A New Smoothness Indicator of Adaptive Order Weighted Essentially Non-Oscillatory Scheme for Hyperbolic Conservation Laws

Omer Musa, Guoping Huang and Mingsheng Wang
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Omer Musa: College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Guoping Huang: College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Mingsheng Wang: College of Energy and Power Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Mathematics, 2020, vol. 9, issue 1, 1-31

Abstract: Adaptive order weighted essentially non-oscillatory scheme (WENO-AO(5,3)) has increased the computational cost and complexity of the classic fifth-order WENO scheme by introducing a complicated smoothness indicator for fifth-order linear reconstruction. This smoothness indicator is based on convex combination of three third-order linear reconstructions and fifth-order linear reconstruction. Therefore, this paper proposes a new simple smoothness indicator for fifth-order linear reconstruction. The devised smoothness indicator linearly combines the existing smoothness indicators of third-order linear reconstructions, which reduces the complexity of that of WENO-AO(5,3) scheme. Then WENO-AO(5,3) scheme is modified to WENO-O scheme with new and simple formulation. Numerical experiments in 1-D and 2-D were run to demonstrate the accuracy and efficacy of the proposed scheme in which WENO-O scheme was compared with original WENO-AO(5,3) scheme along with WENO-AO-N, WENO-Z, and WENO-JS schemes. The results reveal that the proposed WENO-O scheme is not only comparable to the original scheme in terms of accuracy and efficacy but also decreases its computational cost and complexity.

Keywords: computational fluid dynamics; finite difference; WENO; smoothness indicator; hyperbolic systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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