Conservative smoothing on an adaptive quadrilateral grid

The Lax-Wendroff scheme can be freed of spurious oscillations by introducing conservative smoothing. In this paper the approach is first tested in 1-D modeling equations and then extended to multidimensional flows by the finite volume method. The scheme is discretized by a space-splitting method on an adaptive quadrilateral grid. The artificial viscosity coefficients in the conservative smoothing step are specially designed to capture slipstreams and vortices, Algorithms are programmed using a vectorizable data structure, under which not only the flow solver but also the adaptation procedure is well vectorized, The good resolution and high efficiency of the approach are demonstrated in calculating both unsteady and steady compressible flows with either weak or strong shock waves, (C) 1999 Academic Press.