Technical Report of National Aerospace Laboratory. Detail of the Leith Type Third-211 Order of Upwind Scheme and Application to Viscous Incompressible Unbounded Flows 211 for Re greater than or less than 1000

摘要

In this paper, the authors give a detailed description of the Leith type three-211u001eorder upwind finite difference schemes-indispensable to compute numerical 211u001esolutions of incompressible unbounded flows for Re greater than or equal to 211u001e1,000. To test the effectiveness of this scheme, the authors define three 211u001eproblems: the backward-facing step, the blunt based body and the rectangular 211u001ecylinder obstacle; give a detailed description of finite difference 211u001eapproximations of initial conditions, boundary conditions and sharp corners for 211u001eeach problem; and give a detailed description of finite difference approximations 211u001efor the four investigated open boundary conditions. The results of numerical 211u001eexperiments showed that this scheme is stable and accurate as was expected, and 211u001ealso that there are large differences among four open boundary conditions in 211u001eflows in the domain near the open boundary, when the problem becomes more 211u001ecomplicated.