemann solver for multidimensional Euler and Navier-Stokes equations, A new Rusanov-type solver with a local linear solution reconstruction for numerical modeling of white dwarf mergers by means massive parallel supercomputers, A genuinely two-dimensional Riemann solver for compressible flows in curvilinear coordinates, A simple diffuse interface approach on adaptive Cartesian grids for the linear elastic wave equations with complex topography, Fluctuation splitting Riemann solver for a non-conservative modeling of shear shallow water flow, An efficient hyperbolic relaxation system for dispersive non-hydrostatic water waves and its solution with high order discontinuous Galerkin schemes, Fully-conservative contact-capturing schemes for multi-material advection, A unified Eulerian framework for multimaterial continuum mechanics, Numerical issues in gas flow dynamics with hydraulic shocks using high order finite volume WENO schemes, The simulation of compressible multi-fluid flows by a GRP-based energy-splitting method, Development of accurate and robust genuinely two-dimensional HLL-type Riemann solver for compressible flows, Investigation of Riemann Solver with Internal Reconstruction (RSIR) for the Euler Equations, An efficient, second order accurate, universal generalized Riemann problem solver based on the HLLI Riemann solver, On asymptotic behavior of HLL-type schemes at low Mach numbers, SLAU2 applied to two-dimensional, ideal magnetohydrodynamics simulations, Bounds for wave speeds in the Riemann problem: direct theoretical estimates, On solving the Riemann problem for non-conservative hyperbolic systems of partial differential equations, Approximate Riemann solver for compressible liquid vapor flow with phase transition and surface tension, Complete Riemann solvers for the hyperbolic GPR model of continuum mechanics, A posteriori subcell finite volume limiter for general \(P_NP_M\) schemes: applications from gasdynamics to relativistic magnetohydrodynamics, A simple robust and accurate \textit{a posteriori} sub-cell finite volume limiter for the discontinuous Galerkin method on unstructured meshes, A subluminal relativistic magnetohydrodynamics scheme with ADER-WENO predictor and multidimensional Riemann solver-based corrector, Improvement of the genuinely multidimensional ME-AUSMPW scheme for subsonic flows, High order finite volume schemes for solving the non-conservative convection equations on the unstructured grids, Efficient implementation of ADER discontinuous Galerkin schemes for a scalable hyperbolic PDE engine, High-order low-dissipation targeted ENO schemes for ideal magnetohydrodynamics, Numerical simulation of compressible multiphase hydrodynamic problems using reduced five-equation model on body-fitted grids, Low-dissipation centred schemes for hyperbolic equations in conservative and non-conservative form, Validation of a computational algorithm based on the discontinuous Galerkin method for the Baer-Nunziato relaxation model, A new diffusion-regulated flux splitting method for compressible flows, HLLC-type and path-conservative schemes for a single-velocity six-equation two-phase flow model: a comparative study, Using a combination of Godunov and Rusanov solvers based on the piecewise parabolic reconstruction of primitive variables for numerical simulation of supernovae Ia type explosion, A discontinuous Galerkin spectral element method for a nonconservative compressible multicomponent flow model, Implementation of the HLL-GRP solver for multidimensional ideal MHD simulations based on finite volume method, Exact solution for Riemann problems of the shear shallow water model, Numerical study of multiphase hyperbolic models, A Flux Splitting Method for the Baer-Nunziato Equations of Compressible Two-Phase Flow

Uses Software

Cites Work