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Fully discrete ener...
Fully discrete energy stable high order finite difference methods for hyperbolic problems in deforming domains
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- Nikkar, Samira (författare)
- Linköpings universitet,Beräkningsmatematik,Tekniska högskolan
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- Nordström, Jan (författare)
- Linköpings universitet,Beräkningsmatematik,Tekniska högskolan
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(creator_code:org_t)
- Elsevier, 2015
- 2015
- Engelska.
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Ingår i: Journal of Computational Physics. - : Elsevier. - 0021-9991 .- 1090-2716. ; 291, s. 82-98
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Abstract
Ämnesord
Stäng
- A time-dependent coordinate transformation of a constant coefficient hyperbolic system of equations which results in a variable coefficient system of equations is considered. By applying the energy method, well-posed boundary conditions for the continuous problem are derived. Summation-by-Parts (SBP) operators for the space and time discretization, together with a weak imposition of boundary and initial conditions using Simultaneously Approximation Terms (SATs) lead to a provable fully-discrete energy-stable conservative finite difference scheme. We show how to construct a time-dependent SAT formulation that automatically imposes boundary conditions, when and where they are required. We also prove that a uniform flow field is preserved, i.e. the Numerical Geometric Conservation Law (NGCL) holds automatically by using SBP-SAT in time and space. The developed technique is illustrated by considering an application using the linearized Euler equations: the sound generated by moving boundaries. Numerical calculations corroborate the stability and accuracy of the new fully discrete approximations.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Deforming domain; Initial boundary value problems; High order accuracy; Well-posed boundary conditions; Summation-by-parts operators; Stability; Convergence; Conservation; Numerical geometric conservation law; Euler equation; Sound propagation
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