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A multi-domain summ...
A multi-domain summation by-parts formulation for complex geometries
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- Lundquist, Tomas, 1986- (författare)
- Linköpings universitet,Tillämpad matematik,Tekniska fakulteten
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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,Department of Mathematics and Applied Mathematics, University of Johannesburg, South Africa
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(creator_code:org_t)
- Linköping : Linköping University Electronic Press, 2021
- Engelska 11 s.
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Serie: LiTH-MAT-R, 0348-2960 ; LiTH-MAT-R--2021/05--SE
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Abstract
Ämnesord
Stäng
- We combine existing discretization methods to obtain a simplified numerical formulation of partial derivative equations posed on multi-block/element domains. The interfaces (conforming or non-conforming) between blocks are treated with inner-product-preserving interpolation operators. The result is a single set of high-order multi-block summation-by-parts operators that encapsulates both the metric terms and the interface treatments. This enables for a clean description of the numerical scheme that mimics the essential features of its continuous counterpart. Furthermore, the stability analysis on a multi-block domain is simplified both for linear and nonlinear equations, since no problem-specific interface conditions must be derived and implemented. The theoretical developments are valid for all discretization methods that are included in the summation-by-parts framework. We exemplify the combined operator technique by considering a nonlinearly stable discrete formulation of the incompressible Navier-Stokes equations and perform calculations on an underlying multiblock domain.
Ämnesord
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Nyckelord
- Summation-by-parts; Multi-block operators; Partial derivative approximations; Nonlinear stability
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