A multi-dimensional extension of the preprocessing approach for cell-centered finite volume scheme

A multi-dimensional extension of preprocessing approach (MUSCL) is formulated for solving the two dimensional Euler equations (1) to reduce the possible grid dependence of the conventional dimensionally splitting schemes and (2) to construct a truely multi-dimensional, uniformly higher order accurate cell-centered finite volume scheme. Numerical experiments are carried out to see these aspects of the present formulation. The third order scheme, as is expected, gives the best result comparing with the other second order schemes in capturing moving discontinuities.