International Journal of Mathematical, Engineering and Management Sciences

ISSN: 2455-7749

Discontinuity Preserving Scheme

Arun Govind Neelan
Department of Aerospace Engineering, Indian Institute of Space Science and Technology, Thiruvananthapuram - 695547, Kerala, India.

Manoj T. Nair
Department of Aerospace Engineering, Indian Institute of Space Science and Technology, Thiruvananthapuram - 695547, Kerala, India.

DOI https://doi.org/10.33889/IJMEMS.2020.5.4.051

Received on December 23, 2019
  ;
Accepted on April 14, 2020

Abstract

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.

Keywords- Shock capturing scheme, WENO, High-resolution schemes, Conservative schemes, Finite volume method.

Citation

Neelan, A. G., & Nair, M. T. (2020). Discontinuity Preserving Scheme. International Journal of Mathematical, Engineering and Management Sciences, 5(4), 631-642. https://doi.org/10.33889/IJMEMS.2020.5.4.051.

Conflict of Interest

The author confirms that there is no conflict of interest to declare for this publication.

Acknowledgements

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors. We thank the Department of Space (Government of India) for supporting this work. We also like to thank Dr Manuel A. Diaz for sharing his knowledge. The authors sincerely appreciate the editor and reviewers for their precious time and valuable comments.

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