Numerical entropy generation is studied in the case of steady, subsonic Euler flow along a kinked solid wall. For a standard upwind finite volume discretization the numerical entropy error, a component of the global discretization 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 truncation error on a kinked grid. Although this error also appears to be zeroth-order in the neighbourhood of the kink, it probably does not cause the zeroth-order entropy 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 this likely singularity is unknown. Therefore the construction of a computational method which uses a priori knowledge about the singularity is not possible. Finally it is shown by numerical experiments that the subsonic Euler flow along a kinked wall still can be computed with vanishing entropy errors by using an appropriate sequence of continuously curved walls which converge to the kinked wall in the limit of zero mesh width.
|Journal||International Journal for Numerical Methods in Fluids|
|Publication status||Published - 1991|
Maarel, van der, E., & Koren, B. (1991). Spurious, zeroth-order entropy generation along a kinked wall. International Journal for Numerical Methods in Fluids, 13(9), 1112-1129. https://doi.org/10.1002/fld.1650130904