A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics

By T. Miyoshi, Kanya Kusano. 2005

608 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/8d2ff79363e429d130e1e8d9c5c11941d36b97b8

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

THREE-DIMENSIONAL KINETIC-MHD MODEL OF THE GLOBAL HELIOSPHERE WITH THE HELIOPAUSE-SURFACE FITTING (2015, methodology): “Non-stationary versions of MHD Equations (2)–(5) are solved using a 3D modification of the finitevolume Godunov-type scheme that employs a Harten-Lax-van Leer Discontinuity MHD Riemann solver (see, for example, Miyoshi & Kusano 2005).”
RADIATION MAGNETOHYDRODYNAMIC SIMULATIONS OF PROTOSTELLAR COLLAPSE: PROTOSTELLAR CORE FORMATION (2012, methodology): “We solve the MHD system using the HLLD approximate Riemann solver (Miyoshi & Kusano 2005).”
PLUTO: A Numerical Code for Computational Astrophysics (2007, methodology): “Indeed, for a given accuracy, the computing time offered by HLLD signiﬁcantly improves over the Roe solver and it is still slightly better than the cheaper HLL scheme.”
A simple unsplit Godunov method for multidimensional MHD (2009, methodology): “These include nonlinear solvers such as HLLE (Harten et al., 1983; Einfeldt et al., 1991), HLLC for hydrodynamics (Batten et al., 1997; Toro, 1999), and HLLD for MHD (Miyoshi and Kusano, 2005), or linear solvers such as Roe’s method (Roe, 1981) extended to MHD (Cargo and Gallice, 1997).”
Gaps, Rings, and Non-Axisymmetric Structures in Protoplanetary Disks - From Simulations to ALMA Observations (2014, methodology): “We used the HLLD Riemann solver (Miyoshi & Kusano 2005).”
A new class of accurate, mesh-free hydrodynamic simulation methods (2014, methodology): “We therefore have also implemented a standard approximate HLLC Riemann solver (see Toro 1999; Miyoshi & Kusano 2005).”
Simulating galaxy formation with the IllustrisTNG model (2017, methodology): “The TNG model employs cell-centered magnetic fields to solve the equations of ideal magneto-hydrodynamics (Pakmor, Bauer & Springel 2011) combined with an approximate HLLD (Harten-Lax-van Leer with contact and Alfvén mode) Riemann solver (Miyoshi & Kusano 2005).”
RADIATION MAGNETOHYDRODYNAMIC SIMULATIONS OF PROTOSTELLAR COLLAPSE: NONIDEAL MAGNETOHYDRODYNAMIC EFFECTS AND EARLY FORMATION OF CIRCUMSTELLAR DISKS (2015, methodology): “The MHD part is solved using the HLLD approximate Riemann solver (Miyoshi & Kusano 2005) and the mixed divergence cleaning method (Dedner et al. 2002).”
An HLLC Riemann solver for relativistic flows – II. Magnetohydrodynamics (2006, methodology): “This has been done, for example, by Miyoshi & Kusano (2005) in the context of classical MHD.”
Simulations of magnetic fields in isolated disc galaxies (2012, methodology): “(ii) We scale the magnetic field as B′c = Bc/ √ a. (iii) We then calculate the fluxes across the moving interface from the reconstructed primitive variables and B′c using the HLLD riemann solver (Miyoshi & Kusano 2005), as described in Pakmor et al. (2011).”
Adaptive numerical algorithms in space weather modeling (2012, background): “A large variety of numerical ﬂux functions are available, including the local Lax-Friedrichs or Rusanov [79], HLLE [73,74], Artiﬁcial Wind [80], HLLD [81], Roe [82] and Godunov [83] ﬂuxes.”