a Pressure-Based Finite-Volume Time-Stepping Algorithm for the Numerical Simulation of Incompressible Flows
A novel pressure-based algorithm for obtaining computational solutions to the incompressible form of the Navier-Stokes equations is presented. A significant aspect of this technique is that it is based upon the regular grid variable arrangement whereby all flow variables are defined at the center of a computational cell. This is shown to be more desirable than classical staggered grid formulations for large-scale three-dimensional computations. Mathematical considerations for such algorithms including the well-known checkerboard numerical instability are discussed and the related work in this area is summarized for the first time. A code based on the new formulation is implemented and benchmark examples in two- and three-dimensions are examined to evaluate its accuracy and stability. The cases encompass a range of geometric complexities and the results for each case are found to be acceptable when compared to published data. As a result, the contribution is a method for handling the limiting case of zero Mach number as part of a unified regular grid solver for all flows governed by the general Navier-Stokes equations.
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- Engineering: Aerospace; Physics: Fluid and Plasma; Mathematics