A nonlinear mathematical model with a free moving boundary was introduced to study viscous flow in stenotic elastic tubes subject to a prescribed external pressure at the tube wall and pulsatile pressure drop between the tube inlet and outlet. An iterative numerical method using boundary iteration, pseudocompressibility, and the ADI technique was developed to solve the model. Unsteady effects o...

We propose a simple numerical method for calculating both unsteady and steady state solution of hyperbolic system with geometrical source terms having concentrations. Physical problems under consideration include the shallow water equations with topography, and the quasi one-dimensional nozzle flows. We use the interface value, rather than the cell-averages, for the source terms, which results ...

This paper presents an adjoint method for the optimal control of unsteady flows. The goal is to develop the continuous and discrete unsteady adjoint equations and their corresponding boundary conditions for the time accurate method. First, this paper presents the complete formulation of the time dependent optimal design problem. Second, we present the time accurate unsteady continuous and discr...