The high-order methods is difficultly applied in various elements. The development of a 3D solver by using the spectral difference method of unstructured grids via mixed elements is presented. A mixed tri-prism and tetrahedral grid is firstly refined using one-level h-refinement to generate a hexahedral grid while keeping the curvature of wall boundaries. The SD method designed for hexahedral elements can subsequently be applied for refining the unstructured grid. Through a series of numerical tests, the present method is high-order accurate for both inviscid and viscous flows is demonstrated; the results obtained for inviscid and viscous compressible flows compare well with other published results.
Some Serrin type blow‐up criteria for the three‐dimensional viscous compressible flows with large external potential force