2012/09/25 by Omer San, Anne Staples, Anne E. Staples · 39 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Numerical Methods in Computational Mathematics #Algorithm #Applied mathematics #Cartesian coordinate system #Computational Fluid Dynamics and Aerodynamics #Computational science #Computer science #Curvilinear coordinates #Dykstra's projection algorithm #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Geometry #Grid #Incompressible flow #Interpolation (computer graphics) #Mathematical analysis #Mathematical optimization #Mathematics #Poisson's equation #Projection (relational algebra) #Projection method #Regular grid #Solver #Stencil #physics.flu-dyn
paper · pdf · doi:10.1016/j.jcp.2012.09.005
published in Journal of Computational Physics 233, 480-508 (Elsevier BV)
openalex publication_date 2012/09/25 · arxiv created 2012/12/05 · arxiv updated 2013/10/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present a coarse-grid projection (CGP) method for accelerating incompressible flow computations, which is applicable to methods involving Poisson equations as incompressibility constraints. The CGP methodology is a modular approach that facilitates data transfer with simple interpolations and uses black-box solvers for the Poisson and advection-diffusion equations in the flow solver. After solving the Poisson equation on a coarsened grid, an interpolation scheme is used to obtain the fine data for subsequent time stepping on the full grid. A particular version of the method is applied here to the vorticity-stream function, primitive variable, and vorticity-velocity formulations of incompressible Navier-Stokes equations. We compute several benchmark flow problems on two-dimensional Cartesian and non-Cartesian grids, as well as a three-dimensional flow problem. The method is found to accelerate these computations while retaining a level of accuracy close to that of the fine resolution field, which is significantly better than the accuracy obtained for a similar computation performed solely using a coarse grid. A linear acceleration rate is obtained for all the cases we consider due to the linear-cost elliptic Poisson solver used, with reduction factors in computational time between 2 and 42. The computational savings are larger when a suboptimal Poisson solver is used. We also find that the computational savings increase with increasing distortion ratio on non-Cartesian grids, making the CGP method a useful tool for accelerating generalized curvilinear incompressible flow solvers.