Computational of the Flow Past the U.S. Navy Combatant DTMB 5415 by a Godunov-Type Scheme

The results presented in this paper for the flow past the DTMB 5415 model has been obtained by a method implemented in Di Mascio et al., devised for flows of naval interest. Such kind of flows are, in general, characterized by very high Reynolds number regimes (typically 10^6-10^7 for towing tank tests and up to 10^9 for full scale problems), complex geometry, and a great variety of physical phenomena like boundary layer thickening and separation, complex vortex structures in the field, evolution and breaking of free surface waves, cavitation, and so on. Such a rich phenomenology imposes very stiff constraints on the development of numerical methods for the simulation of naval problems. On the basis of our previous experiences in this field, Godunov schemes in ENO formulation proved to be effective in terms of stability properties and convergence rate. Since the non-viscous problem for incompressible flows is not described by a hyperbolic system of equations, the Godunov approach can be adopted by following two different paths: by applying it only to the convection terms in the momentum equation, in the framework of the projection method, or by adopting a pseudo-compressible formulation, and then including also the continuity equation and the pressure term in the momentum equation. When only the steady state solution has to be computed, as for the considered test case, the latter approach turns out to be very effective, and therefore is the one adopted in the present paper. In the following, details of the discretization scheme will be given. It will be seen that a second order ENO-type method is adopted for the convective and pressure part in conjunction with a Riemann solver, used for the computation of the fluxes at cell interfaces. The viscous terms are approximated by a centred finite volume scheme. Steady state convergence rate is improved by a standard Full-Multigrid technique, and a Runge-Kutta time integration with local time step is used as relaxation scheme. To assess the convergence properties of the scheme, the 2D flow in a driven cavity will be first examined. Then, the flow past the U.S. Navy Combatant DTMB~5415 will be considered and the results compared with experimental results.