Volume 4 (2010) Issue 2 Pages 121-135
Numerical solutions for large scale models face the problem of poor convergence and for non-stationary problems the situation becomes worse. To speed up the convergence, an algorithm to perform the Balancing Domain Decomposition (BDD) preconditioning for non-stationary incompressible flow problems is constructed. The problem caused by the presence of nonlinear convection term in the non-stationary Navier-Stokes equations, which complicates the solving of the equations numerically, is solved by a characteristic-curve method. The method is advantageous as it renders the matrix for linear equations symmetric, thus enabling the Conjugate Gradient (CG) method to be used to solve the interface problem of the Domain Decomposition Method (DDM). The related algorithms are all implemented in parallel by the Hierarchical Domain Decomposition Method (HDDM) and the program has the capability of solving non-stationary problems with up to 10 million degrees of freedom (DOF). The BDD algorithm together with characteristic-curve method is applied to a benchmark problem, a three-dimensional driven cavity flow model, and the results are compared with available solutions.