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Summation by parts operators for finite difference approximations of second derivatives
Finite difference operators approximating second derivatives and satisfying a summation by parts rule have been derived for the fourth, sixth and eighth order case by using the symbolic mathematicsExpand
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A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy
Stable and accurate interface conditions based on the SAT penalty method are derived for the linear advection?diffusion equation. The conditions are functionally independent of the spatial order ofExpand
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On the order of accuracy for difference approximations of initial-boundary value problems
TLDR
Finite difference approximations of the second derivative in space appearing in, parabolic, incompletely parabolic systems of, and 2nd-order hyperbolic partial differential equations can be closed with two orders less accuracy at the boundary without reducing the global order of accuracy. Expand
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A stable high-order finite difference scheme for the compressible Navier-Stokes equations: No-slip wall boundary conditions
TLDR
A stable wall boundary procedure is derived for the discretized compressible Navier-Stokes equations using high-order accurate finite difference summation-by-parts. Expand
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A stable high-order finite difference scheme for the compressible Navier-Stokes equations, far-field boundary conditions
TLDR
We construct a stable high-order finite difference scheme for the compressible Navier-Stokes equations, that satisfy an energy estimate. Expand
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Summation-by-parts in time
TLDR
The new time-integration method is global, high order accurate, unconditionally stable and together with the approximation in space, it generates optimally sharp fully discrete energy estimates. Expand
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Review of summation-by-parts schemes for initial-boundary-value problems
TLDR
In this paper we will review this development, point out the main contributions and speculate about the next lines of research in this area. Expand
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Stable and Accurate Artificial Dissipation
TLDR
In this paper we present dissipation operators that preserve both stability and accuracy for high order finite difference approximations of initial boundary value problems. Expand
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A Roadmap to Well Posed and Stable Problems in Computational Physics
  • J. Nordström
  • Mathematics, Computer Science
  • J. Sci. Comput.
  • 1 April 2017
TLDR
We show that the continuous analysis of well posed boundary conditions implemented with weak boundary procedures together with schemes on Summation-by-parts (SBP) form automatically leads to stability. Expand
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The Fringe Region Technique and the Fourier Method Used in the Direct Numerical Simulation of Spatially Evolving Viscous Flows
TLDR
We show that the primary importance of the fringe region technique is to damp out the deviation associated with large scales in the direction normal to the wall. Expand
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