In this article the weakly compressible two-phase diffuse interface method (DIM) for the simulation of complex two-dimensional non-hydrostatic free surface flows proposed by Dumbser in is extended to three-dimensional
unstructured tetrahedral
meshes. As in the 2D case, a reduced version of the Baer-Nunziato model for compressible multiphase flows is used. The physical model is closed by the Tait equation of state for water and can be implemented easily into existing compressible codes based on high resolution shock capturing
finite volume schemes. Since the proposed model is fully three-dimensional, it includes the fluid accelerations in gravity direction and hence does not assume a hydrostatic pressure distribution, like the classical shallow water equations. Furthermore, the 3D two-phase model can naturally deal also with
breaking waves. To solve the system of conservation laws of mass and momentum coupled with the non-
conservative evolution equation of the fluid
volume fraction, a high order
path-
conservative one-step WENO
finite volume scheme is applied, together with a new generalized Osher-type Riemann solver at the element interfaces. The accurate Riemann solver in combination with a high order
finite volume approach leads to a simple but sharp resolution of the free surface.
A thorough comparison of experimental reference data with the computational results obtained for a large set of three-dimensional test cases shows the suitability of the present approach for the accurate simulation of complex three-dimensional free surface flows. The use of a compressible flow model allows the method to simulate both, low speed and high speed free surface flow problems, which makes the approach applicable to a very wide class of environmental and industrial free surface flow problems.