An upwind finite volume method for incompressible inviscid free surface flows

• An upwind finite volume method has been developed for free surface flows.
• The Euler equations and the level set equation were combined into a system equation.
• Artificial compressibility method was applied in this study.
• The re-initialization method based on non-Cartesian grids has been developed.

An upwind finite volume method on curvilinear grids has been developed to simulate two-dimensional, inviscid, incompressible free surface flows. In this method, the level set method is used to capture the interface. The level set equation and the flow governing equations (Euler equations) are not solved separately, but incorporated into a system equation. The artificial compressibility method is adopted to solve the resulting hyperbolic equations. The MUSCL-Roe scheme, which is widely used in compressible flow computations, is employed to discretize the convective terms. A fully implicit dual-time stepping method with a highly efficient LU-SSOR algorithm as sub-iteration scheme is applied to advance the solution in time. In the present study, a re-initialization method on curvilinear grids for level set function is presented. An example of re-initialization for level set function on curvilinear grids is demonstrated and the resulting level set function is in good agreement with the exact distance function. Numerical results of a sloshing tank problem and a broken dam problem agree well with the theoretical and experimental data, respectively. The free surface flow over a submerged hydrofoil is also simulated using overset grids to demonstrate the capability of dealing with complex geometry. At last, the simulation of droplet splash problem is performed to show the ability of the present method in handling topological changes of the free surface.