A Cartesian ghost-cell multigrid Poisson solver for incompressible flows

Ma, ZH, Qian, L, Causon, DM, Gu, HB and Mingham, CG (2010) A Cartesian ghost-cell multigrid Poisson solver for incompressible flows. International Journal for Numerical Methods in Engineering, 85 (2). pp. 230-246. ISSN 0029-5981

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Abstract

In this paper, a simple Cartesian ghost-cell multigrid Poisson solver is proposed for simulating incompressible fluid flows. The flow field is discretized efficiently on a rectangular mesh, in which solid bodies are immersed. A small number of ghost mesh cells and their symmetric image cells are distributed in the vicinity of the solid boundary. With the aid of the ghost and image cells, the Dirichlet and Neumann boundary conditions can be implemented effectively. Chorin's fractional-step projection method is adopted for the coupling of velocity and pressure for the solution of the Navier-Stokes equations. Point-wise Gauss-Seidel iteration is used to solve the pressure Poisson equation. To speed up the convergence of the solution to the corresponding linear system, sub-level coarse meshes embedded with ghost and image cells are also introduced and operated in a sequential V-cycle. Several test cases including the classical ideal incompressible flow around a cylinder, a lid-driven cavity flow and viscous flow past a fixed/rotating cylinder are presented to demonstrate the accuracy and efficiency of the current approach. © 2010 John Wiley & Sons, Ltd.