Application of local mesh refinement in the DSMC method

The implementation of an adaptive mesh embedding (h-refinement) schemes using unstructured grid in two-dimensional Direct Simulation Monte Carlo (DSMC) method is reported. In this technique, local isotropic refinement is used to introduce new meshes where local cell Knudsen number is less than some preset value. This simple scheme, however, has several severe consequences affecting the performance of the DSMC method. Thus, we have applied a technique to remove the hanging mode, by introducing anisotropic refinement in the interfacial cells. This is completed by simply connect the hanging node(s) with the other non-hanging node(s) in the non-refined, interfacial cells. In contrast, this remedy increases negligible amount of work; however, it removes all the difficulties presented in the first scheme with hanging nodes. We have tested the proposed scheme for Argon gas using different types of mesh, such as triangular and quadrilateral or mixed, to high-speed driven cavity flow. The results show an improved flow resolution as compared with that of unadaptive mesh. Finally, we have triangular adaptive mesh to compute two near-continuum gas flows, including a supersonic flow over a cylinder and a supersonic flow over a 35° compression ramp. The results show fairly good agreement with previous studies. In summary, the computational penalties by the proposed adaptive schemes are found to be small as compared with the DSMC computation itself. Nevertheless, we have concluded that the proposed scheme is superior to the original unadaptive scheme considering the accuracy of the solution.