Stable and Accurate Artificial Dissipation

Journal of Computational Physics

2014

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In this paper we derive new farfield boundary conditions for the time-dependent Navier-Stokes and Euler equations in two space dimensions. The new boundary conditions are derived by simultaneously considering well-posedess of both the primal and dual problems. We moreover require that the boundary conditions for the primal and dual Navier-Stokes equations converge to well-posed boundary conditions for the primal and dual Euler equations.We perform computations with a high-order finite difference scheme on summationby-parts form with the new boundary conditions imposed weakly by the simultaneous approximation term. We prove that the scheme is both energy stable and dual consistent and show numerically that both linear and non-linear integral functionals become superconvergent.

Section: Numerical Resultsmentioning

confidence: 87%

“…The SBP-SAT technique has been extended to include curvilinear coordinate transforms [32,42], multi-block couplings [6,31,7,34,23,28], artificial dissipation operators [26,8], and has been applied to numerous applications where it has proven to be robust. See for example [44,25,14,16].…”

Section: Introductionmentioning

confidence: 99%

Duality based boundary conditions and dual consistent finite difference discretizations of the Navier–Stokes and Euler equations

Berg

Journal of Computational Physics

2014

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“…3 converge from the left side implying strict stability. For a discussion on how to build artificial dissipation operators for SBP operators without losing accuracy and stability, see [9].…”

Section: The Spectrummentioning

confidence: 99%

Well-Posedness, Stability and Conservation for a Discontinuous Interface Problem: An Initial Investigation

Cognata

Lecture Notes in Computational Science and Engineering

2015

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A robust interface treatment for the discontinuous coefficient advection equation satisfying time-independent jump conditions is presented. The aim of the investigation is to show how the different concepts like well-posedness, conservation and stability are related. The equations are discretized using high order finite difference methods on Summation By Parts (SBP) form. The interface conditions are weakly imposed using the Simultaneous Approximation Term (SAT) procedure. Spectral analysis and numerical simulations corroborate the theoretical findings.

“…It uses summation-byparts operators and imposes boundary and interface conditions weakly as described in Carpenter et al (1999), , Nordström & Carpenter (2001), Mattsson et al (2004), Svärd et al (2007), Svärd & Nordström (2008) and Nordström et al (2009). The code runs with 2,3,4 and 5th order global accuracy.…”

Section: Numerical Calculationsmentioning

confidence: 99%

Energy decay of vortices in viscous fluids: an applied mathematics view

Lönn

2012

J. Fluid Mech.

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The energy decay of vortices in viscous fluids governed by the compressible NavierStokes equations is investigated. It is shown that the main reason for the slow decay is that zero eigenvalues exist in the matrix related to the dissipative terms. The theoretical analysis is purely mathematical and based on the energy method. To check the validity of the theoretical result in practice, numerical solutions to the Navier-Stokes equations are computed using a stable high order finite difference method. The numerical computations corroborate the theoretical conclusion.