Nonlinear hyperbolic conservation laws with source terms: errors of the shock location

Klingenstein, Petra

doi:10.3929/ethz-a-001772763

1997

DOI: 10.3929/ethz-a-001772763

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Nonlinear hyperbolic conservation laws with source terms: errors of the shock location

Petra Klingenstein¹

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1999

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Error estimators for the position of discontinuities in hyperbolic conservation laws with source terms which are solved using operator splitting

Jeltsch

Klingenstein

1999

Computing and Visualization in Science

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When computing numerical solutions of hyperbolic conservation laws with source terms, one may obtain spurious solutions | these are unphysical solutions that only occur in numerics such a s s h o c k w aves moving with wrong speeds, cf. 7], 2], 1], 10], 3]. Therefore it is important to know h o w errors of the location of a discontinuity can be controlled.To d e r i v e appropriate error-estimates and to use them to control such errors, is the aim of our investigations in this paper. We restrict our considerations t o numerical solutions which are computed by using a splitting method. In splitting methods, the homogeneous conservation law and an ordinary di erential equation (modelling the source term) are solved separately in each t i m e s t e p .Firstly, w e d e r i v e error-estimates for the scalar Riemann problem. The analysis shows that the local error of the location of a discontinuity mainly consists of two parts. The rst part is introduced by the splitting and the second part is due to smearing of the discontinuity.Next, these error-estimates are used to construct an adaptation of the step size so that the error of the location of the discontinuity remains su ciently small. The adaptation is applied to several examples, which are a scalar problem, a simpli ed combustion model, and the one-dimensional i n viscid reacting compressible Euler equations. All the examples show that the adaptation based on the derived error-estimates works well.The theory can also be extended to planar two-dimensional problems.

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Error estimators for the position of discontinuities in hyperbolic conservation laws with source terms which are solved using operator splitting

Jeltsch

Klingenstein

1999

Computing and Visualization in Science

View full text Add to dashboard Cite

show abstract

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Nonlinear hyperbolic conservation laws with source terms: errors of the shock location

Cited by 1 publication

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Error estimators for the position of discontinuities in hyperbolic conservation laws with source terms which are solved using operator splitting

Error estimators for the position of discontinuities in hyperbolic conservation laws with source terms which are solved using operator splitting

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