Weak Versus Strong No-Slip Boundary Conditions for the Navier-Stokes Equations

Abbas, Qaisar; Nordström, Jan

doi:10.1080/19942060.2010.11015297

Cited by 16 publications

(18 citation statements)

References 10 publications

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“…If we let β, ψ → 0 we recover the standard no-slip boundary conditions which have the energy estimate ||w|| 2 t ≤ 0. Compared to the Robin boundary conditions (13), the no-slip boundary conditions are less damping than if we keep α, β, φ and ψ non-zero.…”

Section: Continuous Casementioning

confidence: 99%

“…Assume that g 1,2 = 0. If we restrict ourselves to the case where β, ψ = 0 and insert (13) into (12) we obtain the energy estimate…”

Section: Continuous Casementioning

confidence: 99%

“…Together the SBP and SAT technique provide a tool for creating stable approximations for well-posed initial-boundary value problems. The relation between weak and strong boundary conditions in terms of accuracy is discussed in [13].…”

Section: Introductionmentioning

confidence: 99%

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Stable Robin solid wall boundary conditions for the Navier–Stokes equations

Berg

Nordström

2011

Journal of Computational Physics

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In this paper we prove stability of Robin solid wall boundary conditions for the compressible Navier-Stokes equations. Applications include the no-slip boundary conditions with prescribed temperature or temperature gradient and the first order slip-flow boundary conditions. The formulation is uniform and the transitions between different boundary conditions are done by a change of parameters. We give different sharp energy estimates depending on the choice of parameters.The discretization is done using finite differences on Summation-By-Parts form with weak boundary conditions using the Simultaneous Approximation Term. We verify convergence by the method of manufactured solutions and show computations of flows ranging from no-slip to almost full slip.

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Section: Continuous Casementioning

confidence: 99%

“…Assume that g 1,2 = 0. If we restrict ourselves to the case where β, ψ = 0 and insert (13) into (12) we obtain the energy estimate…”

Section: Continuous Casementioning

confidence: 99%

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Stable Robin solid wall boundary conditions for the Navier–Stokes equations

Berg

Nordström

2011

Journal of Computational Physics

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“…The SAT technique (weak imposition of boundary condition or penalty technique) is normally applied only at one grid point (as in the example above) [2,3,22,23,31,36,37,44,46]. However, in some cases, it is possible to impose the weak boundary conditions at multiple grid points.…”

Section: Introductionmentioning

confidence: 99%

“…(A boundary condition at x=0 is necessary for stability, and it will be imposed below.) For more details using this technique, see [2,7,8,31,42].…”

Section: Introductionmentioning

confidence: 99%

A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain

Nordström

Abbas

Erickson

et al. 2014

Commun. comput. phys.

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Abstract.A new weak boundary procedure for hyperbolic problems is presented. We consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that technique. The new boundary procedure is applied near boundaries in an extended domain where data is known. We show how to raise the order of accuracy of the scheme, how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the boundaries. The new boundary procedure is cheap, easy to implement and suitable for all numerical methods, not only finite difference methods, that employ weak boundary conditions. Numerical results that corroborate the analysis are presented.

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Finite volume discretization of heat equation and compressible Navier–Stokes equations with weak Dirichlet boundary condition on triangular grids

Chandrashekar

2016

Int J Adv Eng Sci Appl Math

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A vertex-based finite volume method for Laplace operator on triangular grids is proposed in which Dirichlet boundary conditions are implemented weakly. The scheme satisfies a summation-by-parts (SBP) property including boundary conditions which can be used to prove energy stability of the scheme for the heat equation. A Nitsche-type penalty term is proposed which gives improved accuracy. The scheme exhibits second order convergence in numerical experiments. For the compressible Navier-Stokes equations we construct a finite volume scheme in which Dirichlet boundary conditions on the velocity and temperature are applied in a weak manner. Using the centered kinetic energy preserving flux, the scheme is shown to be consistent with the global kinetic energy equation. The SBP discretization of viscous and heat conduction terms together with penalty terms are combined with upwind fluxes in a Godunov-MUSCL scheme. Numerical results on some standard test cases for compressible flows are given to demonstrate the performance of the scheme.

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Weak Versus Strong No-Slip Boundary Conditions for the Navier-Stokes Equations

Cited by 16 publications

References 10 publications

Stable Robin solid wall boundary conditions for the Navier–Stokes equations

Stable Robin solid wall boundary conditions for the Navier–Stokes equations

A Flexible Boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain

Finite volume discretization of heat equation and compressible Navier–Stokes equations with weak Dirichlet boundary condition on triangular grids

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