Pipe-Entrance Flow Simulation Using Multigrid Finite Volume

Wensheng Shen

Email: wensheng@csr.uky.edu
Postal address: 700 Woodland Ave., A308, Lexington, KY 40508

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.