Exact Riemann solver for ideal magnetohydrodynamics that can handle all types of intermediate shocks and switch-on/off waves

Takahashi, Katsuhiko; Yamada, Shoichi

doi:10.1017/s0022377813001268

Cited by 17 publications

(10 citation statements)

References 26 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In this way, FD-Prim is algorithmically quite analogous to FVM, in that it first interpolates (rather than reconstructs) high-order Riemann states at each cell interface, then uses them to calculate interface fluxes by solving Riemann problems using either exact or approximate solvers, and finally makes corrections to the fluxes to deliver high-order-accurate FD numerical fluxes [57,60]. In this way the FD-Prim approach allows the added flexibility of choosing a Riemann solver (e.g., exact [66,67,68,33], HLL-types [69,70,71,72], or Roe [73], etc.) in a manner analogous to the FVM approach.…”

Section: Introductionmentioning

confidence: 99%

A variable high-order shock-capturing finite difference method with GP-WENO

Reyes

Lee

Graziani

et al. 2019

Journal of Computational Physics

View full text Add to dashboard Cite

We present a new finite difference shock-capturing scheme for hyperbolic equations on static uniform grids. The method provides selectable high-order accuracy by employing a kernel-based Gaussian Process (GP) data prediction method which is an extension of the GP high-order method originally introduced in a finite volume framework by the same authors. The method interpolates Riemann states to high order, replacing the conventional polynomial interpolations with polynomial-free GP-based interpolations. For shocks and discontinuities, this GP interpolation scheme uses a nonlinear shock handling strategy similar to Weighted Essentially Non-oscillatory (WENO), with a novelty consisting in the fact that nonlinear smoothness indicators are formulated in terms of the Gaussian likelihood of the local stencil data, replacing the conventional L 2 -type smoothness indicators of the original WENO method. We demonstrate that these GPbased smoothness indicators play a key role in the new algorithm, providing significant improvements in delivering high -and selectable -order accuracy in smooth flows, while successfully delivering non-oscillatory solution behavior in discontinuous flows.. When there is a discontinuity on both S R and S R , both q AO(R ,3) * and q AO(R,3) * will reduce to the centrally stable third-order interpolation as before.

show abstract

Section: Introductionmentioning

confidence: 99%

A variable high-order shock-capturing finite difference method with GP-WENO

Reyes

Lee

Graziani

et al. 2019

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…Over the past more than four decades, there have been a large number of numerical investigations for ISs. In spite of evolutionary conditions, ISs are commonly observed to be stable shocks in numerical simulations (e.g., Wu 1987;Wu & Hada 1991;Takahashi et al 2013Takahashi et al , 2014, and two interplanetary ISs have been observed and reported (Chao et al 1993;Feng & Wang 2008). However, both ISs were identified through fitting the R-H relations based on one spacecraft observation.…”

Section: Discussionmentioning

confidence: 99%

Observations of an Interplanetary Intermediate Shock Associated With a Magnetic Reconnection Exhaust

Feng

Wang

et al. 2016

ApJ

View full text Add to dashboard Cite

Two intermediate shocks (ISs) in interplanetary space have been identified via one spacecraft observation. However, Feng et al. suggested that the analysis using a single spacecraft observation based only on the RankineHugoniot (R-H) relations could misinterpret a tangential discontinuity (TD) as an IS. The misinterpretation can be fixed if two spacecraft observations are available. In this paper, we report an IS-like discontinuity associated with a magnetic reconnection exhaust, which was observed by Wind on 2000 August 9 at 1 au. We investigated this discontinuity by fitting the R-H relations and referring to the Advanced Composition Explorer (ACE) observations. As a result, we found that the observed magnetic field and plasma data satisfy the R-H relations well, and the discontinuity satisfies all the requirements of the  2 3 type IS. Although the discontinuity cannot be identified strictly by using two spacecraft observations, in light of the ACE observations we consider that the discontinuity should be an IS rather than a TD.

show abstract

“…They are related to the question of the existence and the uniqueness of solutions of some Riemann problems. However, there is a ongoing controversy about the significance of non-regular shocks (and compound waves) in MHD (see Takahashi and Yamada, 2014, for an up-to-date overview of the problem).…”

Section: Convexitymentioning

confidence: 99%

Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics

Martí

Müller

2015

Living Rev Comput Astrophys

View full text Add to dashboard Cite

An overview of grid-based numerical methods used in relativistic hydrodynamics (RHD) and magnetohydrodynamics (RMHD) is presented. Special emphasis is put on a comprehensive review of the application of high-resolution shock-capturing methods. Results of a set of demanding test bench simulations obtained with different numerical methods are compared in an attempt to assess the present capabilities and limits of the various numerical strategies. Applications to three astrophysical phenomena are briefly discussed to motivate the need for and to demonstrate the success of RHD and RMHD simulations in their understanding. The review further provides FORTRAN programs to compute the exact solution of the Riemann problem in RMHD, and to simulate 1D RMHD flows in Cartesian coordinates. Article RevisionsLiving Reviews supports two ways of keeping its articles up-to-date:Fast-track revision. A fast-track revision provides the author with the opportunity to add short notices of current research results, trends and developments, or important publications to the article. A fast-track revision is refereed by the responsible subject editor. If an article has undergone a fast-track revision, a summary of changes will be listed here.Major update. A major update will include substantial changes and additions and is subject to full external refereeing. It is published with a new publication number.For detailed documentation of an article's evolution, please refer to the history document of the article's online version at http://dx

show abstract

Exact Riemann solver for ideal magnetohydrodynamics that can handle all types of intermediate shocks and switch-on/off waves

Cited by 17 publications

References 26 publications

A variable high-order shock-capturing finite difference method with GP-WENO

A variable high-order shock-capturing finite difference method with GP-WENO

Observations of an Interplanetary Intermediate Shock Associated With a Magnetic Reconnection Exhaust

Grid-based Methods in Relativistic Hydrodynamics and Magnetohydrodynamics

Contact Info

Product

Resources

About