LU-SGS Scheme For Euler Computations On 2-D Unstructured Grids

A method for 2-D Euler Equation computation, which uses implicit LU-SGS approximate factorization scheme after reordering of 2-D unstructured triangle grids, is discussed. A new way for LU-SGS approximate factorization deducing is proposed. The new way can get the same result as the original way on structured grids, but can be wide-scale applied on unstructured grids while the original one can't. The grids reordering brought out here is for cell-centered finite-volume scheme and it leads to vectorial calculation. The reordering for 2-D triangle grids causes imbalance of grids. (It means that for grid i, the ratio of the sum of its neighbors whose number exceed it and that less than it is 1:2 or 2:1.) The possibility and the efficiency for computation under this condition are discussed. The method is applied to several 2-D flow problems and the results are compared with those from the 4-step explicit Runge-Kutta scheme. The comparison demonstrates the method's efficiency and good convergence. The potentiality of this method in viscous calculation is proposed. Unlike many other traditional implicit methods, it requires much less memory and also computes fast.