Numerical entropy generation is studied in the case of steady, subsonic Euler flow along a kinked wall. For a standard upwind finite volume discretization, the numerical entropy error appears to be zeroth-order in mesh size. Two possible causes of the zeroth-order entropy error are studied. First an investigation is made of the local discretization error on a kinked grid. In the neighbourhood of the kink, this error appears to be zeroth-order as well. For supersonic flow it can be easily removed. However, it seems that the zeroth-order entropy error is yet not caused by the zeroth-order discretization error. Next a study is made of the existence of a singularity in the exact solution. Probably, the Euler flow solution is singular at the kink in the wall. The form of the likely singularity is unknown. Therefore, the construction of a computational method which uses a priori knowledge of the singularity is not possible. Finally it is shown by numerical experiment that the subsonic Euler flow along a kinked wall still can be computed with vanishing entropy errors, by using a continuously curved wall which converges to the kinked wall in the limit of zero mesh width.
|Titel||Integration of Theory and Applications in Applied Mechanics : Choice of Papers Presented at the First National Mechanics Congress, 2-4 April 1990, Rolduc, Kerkrade, The Netherlands|
|Redacteuren||J.F. Dijksman, F.T.M. Nieuwstadt|
|Plaats van productie||Dordrecht|
|Uitgeverij||Kluwer Academic Publishers|
|ISBN van geprinte versie||0-7923-0921-9|
|Status||Gepubliceerd - 1990|
|Evenement||conference; First National Mechanics Congress; 1990-04-02; 1990-04-04 - |
Duur: 2 apr 1990 → 4 apr 1990
|Congres||conference; First National Mechanics Congress; 1990-04-02; 1990-04-04|
|Periode||2/04/90 → 4/04/90|
|Ander||First National Mechanics Congress|
Maarel, van der, H. T. M., & Koren, B. (1990). Entropy errors in the numerical approximation of the Euler flow along a kinked wall. In J. F. Dijksman, & F. T. M. Nieuwstadt (editors), Integration of Theory and Applications in Applied Mechanics : Choice of Papers Presented at the First National Mechanics Congress, 2-4 April 1990, Rolduc, Kerkrade, The Netherlands (blz. 315-328). Kluwer Academic Publishers.