Statistics – Computation
Scientific paper
Jun 1985
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1985jcoph..59..232m&link_type=abstract
Journal of Computational Physics (ISSN 0021-9991), vol. 59, June 1985, p. 232-246.
Statistics
Computation
28
Computational Fluid Dynamics, Euler Equations Of Motion, Inviscid Flow, Shock Waves, Spiral Galaxies, Steady Flow, Convergence, Matrices (Mathematics), Steady State, Stellar Gravitation
Scientific paper
In the present application of several implicit integration schemes for the one-dimensional Euler equations with conservative upwind spatial differencing to a steady discontinuous flow problem, the fastest convergence is obtained with the upwind switching that is furnished by van Leer's (1977) differentiable split fluxes; these easily linearize in time. The trapping of the iterations in a limit cycle with Roe's (1980) nondifferentiable split flux-difference also occurs in a second-order scheme with split fluxes, if the matrix coefficients arising in the implicit time-linearization are not properly centered in space. The use of split flux-derived second-order terms degrades solution accuracy, especially if they are subjected to a limiter for the sake of monotonicity's preservation. The best performance is obtained from second-order terms computed on the basis of the characteristic variables.
Mulder Wim A.
van Leer Bram
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