Development of pressure-based composite multigrid methods for complex fluid flows

Abstract

Progress in the development of a multiblock, multigrid algorithm, and a critical assessment of the κ-ε two-equation turbulent model for solving fluid flows in complex geometries is presented. The basic methodology employed is a unified pressure-based method for both incompressible and compressible flows, along with a TVD-based controlled variation scheme (CVS), which uses a second-order flux estimation bounded by flux limiters.Performance of the CVS is assessed in terms of its accuracy and convergence properties for laminar and turbulent recirculating flows as well as compressible flows containing shocks. Several other conventional schemes are also employed, including the first-order upwind, central difference, hybrid, second-order upwind and QUICK schemes. For better control over grid quality and to obtain accurate solutions for complex flow domains, a multiblock procedure is desirable and often a must.Here, a a composite grid algorithm utilizing patched (abutting) grids is discussed and a conservative flux treatment for interfaces between blocks is presented.A full approximation storage-full multigrid (FAS-FMG) algorithm that is incorporated in the flow solver for increasing the efficiency of the computation is also described. For turbulent flows, implementation of the κ-ε two-equation model and in particular the wall functions at solid boundaries is also detailed.In addition, different modifications to the basic k-e model, which take the non-equilibrium between the production and dissipation of κ and ε and rotational effects into account, have also been assessed.Selected test cases are used to demonstrate the robustness of the solver in terms of the convection schemes, the multiblock interface treatment, the multigrid speedup and the turbulence models.