Non-linear schemes are widely used in high-speed flows to capture the discontinuities present in the solution. Limiters and weighted essentially non-oscillatory schemes (WENO) are the most common non-linear numerical schemes. Most of the high-resolution schemes use the piecewise parabolic reconstruction (PPR) technique for their robustness. However, it may be impossible to achieve non-oscillatory and dissipation-free solutions with the PPR technique without non-linear switches. Most of the shock-capturing schemes use excessive dissipation to suppress the oscillations present in the discontinuities. To eliminate these issues, an algorithm is proposed that uses the shock-capturing scheme (SCS) in the first step, and then the result is refined using a novel scheme called the Discontinuity Preserving Scheme (DPS). The present scheme is a hybrid shock capture-fitting scheme. The present scheme has outperformed other schemes considered in this work, in terms of shock resolution in linear and non-linear test cases. The most significant advantage of the present scheme is that it can resolve shocks with three grid points. KeywordsShock capturing scheme, WENO, High-resolution schemes, Conservative schemes, Finite volume method.

中文翻译：

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不连续性保存方案

非线性方案广泛用于高速流中，以捕获解决方案中存在的不连续性。限制器和加权基本非振荡方案（WENO）是最常见的非线性数值方案。大多数高分辨率方案都使用分段抛物线重构（PPR）技术来增强其鲁棒性。但是，如果没有非线性开关，则无法通过PPR技术实现非振荡和无耗散的解决方案。大多数冲击捕捉方案都使用过多的耗散来抑制不连续中存在的振荡。为了消除这些问题，首先提出了一种使用震荡捕获方案（SCS）的算法，然后使用一种称为不连续性保留方案（DPS）的新颖方案对结果进行细化。本方案是一种混合的冲击捕获-拟合方案。就线性和非线性测试案例中的冲击分辨率而言，本方案已经优于本文中考虑的其他方案。本方案的最大优点是可以解决三个网格点的冲击。关键词震动捕获方案WENO高分辨率方案保守方案有限体积法。