the solution of laminar incompressible flow equation with free surfaces in curvilinear coordinates

in this paper a novel numerical approach is presented for solving the transient incompressible fluid flow problems with free surfaces in generalized two-dimensional curvilinear coordinate systems. solution algorithm is a combination of implicit real-time steps and explicit pseudo-time steps. governing fluid flow equations are discretized using a collocated finite-volume mesh. convective terms are approximated with an accurate monotonicity preserving upwind scheme. free surfaces are first approximated by lines of constant slope and then convected using the volume-of-fluid (vof) technique. a number of problems, both with and without free surfaces, have been solved to demonstrate the ease and usefulness of the scheme. accuracy of the results thus obtained is assessed by comparison with other numerical as well as analytical results in the literature.