Preliminary Developments of a Two-Fluid Cartesian-Grid Explicit Finite-Volume Model for Marine Applications

Abstract

An explicit Finite Volume method for solving hydrodynamic flows is presented in this paper. These developments are based on an explicit cell-centered scheme solving the compressible fluid equations in a pseudo-compressible strategy where second-order accuracy is provided by using a MUSCL scheme together with various limiters for the hyperbolic part. In this recent model, boundaries are handled through a Cut-Cell method, so that solids as well as fluid interfaces are explicitly moved in a non-diffusive way, ensuring local mass conservation within fluids. An improved cut-cell algorithm based on the Voxel traversal algorithm coupled with a local Floodfill Scanline has been developed, in order to handle boundaries of arbitrary geometrical complexity. To cope with small cells instability problems near the boundaries, a fully conservative merging method is implemented. In this paper, this solver is validated on 2-D hydrodynamic test cases, such as flows past obstacles. Test cases involving large body movement are then performed and discussed. The latter test cases are performed both in the frame of the body and in a fixed frame where the body is moving across the grid. Then, a two-fluid formulation is introduced in the model and described in detail in the present paper. First validations of this two-fluid formulation are eventually presented.