Adaptive Local Refinement with Octree Load Balancing for the Parallel Solution of Three-Dimensional Conservation Laws
Joseph E. Flaherty,R. M. Loy,Mark S. Shephard,Boleslaw K. Szymanski,James D. Teresco,Louis H. Ziantz +5 more
TLDR
To accommodate the variable time steps, octree partitioning is extended to use weights derived from element size and processor load imbalances are corrected by using traversals of an octree representing a spatial decomposition of the domain.About:
This article is published in Journal of Parallel and Distributed Computing.The article was published on 1997-12-01 and is currently open access. It has received 210 citations till now. The article focuses on the topics: Octree & Euler equations.read more
Citations
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Review Article Runge-Kutta Discontinuous Galerkin Methods for Convection-Dominated Problems
Bernardo Cockburn,Chi-Wang Shu +1 more
TL;DR: The theoretical and algorithmic aspects of the Runge–Kutta discontinuous Galerkin methods are reviewed and several applications including nonlinear conservation laws, the compressible and incompressible Navier–Stokes equations, and Hamilton–Jacobi-like equations are shown.
Book
Runge-Kutta discontinuous Galerkin methods for convection-dominated problems
Bernardo Cockburn,Chi-Wang Shu +1 more
TL;DR: The Runge-Kutta discontinuous Galerkin (RKDG) method as discussed by the authors is one of the state-of-the-art methods for non-linear convection-dominated problems.
Book ChapterDOI
The Development of Discontinuous Galerkin Methods
TL;DR: An overview of the evolution of the discontinuous Galerkin methods since their introduction in 1973 by Reed and Hill, in the framework of neutron transport, until their most recent developments is presented.
Journal ArticleDOI
Discontinuous Galerkin methods
TL;DR: The exposition of the ideas behind the devising of these methods as well as on the mechanisms that allow them to perform so well in such a variety of problems are concentrated on.
Journal ArticleDOI
p4est : Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees
TL;DR: This work presents scalable algorithms for parallel adaptive mesh refinement and coarsening (AMR), partitioning, and 2:1 balancing on computational domains composed of multiple connected two-dimensional quadtrees or three-dimensional octrees, referred to as a forest of octrees.
References
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Journal ArticleDOI
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Chi-Wang Shu,Stanley Osher +1 more
TL;DR: Two methods of sharpening contact discontinuities-the subcell resolution idea of Harten and the artificial compression idea of Yang, which those authors originally used in the cell average framework-are applied to the current ENO schemes using numerical fluxes and TVD Runge-Kutta time discretizations.
Journal ArticleDOI
High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
TL;DR: The technique of obtaining high resolution, second order, oscillation free (TVD), explicit scalar difference schemes, by the addition of a limited antidiffusive flux to a first order scheme is described in this article.
Journal ArticleDOI
A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
Gary A. Sod,Gary A. Sod +1 more
TL;DR: In this paper, the finite difference methods of Godunov, Hyman, Lax and Wendroff (two-step), MacCormack, Rusanov, the upwind scheme, the hybrid scheme of Harten and Zwas, the antidiffusion method of Boris and Book, and Glimm's method, a random choice method, are discussed.
Journal ArticleDOI
Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection
TL;DR: In this paper, an approach to numerical convection is presented that exclusively yields upstream-centered schemes, which start from a meshwise approximation of the initial-value distribution by simple basic functions, e.g., Legendre polynomials.
Book
Adaptive mesh refinement for hyperbolic partial differential equations
Marsha Berger,Joseph Oliger +1 more
TL;DR: This work presents an adaptive method based on the idea of multiple, component grids for the solution of hyperbolic partial differential equations using finite difference techniques based upon Richardson-type estimates of the truncation error, which is a mesh refinement algorithm in time and space.
Related Papers (5)
TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General framework
Bernardo Cockburn,Chi-Wang Shu +1 more