Explicit MacCormack Scheme for Flows over Objects
Abstract
Most incompressible flow solvers are implicit; large systems of equations are constructed and solved, demanding gobs of memory and special schemes for parallelization. We can evade these difficulties by solving flow problems with explicit finitedifferences on a fixed, uniform grid at each time step. The explicit scheme eliminates the Poisson equation for pressure by relating pressure to density through an artificial equation of state, then updating density with the compressible continuity equation. The explicit scheme requires local information only, smearing the pressure update over several timesteps by introducing a finite speed of sound. This sound speed imposes a constraint on the time step. We find empirically that for moderate Re, the CFL condition applies. In this study, we compute flows around a square block and a circular cylinder for Reynolds numbers up to 1000 using an explicit MacCormack scheme. The Mach number of the flow is kept low to approximate the incompressible limit. We find that a Mach number of 0.05 provides a balance between maximizing the time step and minimizing the deviation from incompressibility. We observed excellent convergence to incompressible values for the block problem. This explicit scheme is perfectly suited for parallelization. We plan to extend the current scheme to simulate particulate flows.
 Publication:

APS Division of Fluid Dynamics Meeting Abstracts
 Pub Date:
 November 2003
 Bibcode:
 2003APS..DFD.MH006P