Numerical Techniques For Free Surface Problems In Viscous Incompressible And Porous Flows

Three free surface problems have been investigated. The first two involve incompressible flows and the last one involves porous flow. These problems are solved numerically by finite difference technique. In each problem the original physical domain with a free surface is transformed into a rectangular domain and then the appropriate finite difference schemes are used in the new transformed domain to carry out the computation.;In the first problem the attenuation of a large amplitude standing capillary-gravity wave is considered. A finite difference scheme similar to the Crank-Nicolson scheme is developed to handle the equation of the free surface. Convergent numerical results are obtained for Reynolds number up to 200.;In the second problem a side-driven cavity problem with a free surface on the top is considered. When of the side wall moves vertically at a constant speed the profile of the free surface and the flow field in the cavity are calculated numerically. Various techniques such as the slip condition at the contact points of the free surface etc. are employed to enhance convergence of the numerical procedure. Results are obtained for Reynolds number up to 100.;In the third problem the position of the free surface is calculated numerically for a porous slab which is partially filled with a liquid and differently heated from its sides. Results for this fully developed porous flow are obtained for Rayleigh number up to 1000