Low-order finite element preconditioner for spectral element pressure solver in Navier-Stokes equations

High-order spectral element methods (SEM) while very accurate for computational fluid dynamics (CFD) simulations can be prohibitively expensive for meshes with difficult geometries. Controlling the number of iterations in the pressure solver can significantly reduce the computing time of CFD applications. A low-order finite element (FEM) operator collocated on the Gauss-Lobatto-Legendre (GLL) points in the SEM discretization is proposed as preconditioner. Three different versions of the preconditioner based on combinations of the low-order stiffness and mass matrices are tested for 2D and 3D geometries. When building the preconditioning operators a new meshing approach that allows elements to overlap and need not fill out the volume of the mesh are explored and proven to be better than traditional schemes. With these preconditioners a bound on the number of iterations is attained regardless of mesh geometry or polynomial degree used. This novel meshing strategy achieves a reduction up to 30% in the number of iterations compared to the best current schemes without increasing the computational cost of the preconditioners, and it also overcomes the shortcommings of other well known preconditioners such as the hybrid Schwarz preconditioner