Numerical Simulation of the Stokes Wave for the Flow around a Ship Hull Coupled with the VOF Model

The surface wave generated by flow around a ship hull moving near free surface of water is simulated numerically in this study. The three-dimensional implicit finite volume method （FVM） is applied to solve Reynolds averaged Navier-Stokes （RANS） equation. The realizable k-e turbulence model has been implemented to capture turbulent flow around the ship hull in the free surface zone. The volume of fluid （VOF） method coupled with the Stokes wave theory has been used to determine the free surface effect of water. By using is a six degrees of freedom model, the ship hull＇s movement is numerically solved with the Stokes wave together. Under the action of Stokes waves on the sea, the interface between the air and water waves at the same regular pattem and so does the pressure and the vertical velocity. The ship hull moves in the same way as the wave. The amplitude of the ship hull＇s heave is less than the wave height because of the viscosity damping. This method could provide an important reference for the study of ships＇ movement, wave and hydrodynamics.

Kinetic Energy Preserving and Entropy Stable Finite Volume Schemes for Compressible Euler and Navier-Stokes Equations

Centered numerical fluxes can be constructed for compressible Euler equations which preserve kinetic energy in the semi-discrete finite volume scheme.The essential feature is that the momentum flux should be of the form ■ are any consistent approximations to the pressure and the mass flux.This scheme thus leaves most terms in the numerical flux unspecified and various authors have used simple averaging.Here we enforce approximate or exact entropy consistency which leads to a unique choice of all the terms in the numerical fluxes.As a consequence novel entropy conservative flux that also preserves kinetic energy for the semi-discrete finite volume scheme has been proposed.These fluxes are centered and some dissipation has to be added if shocks are present or if the mesh is coarse.We construct scalar artificial dissipation terms which are kinetic energy stable and satisfy approximate/exact entropy condition.Secondly,we use entropy-variable based matrix dissipation flux which leads to kinetic energy and entropy stable schemes.These schemes are shown to be free of entropy violating solutions unlike the original Roe scheme.For hypersonic flows a blended scheme is proposed which gives carbuncle free solutions for blunt body flows.Numerical results for Euler and Navier-Stokes equations are presented to demonstrate the performance of the different schemes.

APPLICATION OF FDS SCHEME TO 2D DEPTH-AVERAGED FLOW-POLLUTANTS SIMULATION

A Fulx Difference Splitting (FDS) scheme was used in a 2D depth-averagedflow-pollutant model. Within the framework of the Finite Volume Method (FVM) a 2D simulation wastransferred into solving a series of local ID problems based on the rotational invariance propertyof the flux. The FDS scheme was employed to estimate the normal numerical flux of variablesincluding water mass, momentum and pollutant concentration across the interface between cells. Thescheme was checked with exact solutions and verified by observations in the Nantong reach of theYangtze River. Calculated results well match both exact solutions and observations.