An HLLC Riemann solver for relativistic flows ¿ I. Hydrodynamics

By Andrea Mignone, Gianluigi Bodo. 2005

171 citations recorded by the source corpus.

We present an extension of the HLLC approximate Riemann solver by Toro, Spruce and Speares to the relativistic equations of fluid dynamics. The solver retains the simplicity of the original two-wave formulation proposed by Harten, Lax and van Leer (HLL) but it restores the missing contact wave in the solution of the Riemann problem. The resulting numerical scheme is computationally efficient, robust and positively conservative. The performance of the new solver is evaluated through numerical testing in one and two dimensions.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/0fead230b666c4e456e18752779ce59a2f360988

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Mechanics

Citations in the corpus

A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMIC CODE FOR CORE-COLLAPSE SUPERNOVAE. I. METHOD AND CODE TESTS IN SPHERICAL SYMMETRY (2010, methodology): “I. 107 Quirk (1994), combining the high resolution of the HLLC solver (Toro et al. 1994; Mignone & Bodo 2005) with the robustness of the HLLE solver (Harten et al. 1983; Einfeldt 1988) against odd–even decoupling near grid-aligned shocks (Quirk 1994; Liou 2000; Kifonidis et al. 2003; Sutherland et…”
A NEW MULTI-DIMENSIONAL GENERAL RELATIVISTIC NEUTRINO HYDRODYNAMICS CODE FOR CORE-COLLAPSE SUPERNOVAE. II. RELATIVISTIC EXPLOSION MODELS OF CORE-COLLAPSE SUPERNOVAE (2012, methodology): “Our implementation of CoCoNuT employs a relativistic version of the HLLC approximative Riemann solver (Mignone & Bodo 2005), but adaptively switches to the more diffusive HLLE solver (Einfeldt 1988) in the vicinity of strong shocks to avoid the phenomenon of odd-even-decoupling (Quirk 1994).”
The Status of Multi-Dimensional Core-Collapse Supernova Models (2016, methodology): “For Riemann solvers that take all the wave families into account (e.g. Colella & Glaz 1985; Toro et al. 1994; Mignone & Bodo 2005; Donat & Marquina 1996), the numerical kinematic viscosity νnum in the subsonic regime is roughly given in terms of the typical velocity jump per cell δvgs and the cell…”
PLUTO: A Numerical Code for Computational Astrophysics (2007, methodology): “Several algorithms for relativistic ﬂows presented in Mignone et al. (2005b) and Mignone & Bodo (2005, 2006) are now part of the code and the related veriﬁcation problems will not be repeated here.”
Relativistic jet feedback – III. Feedback on gas discs (2018, methodology): “We use the HLLC Riemann solver to solve the relativistic hydrodynamic equations (Mignone & Bodo 2005), with a piecewise parabolic reconstruction scheme (PPM method, Colella & Woodward 1984).”
The Athena++ Adaptive Mesh Refinement Framework: Design and Magnetohydrodynamic Solvers (2020, methodology): “It also includes the relativistic HLLC solver for hydrodynamics (Mignone & Bodo 2005) and HLLD solver for MHD (Mignone et al. 2009).”
Supernova simulations from a 3D progenitor model - Impact of perturbations and evolution of explosion properties (2017, methodology): “The hydro module CoCoNuT solves the equations of general relativistic hydrodynamics in spherical polar coordinates using piecewise parabolic reconstruction (Colella & Woodward 1984), a hybrid HLLC/HLLE Riemann solver (Mignone & Bodo 2005), and second-order time integration.”
An HLLC Riemann solver for relativistic flows – II. Magnetohydrodynamics (2006, background): “In Mignone & Bodo (2005) (Paper I henceforth), we proposed an approach that cured this deficiency by restoring the missing contact wave.”