ITERATIVE METHODS IN SOLVING NAVIER-STOKES EQUATIONS BY THE BOUNDARY ELEMENT METHOD

Abstract

The solution of Navier–Stokes equations of time-dependent incompressible viscous fluid flow in planar geometry by the Boundary Domain Integral Method (BDIM) is discussed. The introduction of a subdomain technique to fluid flow problems is considered and improved in order to maintain the stability of BDIM. To avoid problems with flow kinematics computation in the sudomain mesh, a segmentation technique is proposed which combines the original BDIM with its subdomain variant and preserves its numerical stability. In order to reduce the computational cost of BDIM, which greatly depends on the solution of systems of linear equations, iterative methods are used. Conjugate gradient methods, conjugate gradients squared and an improved version of the biconjugate gradient method BiCGSTAB, together with the generalized minimal residual method, are used as iterative solvers. Different types of preconditioning, from simple Jacobi to incomplete LU factorization, are carried out and the performance of chosen iterative methods and preconditioners are reported. Test examples include backward facing step flow and flow through tubular heat exchangers. Test computation results show that BDIM is an accurate approximation technique which, together with the subdomain technique and powerful iterative solvers, can exhibit some significant savings in storage and CPU time requirements.