A level set formulation for the numerical simulation of impact of surge fronts

In this paper we present a level set-based algorithm for the solution of incompressible two-phase flow problems. The technique is applied to the numerical simulation of impact of two surge fronts resulting from the collapse of liquid columns. The incompressible Navier-Stokes equations are solved using a projection method based on forward Euler time-stepping. The Hamilton-Jacobi type equation for the transport of level set function is carried out by a high resolution fifth-order accurate WENO scheme. For efficient implementation of the WENO scheme we have proposed grid staggering for the level set function. The solution of the pressure Poisson equation is obtained using an efficient preconditioned conjugate gradient method. It is shown that the present formulation works very well for large density and viscosity ratios. For the purpose of validation, we have simulated small-amplitude free sloshing of liquid in a container and the well-known two-dimensional broken-dam problem of Martin and Moyce. Simulations of impact of surge fronts have been carried out and the results are discussed.