A Finite Difference Method For Computing Unsteady Incompressible Laminar Boundary Layer Flows PDF Download

A finite difference method for computing velocity and temperature profiles of an unsteady, incompressible, laminar boundary layer around a two-dimensional cylinder of arbitrary cross section is developed. Blowing or suction may be present on the wall of the cylinder. The thermal boundary condition at the wall may be either specified wall temperature or specified heat flux at the wall. The governing finite difference equations are explicit, the velocity and the temperature at the next time step can be directly computed in terms of those at the current time step. Various errors associated with the finite difference method are studied. Great effort has been made to derive the stability and convergence conditions of the method. The upper bound of the local rounding errors is estimated. Two examples, one oscillation in Blasius flow and the other impulsive start of wedge flow, are given; the numerical results are compared with the existing analytical and experimental results. It is concluded that the present method can be used for the aforementioned computation with high accuracy except at and near a singular point where the singular errors become significant. (Author).