MFCAV近似Riemann解法器在相容拉氏方法中的熵条件分析

ENTROPY ANALYSIS OF MFCAV RIEMANN SOLVER FOR A COMPATIBLE LAGRANGIAN METHOD

对基于MFCAV(Multi Fluid Channel on Averaged Volume)近似Riemann解法器的相容拉氏方法的熵条件进行了分析.结果表明与满足声学形式Riemann解法器的熵不同,前者只能在每个网格边界左、右两侧网格的熵随时间变化的和保证大于零,即能保证整体熵增,但不保证传统意义上的在每个网格中的熵增;而后者不仅保证整体熵增,而且还满足传统意义上的熵增.因此MFCAV的熵增相对声学形式解法器而言要弱一些,由此表明其熵增可能要小些,使得格式的耗散可能要小些.数值算例也验证了分析的正确性.

An entropy analysis of MFCAV（Multi Fluid Channel on Averaged Volume） Riemann solver for a compatible Lagrangian method is shown. The analysis indicates that the entropy of MFCAV Riemann solver is different from that of the acoustics Riemann solver. The entropy of the former does not increase in every cell but only increases on every cell edge, so that the global entropy increases; but the entropy of the latter not only increases in every cell but also increase on every cell edge, then the global entropy increase still maintain. So that the entropy increase of MFCAV may be less than that of acoustic Riemann solver in weak sense, and this indicates that MFCAV may produce less dissipation than the acoustic solver. The numerical examples show the validitv of the analysis.