一种新的LU型隐式格式及其应用

发展了一种新的ＬＵ型隐式格式。新格式除包含ＬＵ－ＳＧＳ格式全部特色外，尽管采用了相似变换而不是近似处理来精确地构造通量矢量的迎风Ｊａｃｏｂｉａｎ矩阵，仍可避免块对角矩阵求逆．且左端项仍可保持矢量化处理。新格式显示出更快的收敛性和更高的稳定性且没有多余的数值耗散和自由参数，尤其适用于求解三维非定常流动问题。

A NEW LU-TYPE IMPLICIT SCHEME AND ITS APPLICATIONS

A new implicit scheme based on the LU-SGS scheme in conjunction with diagonalization and Cramer's rule (LUSGS-DC) has been developed for solving the compressibleNavier-Stokes equations. The new implicit scheme not only contains all features of theLU-SGS scheme, but also displays distinctive advantages. Although similarity transformations are used to construct upwind Jacobian matrices of the flux vectors, the block diagonalmatrix inversions are still eliminated, the left hand side operator can be completely vectorized too. Because the true Jacobian matrices are used, the new implicit scheme leadsto much faster convergency and higher stabilization without improper numerical dissipationand free-parameters. The new implicit scheme is especially suited for solving the unsteadythree dimensional flows.