# MULTIGRID SOLUTION OF STEADY EULER EQUATIONS BASED ON POLYNOMIAL FLUXDIFFERENCE SPLITTING

MULTIGRID SOLUTION OF STEADY EULER EQUATIONS BASED ON POLYNOMIAL FLUXDIFFERENCE SPLITTING A fluxdifference splitting based on the polynomial character of the flux vectors is applied to steady Euler equations, discretized with a vertexcentred finite volume method. In first order accurate form, a discrete set of equations is obtained which is both conservative and positive. Due to the positivity, the set of equations can be solved by collective relaxation methods in multigrid form. A full multigrid method based on successive relaxation, full weighting, bilinear interpolation and Wcycle is used. Second order accuracy is obtained by the ChakravarthyOsher fluxextrapolation technique, using the RoeChakravarthy minmod limiter. In second order form, direct relaxation of the discrete equations is no longer possible due to the loss of positivity. A defectcorrection is used in order to solve the second order system. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png International Journal of Numerical Methods for Heat & Fluid Flow Emerald Publishing

# MULTIGRID SOLUTION OF STEADY EULER EQUATIONS BASED ON POLYNOMIAL FLUXDIFFERENCE SPLITTING

, Volume 1 (1): 12 – Jan 1, 1991
12 pages

Publisher
Emerald Publishing
ISSN
0961-5539
DOI
10.1108/eb017473
Publisher site
See Article on Publisher Site

### Abstract

A fluxdifference splitting based on the polynomial character of the flux vectors is applied to steady Euler equations, discretized with a vertexcentred finite volume method. In first order accurate form, a discrete set of equations is obtained which is both conservative and positive. Due to the positivity, the set of equations can be solved by collective relaxation methods in multigrid form. A full multigrid method based on successive relaxation, full weighting, bilinear interpolation and Wcycle is used. Second order accuracy is obtained by the ChakravarthyOsher fluxextrapolation technique, using the RoeChakravarthy minmod limiter. In second order form, direct relaxation of the discrete equations is no longer possible due to the loss of positivity. A defectcorrection is used in order to solve the second order system.

### Journal

International Journal of Numerical Methods for Heat & Fluid FlowEmerald Publishing

Published: Jan 1, 1991

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