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Accuracy of Stable,...
Accuracy of Stable, High-order Finite Difference Methods for Hyperbolic Systems with Non-smooth Wave Speeds
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- Erickson, Brittany A. (författare)
- Department of Computer and Information Science 1202, University of Oregon, Eugene, USA / Department of Earth Science 1272 University of Oregon, Eugene, USA
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- O’Reilly, Ossian (författare)
- Southern California Earthquake Center, University of Southern California, Los Angeles, USA
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- Nordström, Jan, 1953- (författare)
- Linköpings universitet,Beräkningsmatematik,Tekniska fakulteten
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(creator_code:org_t)
- 2019-11-11
- 2019
- Engelska.
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Ingår i: Journal of Scientific Computing. - : Springer-Verlag New York. - 0885-7474 .- 1573-7691. ; 81:3, s. 2356-2387
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Abstract
Ämnesord
Stäng
- We derive analytic solutions to the scalar and vector advection equation with variable coefficients in one spatial dimension using Laplace transform methods. These solutions are used to investigate how accuracy and stability are influenced by the presence of discontinuous wave speeds when applying high-order-accurate, skew-symmetric finite difference methods designed for smooth wave speeds. The methods satisfy a summation-by-parts rule with weak enforcement of boundary conditions and formal order of accuracy equal to 2, 3, 4 and 5. We study accuracy, stability and convergence rates for linear wave speeds that are (a) constant, (b) non-constant but smooth, (c) continuous with a discontinuous derivative, and (d) constant with a jump discontinuity. Cases (a) and (b) correspond to smooth wave speeds and yield stable schemes and theoretical convergence rates. Non-smooth wave speeds [cases (c) and (d)], however, reveal reductions in theoretical convergence rates and in the latter case, the presence of an instability.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
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- ref (ämneskategori)
- art (ämneskategori)
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