Pipe-Entrance Flow Simulation Using Multigrid Finite Volume

Wensheng Shen, Jun Zhang, and Jie Wang
Laboratory for High Performance Scientific Computing and Computer Simulation
Department of Computer Science
University of Kentucky
Lexington, KY 40506-0046, USA

Fuqian Yang
Department of Chemical and Materials Engineering
University of Kentucky
Lexington, KY 40506-0046, USA

Abstract

This paper describes a multigrid finite volume method and its application to pipe-entrance flow simulation for both laminar and turbulent situations. The incompressible Navier-Stokes equation is used for the laminar pipe flow and the two-equation $k - \omega$ model is applied for turbulent simulation. The solver is written in boundary-fitted non-orthogonal coordinates and based on unsteady-state equations, where temporary terms are discretized by the fully implicit second order Euler method. Multigrid V-cycle algorithm is used to solve the Poisson equation for fast solution, which allows for non-uniform grid spacing and any level of grids. An incomplete lower-upper decomposition (ILU) type of method is used as the smoother for the multigrid procedure.

Key words: Multigrid, Finite volume, Navier-Stokes equation, Pipe-entrance flow, Incompressible flow, Implicit solver, Iterative method.

Mathematics Subject Classification: