A Positive Conservative Method for Magnetohydrodynamics Based on HLL and Roe Methods

By Pekka Janhunen. 2000

204 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/418bef5e1976fd08e6e61c2ba94a30ac06bff744

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In Applied Mathematics

In Computational Mechanics

Citations in the corpus

A multi-state HLL approximate Riemann solver for ideal magnetohydrodynamics (2005, unknown): “Keywords: Magnetohydrodynamics; Approximate Riemann solver; HLL; HLLC; HLLD; Positivity”
Semirelativistic Magnetohydrodynamics and Physics-Based Convergence Acceleration (2002, background): “In recent papers by Janhunen [7] and Dellar [3] it was shown that if one starts from the relativistic MHD equations, which allow the existence of magnetic monopoles, while the momentum and energy equations remain in conservation form.”
An HLLC Riemann solver for magneto-hydrodynamics (2005, methodology): “Examples include Janhunen [13], Wesenberg [25], Linde [15], Gurski [11], and others.”
Divergence-free adaptive mesh refinement for Magnetohydrodynamics (2001, unknown): “11) Janhunen [29] presents an interesting alternative to the scheme of Powell [37] which tries to satisfy the —◊ = 0B constraint up to discretization error, but not machine error.”
An unsplit staggered mesh scheme for multidimensional magnetohydrodynamics: a staggered dissipation-control differencing algorithm (2006, unknown): “Recently, there also have been other approaches [31, 48] to extend the 8-wave schemes that manifest the ∇ ·B source term.”
Second-Order-accurate Schemes for Magnetohydrodynamics with Divergence-free Reconstruction (2003, methodology): “In the past, treating low- plasmas required using corrective techniques of the type described in Balsara & Spicer (1999b) and Janhunen (2000).”
Smoothed Particle Magnetohydrodynamics – II. Variational principles and variable smoothing-length terms (2003, methodology): “In the MHD case this also demonstrates that the treatment of source terms proportional to ∇ · B is consistent, as discussed in paper I with reference to Janhunen (2000) and Dellar (2001).”
PLUTO: A Numerical Code for Computational Astrophysics (2007, methodology): “The user can choose among the following available Riemann solvers: the Roe solver of Cargo & Gallice (1997), the HLL (Janhunen 2000), HLLC (Li 2005), HLLD (Miyoshi & Kusano 2005), and the Lax-Friedrichs solvers.”
Smoothed particle hydrodynamics and magnetohydrodynamics (2010, unknown): “…given by (142) and the momentum and energy equations given by dvi dt = 1 ρ ∂Sij ∂xj − B i ρ ∂Bj ∂xj , (144) de dt = 1 ρ ∂(viS ij) ∂xj − viB i ρ ∂Bj ∂xj , (145) However, Janhunen (2000) and Dellar (2001) have strongly argued that a consistent formulation in the presence of monopoles, whilst…”