Summation-by-parts operators for correction procedure via reconstruction
TLDR
This work reformulates CPR methods using summation-by-parts (SBP) operators with simultaneous approximation terms (SATs), a framework popular for finite difference methods, and proves entropy stability for Burgers' equation is proved for general SBP CPR methods not including boundary nodes.About:
This article is published in Journal of Computational Physics.The article was published on 2016-04-15 and is currently open access. It has received 123 citations till now. The article focuses on the topics: Discontinuous Galerkin method & Summation by parts.read more
Citations
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Journal ArticleDOI
On discretely entropy conservative and entropy stable discontinuous Galerkin methods
TL;DR: In this article, flux differencing, quadrature-based projections, and SBP-like operators are used to construct discretely entropy conservative schemes for DG methods under more arbitrary choices of volume and surface quadratures rules.
Journal ArticleDOI
A general framework to construct schemes satisfying additional conservation relations. Application to entropy conservative and entropy dissipative schemes
TL;DR: This paper shows how to construct a scheme that is consistent with the original PDE and the additional conservation relation, and provides one explicit solution, and shows that the accuracy of the new scheme is at most degraded by one order.
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A Posteriori Correction of High-Order Discontinuous Galerkin Scheme through Subcell Finite Volume Formulation and Flux Reconstruction
TL;DR: A new limiter for discontinuous Galerkin (DG) schemes, based on subcell resolution through reconstructed flux correction, for hyperbolic conservation laws is presented, constructed by means of a subcell Finite Volume (FV) formulation, which is able to retain the very high accurate sub cell resolution of DG schemes.
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Fourier analysis and evaluation of DG, FD and compact difference methods for conservation laws
TL;DR: A Fourier analysis of several popular methods in LES including the discontinuous Galerkin (DG), finite difference (FD), and compact difference (CD) methods finds that the overall numerical dissipation strongly depends on the time step.
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Generalised summation-by-parts operators and variable coefficients
TL;DR: New formulations are proposed, allowing the creation of discretisations using generalSBP operators that are both conservative and stable, and several shortcomings that might be attributed to generalised SBP operators are overcome.
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
A Flux Reconstruction Approach to High-Order Schemes Including Discontinuous Galerkin Methods
Journal ArticleDOI
Review of summation-by-parts schemes for initial–boundary-value problems
Magnus Svärd,Jan Nordström +1 more
TL;DR: This paper will review the development of high order accurate multi-block finite difference schemes, point out the main contributions and speculate about the next lines of research in this area.
Journal ArticleDOI
A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids
Zhi J. Wang,Haiyang Gao +1 more
TL;DR: In an attempt to extend the high-order formulation for 1D conservation laws to other element types such as triangular, tetrahedral or prismatic elements, the idea of ''flux reconstruction'' is generalized into a ''lifting collocation penalty'' approach.
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Review of summation-by-parts schemes for initial–boundary-value problems
Magnus Svärd,Jan Nordström +1 more