Journal ArticleDOI
Space--time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows: I. general formulation
TLDR
Simulations show that using the data at the superconvergence points, the accuracy of the numerical discretization is O(h5/2) in space for smooth subsonic flows, both on structured and on locally refined meshes, and that the space-time adaptation can significantly improve the accuracy and efficiency of the numeric method.About:
This article is published in Journal of Computational Physics.The article was published on 2002-11-01. It has received 352 citations till now. The article focuses on the topics: Discontinuous Galerkin method & Upwind scheme.read more
Citations
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Journal ArticleDOI
A unified framework for the construction of one-step finite volume and discontinuous Galerkin schemes on unstructured meshes
TL;DR: 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.
Journal ArticleDOI
Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems
TL;DR: A quadrature-free essentially non-oscillatory finite volume scheme of arbitrary high order of accuracy both in space and time for solving nonlinear hyperbolic systems on unstructured meshes in two and three space dimensions is presented.
Journal ArticleDOI
High-order methods for the Euler and Navier–Stokes equations on unstructured grids
TL;DR: This article reviews several unstructured grid-based high-order methods for the compressible Euler and Navier–Stokes equations, and presents the basic design principles of each method, and highlights its pros and cons when appropriate.
Journal ArticleDOI
A posteriori subcell limiting of the discontinuous Galerkin finite element method for hyperbolic conservation laws
TL;DR: A novel a posteriori finite volume subcell limiter technique for the Discontinuous Galerkin finite element method for nonlinear systems of hyperbolic conservation laws in multiple space dimensions that works well for arbitrary high order of accuracy in space and time and that does not destroy the natural subcell resolution properties of the DG method.
Journal ArticleDOI
Arbitrary high order PNPM schemes on unstructured meshes for the compressible Navier–Stokes equations
Michael Dumbser,Michael Dumbser +1 more
TL;DR: A new unified family of arbitrary high order accurate explicit one-step finite volume and discontinuous Galerkin schemes on unstructured triangular and tetrahedral meshes for the solution of the compressible Navier–Stokes equations is proposed.
References
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Book
Riemann Solvers and Numerical Methods for Fluid Dynamics
TL;DR: In this article, the authors present references and index Reference Record created on 2004-09-07, modified on 2016-08-08 and a reference record created on 2003-09 -07.
Book
Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction
TL;DR: In this article, the generalized Riemann problem is used to solve the Euler Equation problem and the ADER approach is used for non-linear systems with finite forces in multiple dimensions.
Proceedings ArticleDOI
The design and application of upwind schemes on unstructured meshes
TL;DR: Cell-centered and mesh-vertex upwind finite-volume schemes are developed which utilize multi-dimensional monotone linear reconstruction procedures which differ from existing algorithms (even on structured meshes).
Journal ArticleDOI
TVB Runge-Kutta local projection discontinuous galerkin finite element method for conservation laws. II: General framework
Bernardo Cockburn,Chi-Wang Shu +1 more
TL;DR: In this paper, a classe de methodes a elements finis de Galerkin discontinues a variation totale bornee for the resolution des lois de conservation, and the convergence of the convergence is studied.
Journal ArticleDOI
Restoration of the contact surface in the HLL-Riemann solver
TL;DR: The missing contact surface in the approximate Riemann solver of Harten, Lax, and van Leer is restored and the resulting solver is simpler and computationally more efficient than the latter, particulaly for non-ideal gases.
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