Towards very high-order accurate schemes for unsteady convection problems on unstructured meshes

R. Abgrall; N. Andrianov; M. Mezine

doi:10.1002/fld.870

Towards very high-order accurate schemes for unsteady convection problems on unstructured meshes

R. Abgrall, N. Andrianov, M. Mezine

Research output: Contribution to journal › Conference article in journal › peer-review

14 Citations (Scopus)

Abstract

We construct several high-order residual-distribution methods for two-dimensional unsteady scalar advection on triangular unstructured meshes. For the first class of methods, we interpolate the solution in the space-time element. We start by calculating the first-order node residuals, then we calculate the high-order cell residual, and modify the first-order residuals to obtain high accuracy. For the second class of methods, we interpolate the solution in space only, and use high-order finite difference approximation for the time derivative. In doing so, we arrive at a multistep residual-distribution scheme. We illustrate the performance of both methods on several standard test problems.

Original language	English
Pages (from-to)	679-691
Number of pages	13
Journal	International Journal for Numerical Methods in Fluids
Volume	47
Issue number	8-9
DOIs	https://doi.org/10.1002/fld.870
Publication status	Published - 20 Mar 2005
Externally published	Yes
Event	8th ICFD Conference on Numerical Methods for Fluid Dynamics - Oxford, United Kingdom Duration: 29 Mar 2004 → 1 Apr 2004 Conference number: 8

Keywords

Fluctuation splitting schemes
Hyperbolic problems
Residual-distribution schemes
Unstructured meshes

Programme Area

Programme Area 1: Data

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10.1002/fld.870

Cite this

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title = "Towards very high-order accurate schemes for unsteady convection problems on unstructured meshes",

abstract = "We construct several high-order residual-distribution methods for two-dimensional unsteady scalar advection on triangular unstructured meshes. For the first class of methods, we interpolate the solution in the space-time element. We start by calculating the first-order node residuals, then we calculate the high-order cell residual, and modify the first-order residuals to obtain high accuracy. For the second class of methods, we interpolate the solution in space only, and use high-order finite difference approximation for the time derivative. In doing so, we arrive at a multistep residual-distribution scheme. We illustrate the performance of both methods on several standard test problems.",

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journal = "International Journal for Numerical Methods in Fluids",

issn = "0271-2091",

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TY - JOUR

T1 - Towards very high-order accurate schemes for unsteady convection problems on unstructured meshes

AU - Abgrall, R.

AU - Andrianov, N.

AU - Mezine, M.

N1 - Conference code: 8

PY - 2005/3/20

Y1 - 2005/3/20

N2 - We construct several high-order residual-distribution methods for two-dimensional unsteady scalar advection on triangular unstructured meshes. For the first class of methods, we interpolate the solution in the space-time element. We start by calculating the first-order node residuals, then we calculate the high-order cell residual, and modify the first-order residuals to obtain high accuracy. For the second class of methods, we interpolate the solution in space only, and use high-order finite difference approximation for the time derivative. In doing so, we arrive at a multistep residual-distribution scheme. We illustrate the performance of both methods on several standard test problems.

AB - We construct several high-order residual-distribution methods for two-dimensional unsteady scalar advection on triangular unstructured meshes. For the first class of methods, we interpolate the solution in the space-time element. We start by calculating the first-order node residuals, then we calculate the high-order cell residual, and modify the first-order residuals to obtain high accuracy. For the second class of methods, we interpolate the solution in space only, and use high-order finite difference approximation for the time derivative. In doing so, we arrive at a multistep residual-distribution scheme. We illustrate the performance of both methods on several standard test problems.

KW - Fluctuation splitting schemes

KW - Hyperbolic problems

KW - Residual-distribution schemes

KW - Unstructured meshes

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U2 - 10.1002/fld.870

DO - 10.1002/fld.870

M3 - Conference article in journal

AN - SCOPUS:15744362263

SN - 0271-2091

VL - 47

SP - 679

EP - 691

JO - International Journal for Numerical Methods in Fluids

JF - International Journal for Numerical Methods in Fluids

IS - 8-9

T2 - 8th ICFD Conference on Numerical Methods for Fluid Dynamics

Y2 - 29 March 2004 through 1 April 2004

ER -

Towards very high-order accurate schemes for unsteady convection problems on unstructured meshes

Abstract

Keywords

Programme Area

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