Numerical Simulations of Flow Around a Bluff Body, Using Multigrid and an Immersed Boundary Method

Abstract

Increase in computational efficiency is one of the most prominent factors for successful applications of large CFD models with many grid points. Consequences of the increase are reduction in CPU-time and memory usage, so better mesh refinement could be used. Hence, the CFD-solver will improve the resolution in the computational domain.

This report provides an introduction to the background theory in CFD with basis on methods used to develop a simple incompressible Navier Stokes solver. Different multigrid algorithms and an immersed boundary method are discussed, where the solver exploit the cause of increased computational efficiency, especially by using multigrid. Validation is done based on efficiency and accuracy for the multigrid algorithms compared to Gauss Seidel method and SOR method. Force calculations around a submerged bluff cylinder in a 2D flow are used to validate the immersed boundary method implemented in the solver together with a full multigrid algorithm.

By implementing a full multigrid method, the time used to solve the Poisson equation was reduced significantly and the accuracy of the resolution is kept. The validation tests of a solver combining an immersed boundary method and the full multigrid algorithm was successfully carried out except for too low coefficients at Re = 100 in the final test case. The accuracy of flow resolution was specially affected by the time refinement and the width of the computational domain.