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使用邊界變異消減(BVD)算法的高階中央-上風沖擊捕獲方案 (CS)

在本文中,我們提出了一種新型的基于邊界變化遞減(BVD)重構的沖擊捕捉的混合非線性顯式緊湊方案。在我們的方法中,我們通過BVD算法結合了一個非耗散的六階中心緊湊插值和一個五階單調性儲存方案(MP5)。對于平穩解,BVD重構選擇了可能的最高階插值,也就是現有方法中的中心,即非耗散,對于不連續的地方,算法選擇了單調性方案。該方法為文獻中現有的自适應上風-中心方案提供了一種替代方案。用本方法進行了幾個數值執行個體,結果表明,本方法能夠解決小尺度的流動特征,并且具有與MP5方案相同的捕捉尖銳不連續的能力。

原文:In this paper, we present a novel hybrid nonlinear explicit-compact scheme for shock-capturing based on a boundary variation diminishing (BVD) reconstruction. In our approach, we combine a non-dissipative sixth-order central compact interpolation and a fifth-order monotonicity preserving scheme (MP5) through the BVD algorithm. For a smooth solution, the BVD reconstruction chooses the highest order possible interpolation, which is central, i.e. non-dissipative in the current approach and for the discontinuities, the algorithm selects the monotone scheme. This method provides an alternative to the existing adaptive upwind-central schemes in the literature. Several numerical examples are conducted with the present approach, which suggests that the current method is capable of resolving small scale flow features and has the same ability to capture sharp discontinuities as the MP5 scheme.