A gradient smoothing method (GSM) for fluid dynamics problems
A novel gradient smoothing method (GSM) based oil irregular cells and strong form of governing equations is presented for fluid dynamics problems with arbitrary geometries. Upon the analyses about the compactness and the positivity of coefficients of influence of their Stencils for approximating a derivative. four favorable schemes (II, VI, VII and VIII) with second-order accuracy ire selected among the total eight proposed discretization schemes. These four schemes are successively verified and carefully examined in solving Poisson's equations, subjected to changes in the number of nodes. the shapes of cells and the irregularity of triangular Cells, respectively. Numerical results imply us that all the four schemes give very good results: Schemes VI and VIII produce a slightly better accuracy thin) the other two schemes oil irregular cells, but at a hi-her cost in computation. Schemes VII and VIII that consistently rely oil gradient smoothing operations are more accurate than Schemes II and VI in which directional correction is imposed. It is interestingly found that GSM is insensitive to the irregularity of meshes, indicating the robustness of the presented GSM. Among the four schemes of GSM, Scheme VII outperforms the other three schemes, for its outstanding overall performance in terms of numerical accuracy, stability and efficiency. Finally, GSM solutions with Scheme VII to some benchmarked compressible flows including inviscid flow over NACA0012 airfoil, laminar flow over flat plate and turbulent flow over all RAE2822 airfoil are presented. respectively. Copyright (C) 2008 John Wiley & Sons, Ltd.
gsm stencil numerical methods cfd fdm gsd