✍ Scribed by Oleg P. Iliev; Mikhail M. Makarov
No coin nor oath required. For personal study only.
An algorithm for coupled solving 2D Navier-Stokes equations in the stream function ~-vorticity oJ variables is presented. Lid driven cavity flow is computed as a test example. Implicit difference schemes on uniform grids are used for discretizing the unsteady Navier-Stokes equations. An iterative method, similar to the BLOCK-ORTHOMIN(K) method, is used for solving a block-matrix set of linear algebraic equations at each time step. The non-symmetric block is reversed on each block-iteration by using approximate factorization--ORTHOMIN(1) iterative method. The difference Laplace operator is reversed by means of a direct method. The comparison of the results, provided by coupled solving Navier-Stokes equations with those provided by decoupled (consecutive) solving the equations for oJ and ~b, demonstrates the advantages of the suggested computing technique.
📜 SIMILAR VOLUMES
The performance of three iterative methods, local SOR, preconditioned generalized conjugate gradient methods such as ORTHOMIN( 1) and the GCG-LS method with preconditioning matrices derived by incomplete (modified and unmodified) pointwise factorizations of the matrix corresponding to implicit finit
## Abstract An iterative method for numerically solving the time independent Navier–Stokes equations for viscous compressible flows is presented. The method is based upon partial application of the Gauss–Seidel principle in block form to the systems of the non‐linear algebraic equations which arise