Abstract
The present paper deals with the finite element analysis of two-dimensional two-layer density flows in a gravitational field. A fluid in each layer is replaced with a large number of discrete particles, and the motion and deformation of each layer is represented by moving those particles in a Lagrangian manner. The velocity distribution in the whole fluid region is given as the finite element solution of the Navier-Stokes equations and the equation of continuity. In the finite element calculation, free-slip conditions are used on solid wall boundaries because no-slip conditions may cause sticking of some particles to walls. Then, a new technique for the implementation of free-slip conditions on arbitrary curved boundaries is presented. As numerical examples, density flows in a rectangular closed container and Rayleigh-Taylor instability in the container with a circular cross-section have been computed.
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