Symmetry-preserving enforcement of low-dissipation method based on boundary variation diminishing principle

Wakimura, Hiro; Takagi, Shinichi; Xiao, Feng

doi:10.1016/j.compfluid.2021.105227

Cited by 16 publications

(1 citation statement)

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“…2 for all j, k. For more sophisticated symmetry enforcement techniques, we refer the reader to, e.g., [16,17,20,61].…”

Section: Two-dimensional Examplesmentioning

confidence: 99%

Adaptive High-Order A-WENO Schemes Based on a New Local Smoothness Indicator

Chertock¹,

Kurganov²

2023

EAJAM

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We develop new adaptive alternative weighted essentially non-oscillatory (A-WENO) schemes for hyperbolic systems of conservation laws. The new schemes employ the recently proposed local characteristic decomposition based central-upwind numerical fluxes, the three-stage third-order strong stability preserving Runge-Kutta time integrator, and the fifth-order WENO-Z interpolation. The adaptive strategy is implemented by applying the limited interpolation only in the parts of the computational domain where the solution is identified as rough with the help of a smoothness indicator. We develop and use a new simple and robust local smoothness indicator (LSI), which is applied to the solutions computed at each of the three stages of the ODE solver. The new LSI and adaptive A-WENO schemes are tested on the Euler equations of gas dynamics. We implement the proposed LSI using the pressure, which remains smooth at contact discontinuities, while our goal is to detect other rough areas and apply the limited interpolation mostly in the neighborhoods of the shock waves. We demonstrate that the new adaptive schemes are highly accurate, non-oscillatory, and robust. They outperform their fully limited counterparts (the A-WENO schemes with the same numerical fluxes and ODE solver but with the WENO-Z interpolation employed everywhere) while being less computationally expensive.

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“…2 for all j, k. For more sophisticated symmetry enforcement techniques, we refer the reader to, e.g., [16,17,20,61].…”

Section: Two-dimensional Examplesmentioning

confidence: 99%