Computation of Nonlinear Turbulent Free Surface Flows Using the Parallel UNCLE Code

A numerical approach is presented in this work suitable for the computation of nonlinear free surface flows over complex geometries such as ship hulls in a fast, reliable and robust manner. The governing equations solved are the incompressible Reynolds Averaged Navier-Stokes (RANS) equations coupled with the free surface kinematic condition and a two equation turbulence model. Simple no normal-gradient dynamic boundary conditions are used at the free surface. The governing equations are cast with respect to an unsteady (non-inertial) general curvilinear coordinate system. The numerical approach uses the modified artificial compressibility formulation. The governing equations are discretized using a finite volume approach where the numerical fluxes at cell interfaces are obtained using Roe's inviscid flux averages coupled with van Leer's MUSCL formulation for higher order flux extrapolation. Viscous fluxes are averaged using central differencing. Time is discretized implicitly using the first order Euler backward differencing. The resulting non-linear algebraic equations are solved using the discretized Newton-relaxation (DNR) approach with symmetrical Gauss-Seidel sweeps. To speed up the solution process a parallel implementation of the numerical algorithm that uses MPI for message passing is used. In order to accelerate the solution convergence process, a multilevel approach coupled with the traditional multigrid approach is taken. The resulting algorithm has been applied to various ship geometries and comparisons with the sequential code solutions and experimental results are presented. The results show that the parallel version of the free surface UNCLE (UNsteady Computation of fieLd Equations) code accurately reproduces these earlier results.