An Improved Component-Wise WENO-NIP Scheme for Euler System

Ruo Li and Wei Zhong ()
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Ruo Li: CAPT, LMAM and School of Mathematical Sciences, Peking University, Beijing 100871, China
Wei Zhong: School of Mathematical Sciences, Peking University, Beijing 100871, China

Mathematics, 2022, vol. 10, issue 20, 1-21

Abstract: As is well known, due to the spectral decomposition of the Jacobian matrix, the WENO reconstructions in the characteristic-wise fashion (abbreviated as CH-WENO) need much higher computational cost and more complicated implementation than their counterparts in the component-wise fashion (abbreviated as CP-WENO). Hence, the CP-WENO schemes are very popular methods for large-scale simulations or situations whose full characteristic structures cannot be obtained in closed form. Unfortunately, the CP-WENO schemes usually suffer from spurious oscillations badly. The main objective of the present work is to overcome this drawback for the CP-WENO-NIP scheme, whose counterpart in the characteristic-wise fashion was carefully studied and well-validated numerically. The approximated dispersion relation (ADR) analysis is performed to study the spectral property of the CP-WENO-NIP scheme and then a negative-dissipation interval which leads to a high risk of causing spurious oscillations is discovered. In order to remove this negative-dissipation interval, an additional term is introduced to the nonlinear weights formula of the CP-WENO-NIP scheme. The improved scheme is denoted as CP-WENO-INIP. Accuracy test examples indicate that the proposed CP-WENO-INIP scheme can achieve the optimal convergence orders in smooth regions even in the presence of the critical points. Extensive numerical experiments demonstrate that the CP-WENO-INIP scheme is much more robust compared to the corresponding CP-WENO-NIP or even CH-WENO-NIP schemes for both 1D and 2D problems modeled via the Euler equations.

Keywords: component-wise WENO-NIP; Euler equations; shock capturing; reducing spurious oscillations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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