Scale-selective Time Integration for Long-Wave Linear Acoustics

Stefan Vater; Rupert Klein; Omar M. Knio

doi:10.1007/978-3-642-20671-9_81

Scale-selective Time Integration for Long-Wave Linear Acoustics

Stefan Vater^*, Rupert Klein, Omar M. Knio

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

In this note, we present a new method for the numerical integration of one dimensional linear acoustics with long time steps. It is based on a scale-wise decomposition of the data using standard multigrid ideas and a scale-dependent blending of basic time integrators with different principal features. This enables us to accurately compute balanced solutions with slowly varying short-wave source terms. At the same time, the method effectively filters freely propagating compressible short-wave modes. The selection of the basic time integrators is guided by their discrete-dispersion relation. Furthermore, the ability of the schemes to reproduce balanced solutions is shortly investigated. The method is meant to be used in semi-implicit finite volume methods for weakly compressible flows.

Original language	English (US)
Pages (from-to)	771-779
Number of pages	9
Journal	Springer Proceedings in Mathematics
Volume	4
DOIs	https://doi.org/10.1007/978-3-642-20671-9_81
State	Published - 2011
Externally published	Yes

Keywords

balanced modes
implicit time discretization
large time steps
linear acoustics
multiscale time integration

ASJC Scopus subject areas

General Mathematics
Statistics, Probability and Uncertainty

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10.1007/978-3-642-20671-9_81

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abstract = "In this note, we present a new method for the numerical integration of one dimensional linear acoustics with long time steps. It is based on a scale-wise decomposition of the data using standard multigrid ideas and a scale-dependent blending of basic time integrators with different principal features. This enables us to accurately compute balanced solutions with slowly varying short-wave source terms. At the same time, the method effectively filters freely propagating compressible short-wave modes. The selection of the basic time integrators is guided by their discrete-dispersion relation. Furthermore, the ability of the schemes to reproduce balanced solutions is shortly investigated. The method is meant to be used in semi-implicit finite volume methods for weakly compressible flows.",

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T1 - Scale-selective Time Integration for Long-Wave Linear Acoustics

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AU - Klein, Rupert

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AB - In this note, we present a new method for the numerical integration of one dimensional linear acoustics with long time steps. It is based on a scale-wise decomposition of the data using standard multigrid ideas and a scale-dependent blending of basic time integrators with different principal features. This enables us to accurately compute balanced solutions with slowly varying short-wave source terms. At the same time, the method effectively filters freely propagating compressible short-wave modes. The selection of the basic time integrators is guided by their discrete-dispersion relation. Furthermore, the ability of the schemes to reproduce balanced solutions is shortly investigated. The method is meant to be used in semi-implicit finite volume methods for weakly compressible flows.

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JO - Springer Proceedings in Mathematics

JF - Springer Proceedings in Mathematics

ER -

Scale-selective Time Integration for Long-Wave Linear Acoustics

Abstract

Keywords

ASJC Scopus subject areas

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