Local characteristic decomposition based central-upwind scheme

Chertock, Alina; Chu, Shaoshuai; Herty, Michaël; Kurganov, Alexander; Lukáčová-Medviďová, Mária

doi:10.1016/j.jcp.2022.111718

Cited by 9 publications

(6 citation statements)

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“…In the numerical experiments reported in Section 5.1, we have used a recently proposed local characteristics decomposition (LCD) based central-upwind (CU) numerical flux from [13], which reads as…”

Section: -D A-weno Schemesmentioning

confidence: 99%

“…In the numerical experiments reported in Section 5.2, we have used the 2-D LCD-based CU numerical fluxes from [13] FV…”

Section: -D A-weno Schemesmentioning

confidence: 99%

“…Example 5.1 (1-D Accuracy Test). In the first example taken from [13,37], we consider the (3.8)-(3.10) subject to the following smooth initial data:…”

Section: One-dimensional Examplesmentioning

confidence: 99%

“…Example 5.6 (2-D Accuracy Test). In the first 2-D example taken from [13,37], we consider the 2-D Euler equations of gas dynamics subject to the following periodic initial conditions:…”

Section: Two-dimensional Examplesmentioning

confidence: 99%

“…The developed scheme adaption strategy is implemented using the recently proposed local characteristic decomposition based central-upwind numerical flux from [13] and applied to both the 1-D and 2-D Euler equations of gas dynamics, for which we design the LSI based on the pressure rather than on the density or any other conservative variable. This choice is motivated by the results obtained in [15], where it has been demonstrated that applying a nonlinear stabilization mechanism is crucial for the shock areas while isolated linearly degenerate contact waves can be accurately captured using the nonlimited high-order reconstruction.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: -D A-weno Schemesmentioning

confidence: 99%

“…In the numerical experiments reported in Section 5.2, we have used the 2-D LCD-based CU numerical fluxes from [13] FV…”

Section: -D A-weno Schemesmentioning

confidence: 99%

“…Example 5.1 (1-D Accuracy Test). In the first example taken from [13,37], we consider the (3.8)-(3.10) subject to the following smooth initial data:…”

Section: One-dimensional Examplesmentioning

confidence: 99%

“…Example 5.6 (2-D Accuracy Test). In the first 2-D example taken from [13,37], we consider the 2-D Euler equations of gas dynamics subject to the following periodic initial conditions:…”

Section: Two-dimensional Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations