Efficient multilevel restriction–prolongation expressions for hybrid finite volume element method

Abstract

A multigrid acceleration technique is suitably extended to solve the 2D incompressible Navier–Stokes equations using a fully implicit hybrid finite volume element method. As is known, the convergence of classical relaxation techniques performs an initial rapid decrease of residuals followed by a slower rate of decrease. This means that a relaxation procedure is efficient for eliminating only the high frequency components of the residuals. This problem can be overcome using a multigrid method. There are different restriction and prolongation operators to establish a multigrid procedure. An efficient operator is suitably extended in this work. It provides data during refining and coarsening stages using modified bilinear finite element interpolators. The extended formulations are then examined by solving a thermobuoyant flow problem, and the effects of using mid cell-face values in the extended restriction and prolongation operators are measured. The results indicate that the current formulation effectively improves the performance of the original fully implicit solver.

Keywords:

• multigrid
• restriction
• prolongation
• finite volume
• finite element
• upwinding