Free surface flow modelling on dynamically refined hexahedral meshes

Abstract

An efficient method for modelling incompressible free surf ace flows is presented. The method unites the projection method for solving the Navier-Stokes equations and the particle level set method for free surface evolution. The method uses adaptively refined hexahedral meshes built on an enhanced octree data structure. Free surface flow simulation has increasingly attracted att ention of the scientific community. It has applications in diverse disciplines, suc h as geophysics, petroleum engineering, biology, etc. The method discussed in this paper is designed for appli- cations in computer graphics. It targets modelling, animating, and controlling vis- cous liquids in a 3D environment. The objectives of practical computer animation impose several partly controver- sial requirements on simulation. It should be efficient enou gh to run various scenar- ios for acceptable time. However, it should retain enough detail to give a realistic behaviour and the possibility of flow control. Direct numeri cal simulation provides the desirable realism, since it is based on accurate simulat ion of physical processes. However, it is computationally expensive and based on the assumption that after set- ting an initial state the fluid is left to flow freely. This appr oach reduces capabilities to control the flow locally and globally. A feasible compromi se between complex- ity, realistic behaviour, and flow control is provided by a co mputational technology which has been developed in the last decade by many researchers (1, 8, 14, 15, 18). In this paper we present our version of the numerical method forming such tech- nology. We do not address the issues of flow control here. We ju st note that this technology opens several possibilities to control the fluid flow (5). The general idea of the method is to use fractional steps in order to unite the projection method for solving the Navier-Stokes equations and the particle level set method for free surface evolution. The computational efficiency of the method is based on two points. First, the pressure projection method is one of the most efficient solvers for the unsteady Navier-Stokes equations (22). Second, the particle level set method is one of the most convenient and efficient approaches in simulation of free surface evolution (18). The framework of fractional steps allows us to combine both approaches and gives additional control over liquid motion.