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Discontinuity Preserving Scheme
International Journal of Mathematical, Engineering and Management Sciences  (IF),  Pub Date : 2020-08-01, DOI: 10.33889/ijmems.2020.5.4.051
Arun Govind Neelan, Manoj T. Nair

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.