Journal ArticleDOI
Generalized conservative approximations of split convective derivative operators
TLDR
A strategy to design locally conservative finite-difference approximations of convective derivatives for shock-free compressible flows with arbitrary order of accuracy that can be applied as a building block of low-dissipative, hybrid shock-capturing methods.About:
This article is published in Journal of Computational Physics.The article was published on 2010-09-01. It has received 222 citations till now. The article focuses on the topics: Numerical stability & Euler equations.read more
Citations
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Journal ArticleDOI
Numerical Methods for High-Speed Flows
TL;DR: In this paper, the authors review numerical methods for direct numerical simulation (DNS) and large-eddy simulation (LES) of turbulent compressible flow in the presence of shock waves.
Journal ArticleDOI
Split form nodal discontinuous Galerkin schemes with summation-by-parts property for the compressible Euler equations
TL;DR: It is shown that besides the construction of entropy stable high-order schemes, a careful choice of subcell finite volume fluxes generates split formulations of quadratic or cubic terms, which are able to generate, in a systematic way, all common split forms of the compressible Euler advection terms.
Journal Article
Turbulence in supersonic boundary layers at moderate Reynolds number
TL;DR: In this paper, the organization of turbulence in supersonic boundary layers through large-scale direct numerical simulations (DNS) at, and momentum-thickness Reynolds number up to (corresponding to ) was studied.
Journal ArticleDOI
Turbulence in supersonic boundary layers at moderate Reynolds number
TL;DR: In this paper, the organization of turbulence in supersonic boundary layers through large-scale direct numerical simulations (DNS) at, and momentum-thickness Reynolds number up to (corresponding to ) was studied.
Journal ArticleDOI
Discretely conservative finite-difference formulations for nonlinear conservation laws in split form: Theory and boundary conditions
TL;DR: In this article, the Lax-Wendroff theorem states that conservation law equations that are split into linear combinations of the divergence and product rule form and then discretized using any diagonal-norm skew-symmetric summation-by-parts spatial operator yield discrete operators that are conservative.
References
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Journal ArticleDOI
Compact finite difference schemes with spectral-like resolution
TL;DR: In this article, the authors present finite-difference schemes for the evaluation of first-order, second-order and higher-order derivatives yield improved representation of a range of scales and may be used on nonuniform meshes.
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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
Boundary conditions for direct simulations of compressible viscous flows
TL;DR: In this article, a boundary condition formulation for the Navier-Stokes equations is proposed, which is compatible with non-disjoint algorithms applicable to direct simulations of turbulent flows.
Journal ArticleDOI
Systems of conservation laws
Peter D. Lax,Burton Wendroff +1 more
TL;DR: In this article, a wide class of difference equations is described for approximating discontinuous time dependent solutions, with prescribed initial data, of hyperbolic systems of nonlinear conservation laws, and the best ones are determined, i.e., those which have the smallest truncation error and in which the discontinuities are confined to a narrow band of 2-3 meshpoints.
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Dispersion-relation-preserving finite difference schemes for computational acoustics
TL;DR: In this article, a set of radiation and outflow boundary conditions compatible with the DRP schemes is constructed, and a sequence of numerical simulations is conducted to test the effectiveness of the time-marching dispersion-relation-preserving (DRP) schemes.