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A provably stable a...
A provably stable and high-order accurate finite difference approximation for the incompressible boundary layer equations
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- Nchupang, Mojalefa P. (författare)
- University of Cape Town, South Africa
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- Malan, Arnaud G. (författare)
- University of Cape Town, South Africa
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- Laurén, Fredrik, 1990- (författare)
- Linköpings universitet,Tillämpad matematik,Tekniska fakulteten
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- Nordström, Jan, 1953- (författare)
- Linköpings universitet,Tekniska fakulteten,Tillämpad matematik,University of Johannesburg, South Africa
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(creator_code:org_t)
- PERGAMON-ELSEVIER SCIENCE LTD, 2023
- 2023
- Engelska.
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Ingår i: Computers & Fluids. - : PERGAMON-ELSEVIER SCIENCE LTD. - 0045-7930 .- 1879-0747. ; 267
- Relaterad länk:
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https://doi.org/10.1...
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https://liu.diva-por... (primary) (Raw object)
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- In this article we develop a high order accurate method to solve the incompressible boundary layer equations in a provably stable manner. We first derive continuous energy estimates, and then proceed to the discrete setting. We formulate the discrete approximation using high-order finite difference methods on summation-by-parts form and implement the boundary conditions weakly using the simultaneous approximation term method. By applying the discrete energy method and imitating the continuous analysis, the discrete estimate that resembles the continuous counterpart is obtained proving stability. We also show that these newly derived boundary conditions removes the singularities associated with the null-space of the nonlinear discrete spatial operator. Numerical experiments that verifies the high-order accuracy of the scheme and coincides with the theoretical results are presented. The numerical results are compared with the well-known Blasius similarity solution as well as that resulting from the solution of the incompressible Navier–Stokes equations.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Incompressible Navier–Stokes equationsBoundary layer equationsHigh order methods; Summation-by-parts; Boundary conditions; Simultaneous approximation terms
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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