Large eddy simulation using P2P1 finite element formulation

A finite element code based on P2P1 tetra element has been developed for the Large Eddy Simulation (LES) of turbulent flows around a complex geometry. Fractional 4-step algorithm is employed to obtain time accurate solution since it is less expensive than the integrated formulation, in which the velocity and pressure fields are solved at the same time. Crank-Nicolson method is used for second order temporal discretization and Galerkin method is adopted for spatial discretization. For very high Reynolds number flows, which would require a formidable number of nodes to resolve the flow field, SUPG(Streamline Upwind Petrov-Galerkin) method is applied to the quadratic interpolation function for velocity variables. Nothing that the calculation of intrinsic time scale is very complicated when using SUPG for quadratic tetra element of velocity variables, the present study uses a unique intrinsic time scale proposed by Codina et al. since it makes the present three-dimensional unstructured code much simpler in terms of implementing SUPG. In order to see the effect of numerical diffusion caused by using an upwind scheme(SUPG), those obtained from P2P1 Galerkin method and P2P1 Petrov-Galerkin approach are compared for the flow around a sphere at some Reynolds number. Smagorinsky model is adopted as sub grid scale models in the context of P2P1 finite element method. As a benchmark problem for code validation, turbulent flows around a sphere and a MIRA model have been studied at various Reynolds numbers