By J. F Clarke
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Extra resources for The Dynamics of Real Gases
1 Figure 11 histories. 8000 Comparison of convergence N umerical Results Subsonic and Transonic Inviscid Flow Tests An invscid subsonic flow about a four-element airfoil of Suddhoo and Hall  is first considered as a representative test problem, since an exact solution of the incompressible potential flow is given. Figure 8 shows the partial view of computational points distributed over the flow field using the local mesh refinement method of a Cartesian grid. The whole computational domain is a square with a length of 32 chord lengths.
15) and d(m) E (0,0,0,2,0,2,' .. ) . 8. 17) Dirichlet boundary conditions are given at the boundaries, so that following stream line function 'IjJ of a irrotational ftow about a circular cylinder is obtained. 'IjJ = U=y (1- 21 2) . 18) The first grid convergence study is done for five structured grids which are generated with sequential mesh refinement. Figure 4 shows the coarsest grid. The coarsest grids consists of 16 x 5 points and the finest grid consists of 256 x 65 points, respectively. Numerical solutions of the Laplace equations are obtained using a GMRES method [6J.
Figure 6 shows the coarsest grid for this experiment. The coarsest grid consists of 80 points, while the finest unstructured grid consists of 16,640 points. The L 2 errors obtained on the five grids are plot ted as a function of normalized mean point spacing in Figure 7. Two series of numerical data for the sequential evaluating method and the di1'ect evaluating method are plotted in the figure. Even for the numerical test on the unstructured grids, both gridless evaluating methods are effectively second order accurate.