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Monotonicity Preserving Weighted Essentially Non-oscillatory Schemes with Increasingly High Order of Accuracy
In this paper we design a class of numerical schemes that are higher-order extensions of the weighted essentially non-oscillatory (WENO) schemes of G.-S. Jiang and C.-W. Shu (1996) and X.-D. Liu, S.
A Staggered Mesh Algorithm Using High Order Godunov Fluxes to Ensure Solenoidal Magnetic Fields in Magnetohydrodynamic Simulations
The equations of magnetohydrodynamics (MHD) have been formulated as a hyperbolic system of conservation laws. In that form it becomes possible to use higher order Godunov schemes for their solution.
von Neumann stability analysis of smoothed particle hydrodynamics—suggestions for optimal algorithms
We present a von Neumann stability analysis of the equations of smoothed particle hydrodynamics (SPH) along with a critical discussion of various parts of the algorithm. The stability analysis is
The Distribution of Pressures in a Supernova-Driven Interstellar Medium
Observations have suggested substantial departures from pressure equilibrium in the interstellar medium (ISM) in the plane of the Galaxy, even on scales under 50 pc. Nevertheless, multi-phase models
Total Variation Diminishing Scheme for Relativistic Magnetohydrodynamics
In this paper we present a total variation diminishing (TVD) scheme for numerical relativistic magnetohydrodynamics (MHD). The eigenstructure of the equations of relativistic MHD has been cataloged
Second-Order-accurate Schemes for Magnetohydrodynamics with Divergence-free Reconstruction
While working on an adaptive mesh refinement (AMR) scheme for divergence-free magnetohydrodynamics (MHD), Balsara discovered a unique strategy for the reconstruction of divergence-free vector fields.
Divergence-free adaptive mesh refinement for Magnetohydrodynamics
Abstract Several physical systems, such as nonrelativistic and relativistic magnetohydrodynamics (MHD), radiation MHD, electromagnetics, and incompressible hydrodynamics, satisfy Stoke's law type
There is a general agreement that the conspicuous extranuclear X-ray, optical-line, and radio-contiuum emission of starbursts is associated with powerful galactic superwinds blowing from their
Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics
  • D. Balsara
  • Mathematics, Computer Science
    J. Comput. Phys.
  • 1 September 2012
In this work, weighted non-oscillatory reconstruction was applied to the conserved variables, and the less expensive reconstruction works very well in two and three dimensions, suggesting that when designing robust, high accuracy schemes, having a self-adjusting positivity criterion is almost as important as the non-linear hybridization.
A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes
A conservative least-squares polynomial reconstruction operator is applied to the discontinuous Galerkin method, which yields space–time polynomials for the vector of conserved variables and for the physical fluxes and source terms that can be used in a natural way to construct very efficient fully-discrete and quadrature-free one-step schemes.