PARABOLIC NUMERICAL-METHOD FOR INVESTIGATING FREE-SURFACE FLOWS

Although one-dimensional analysis is a classical, accepted method used extensively in the literature and has been commonly used for the comp arison with approximation methods for the solution of free surface flo ws, the requirement to specify the skin friction coefficient value has always been a constraint with which previous investigators have had t rouble. The alternative method of solving the full Navier-Stokes equat ions requires substantial computer time because of the iteration neces sary to resolve the location of the free surface boundary. A relativel y simple parabolic numerical method for the thin-layer equations in tw o dimensions to solve the free surface flows without the need of assum ing the skin friction coefficient and the need of iterating the free s urface boundary is the purpose of this investigation. An order-of-magn itude analysis is used to reduce the elliptic governing Navier-Stokes equations to a parabolized set for high Reynolds numbers. The resultin g equations are discretized and solved numerically for different sub a nd supercritical flows, various Pr, Fr, and Re numbers and for many di fferent thermal boundary conditions using an implicit marching method employing the tridiagonal algorithm.