Incompressible Navier–Stokes method with general hybrid meshes

Abstract

A new incompressible Navier–Stokes numerical method is presented, capable of utilizing general hybrid meshes containing all four types of three-dimensional elements: hexahedra, prisms, tetrahedra, and pyramids. It is an artificial compressibility type of method using dual time stepping for time accuracy. The presented algorithms for (i) spatial discretization, (ii) time integration, and (iii) parallel implementation are transparent to the different types of elements. Further, the presence of grid interfaces between the multiple types of elements does not deteriorate accuracy of the solution. Efficient evaluation of the viscous terms is addressed via a special technique that avoids multiple spatial integration of the same edge of the mesh. An upwind spatial discretization, and a central scheme with two different formulations of the artificial dissipation operator are tested with the general hybrid meshes. Use of local blocks of hexahedra is evaluated in terms of accuracy and efficiency via simulations of high Reynolds number flows. Finally, the developed methods are implemented in parallel using partitioned general hybrid meshes and an efficient parallel communication scheme to minimize CPU time.