A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy
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In this paper, the authors derived stable and accurate interface conditions based on the SAT penalty method for the linear advection?diffusion equation, which are functionally independent of the spatial order of accuracy and rely only on the form of the discrete operator.About:
This article is published in Journal of Computational Physics.The article was published on 1999-01-20 and is currently open access. It has received 525 citations till now. The article focuses on the topics: Order of accuracy & Boundary value problem.read more
Citations
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Computational aeroacoustics: progress on nonlinear problems of sound generation
Tim Colonius,Sanjiva K. Lele +1 more
TL;DR: A hierarchy of computational approaches that range from semi-empirical schemes that estimate the noise sources using mean-flow and turbulence statistics, to high-fidelity unsteady flow simulations that resolve the sound generation process by direct application of the fundamental conservation principles is discussed in this paper.
Journal ArticleDOI
Pade-Type Higher-Order Boundary Filters for the Navier-Stokes Equations
TL;DR: In this article, the use of procedures based on higher-order finite-difference formulas is extended to solve complex fluid-dynamic problems on highly curvilinear discretizations and with multidomain approaches.
Journal ArticleDOI
Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble
Emile Touber,Neil D. Sandham +1 more
TL;DR: In this paper, a large-eddy simulation of the interaction between an impinging oblique shock and a Mach 2.3 turbulent boundary layer is presented, which does not introduce any energetic low frequencies into the domain, hence avoiding possible interference with the shock/boundary layer interaction system.
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.
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Summation by parts operators for finite difference approximations of second derivatives
Ken Mattsson,Jan Nordström +1 more
TL;DR: In this article, a finite difference operator approximating second derivatives and satisfying a summation by parts rule was derived for the fourth, sixth and eighth order case by using the symbolic mathematics software Maple.
References
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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.
Journal ArticleDOI
Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes
TL;DR: In this paper, a method for constructing boundary conditions (numerical and physical) of the required accuracy for compact (Pade-like) high-order finite-difference schemes for hyperbolic systems is presented.
Journal ArticleDOI
Summation by parts for finite difference approximations for d/dx
TL;DR: In this article, the authors presented a multi-parameter family of difference operators when τ⩾3, where τ is the dimension of the difference operator and λ is the number of points in the difference matrix.
Journal ArticleDOI
A conservative staggered-grid chebyshev multidomain method for compressible flows
David A. Kopriva,John H. Kolias +1 more
TL;DR: A new multidomain spectral collocation method that uses a staggered grid for the solution of compressible flow problems that is conservative, free-stream preserving, and exponentially accurate.
Book ChapterDOI
Finite Element and Finite Difference Methods for Hyperbolic Partial Differential Equations
Heinz-Otto Kreiss,Godela Scherer +1 more
TL;DR: In this paper, the authors define finite element and finite difference methods for hyperbolic partial differential equations and show that the resulting procedures are automatically stable and there is extreme flexibility in choosing the basic functions, therefore, in very complicated domains or for problems with complicated interfaces, the method is the only feasible one.
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