A flux‐difference splitting based on the polynomial character of the flux vectors is applied to steady Euler equations, discretized with a vertex‐centred 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 W‐cycle is used. Second order accuracy is obtained by the Chakravarthy‐Osher flux‐extrapolation technique, using the Roe‐Chakravarthy minmod limiter. In second order form, direct relaxation of the discrete equations is no longer possible due to the loss of positivity. A defect‐correction is used in order to solve the second order system.
DICK, E. (1991), "MULTIGRID SOLUTION OF STEADY EULER EQUATIONS BASED ON POLYNOMIAL FLUX‐DIFFERENCE SPLITTING", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 1 No. 1, pp. 51-62. https://doi.org/10.1108/eb017473
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