A block iterative nodal integral method for fluid dynamics problems

An efficient block iterative scheme for the nodal integral method discretization of fluid dynamics problems has been developed, implemented and tested. Starting from the time-dependent Navier-Stokes equations, the approach introduced by Azmy and Dorning, and extended by Wilson, et al. is used to develop a computationally efficient method that is very accurate when coarse meshes and large time steps are used. The final nonlinear discrete-variable equations are solved using a Newton-Raphson procedure. Since the matrix that is to be inverted is comprised of overlapping blocks along the diagonal, an extension of a scheme by Radicati and Robert has been developed resulting in a Jacobi/Seidal-like iterative scheme to invert the Jacobian matrix within the Newton-Raphson framework. The dramatically reduced memory requirements of this iterative scheme makes possible on workstations and even PCs fluid dynamics calculations that previously required mainframes and supercomputers. The iterative method is discussed, and the effectiveness of the overall method based on it is illustrated by results for the solution of the time-dependent versions of the driven-cavity problem and the double-glazing problem in both two and three dimensions. (orig.)