利用非結構調適網格於直接模擬蒙地卡羅法及其應用

Abstract

本研究完成非結構調適網格(h-refinement)於二維直接模擬蒙地卡羅法(Direct Simulation Monte Carlo Method)之應用。當網格內的Kn 小於標準值時，使用isotropic調適法建立新的網格。然而，這個簡易的方法會有多個重要的因素影響了蒙地卡羅法(DSMC)的表現。因此，我們應用了anisotropic調適法，移除懸掛點(hanging node)。它解決調適網格所會遇到懸掛點(hanging node)的所有困難。同時，這個方法所增加的工作量是可以忽略不計的。我們已然使用以氦氣，不同的網格:三角形的，四邊形的，或是兩者混合的網格，測試高速度cavity流場，和超音流流經一方形障礙物。結果證明，利用調適網格得到較好的改善。最後我們使用三角形的調適網格計算兩個接近連續流流場，經過一圓柱的超音速流和經過一個35度斜板的超音速流。結果證實與先前的研究相當的吻合。總之，利用調適網格計算上的代價遠小於蒙地卡羅法(DSMC)本身。因此，我們得到一個結論，利用調適網格法較原始的非調適網格法有較正確的結果。

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 node, by introducing the anisotropic refinement. 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 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 a high-speed driven cavity flow and, then, a hypersonic flow over a block. The results show an improved flow resolution as compared with that of unadaptive mesh. Finally, we have used triangular adaptive mesh to compute two near-continuum gas flows, including a supersonic flow over a cylinder and a supersonic flow over a flat plate with 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 without hanging node(s) is superior to the original unadaptive scheme considering the accuracy of the solution.