A Characteristic-wise Alternative WENO-Z Finite Difference Scheme for Solving the Compressible Multicomponent Non-reactive Flows in the Overestimated Quasi-conservative Form

Don, Wai Sun; Li, Dongmei; Gao, Zhen; Wang, Baoshan

doi:10.1007/s10915-020-01126-y

Cited by 28 publications

(10 citation statements)

References 24 publications

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“…The effect of symmetry breaking was first connected to floating point round-off errors by Remacle et al [31], and first systematically controlled by Fleischmann et al [8]. Alternatively, Dong et al [5,6] proposed to modify the smoothness indicators of WENO-type schemes to reduce adverse floating-point effects, whereas Wang et al [42] applied a symmetrization procedure with an active averaging of state values in symmetrically placed cells.…”

Section: Treatment Of Floating-point Induced Disturbancesmentioning

confidence: 99%

High‐order modeling of interface interactions using level sets

et al. 2022

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Most technological advancements in medicine, process and energy engineering, life and food science, mobility and environmental engineering involve mastering fluid mechanical effects. In particular, compressible flow physics including shockwaves and phase‐interface interactions exhibit multi‐scale phenomena spanning several orders of magnitude upwards from nanometer and nanosecond time scales. Clearly, detailed analysis of such effects is impossible by means of experimental techniques. On the contrary, numerical modeling and simulations allow to capture the aforementioned mechanisms and provide non‐invasive access to any quantity of interest. Yet, the complex fluid physics require powerful computational methods utilizing recent advancements for high‐order schemes. In this work, we provide an overview on latest high‐order low‐dissipation schemes using level sets to model discontinuous phase‐interface interactions.

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Section: Treatment Of Floating-point Induced Disturbancesmentioning

confidence: 99%

High‐order modeling of interface interactions using level sets

et al. 2022

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“…Given the SF function defined in (44), the symmetric reconstruction in x-direction, regarding the y-axis symmetry, requires the following relations to be satisfied,…”

Section: Symmetry Enforcement Using Sf and Si Reconstructionsmentioning

confidence: 99%

“…Remacle et al [35] initially reported that the symmetry error is caused by the rounding error of floating-point arithmetic, which grows asymmetrically with time evolution. Don et al suggested a numerically stable form of the smooth indicator in the WENO framework [43,44]. In this scheme, the symmetry error was effectively reduced compared to the original 7th-and 9th-order WENO schemes, but the cause of the symmetry error has not been completely eliminated.…”

Section: Introductionmentioning

confidence: 99%

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

Wakimura¹,

Takagi²,

Xiao³

2021

Preprint

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A class of high-order shock-capturing schemes, P n T m -BVD (Deng et al., J. Comp. Phys., 386:323-349, 2019; Comput. & Fluids, 200:104433, 2020.) schemes, have been devised to solve the Euler equations with substantially reduced numerical dissipation, which enable high-resolution simulations to resolve flow structures of wider range scales. In such simulations with low dissipation, errors of round-off level might grow and contaminate the numerical solutions. A typical example of such problems is the loss of symmetry in the numerical solutions for physical problems of symmetric configurations even if the schemes are mathematically in line with the symmetry rules. In this study, the mechanisms of symmetry-breaking in a finite volume framework with the P 4 T 2 -BVD reconstruction scheme are thoroughly examined. Particular attention has been paid to remove the possible causes due to the lack of associativity in floating-point arithmetic which is associated with round-off errors. Modifications and new techniques are proposed to completely remove the possible causes for symmetry breaking in different components of the P 4 T 2 -BVD finite volume solver. Benchmark tests that have symmetric solution structures are used to verify the proposed methods. The numerical results demonstrate the perfect symmetric solution structures.

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“…Gao et al [28] have extended the alternative WENO scheme framework to seventh and ninth order. This methodology has also been applied to shallow water equations, and multicomponent flows [29][30][31]. In the present work, we have designed a fifth-order alternative mapped WENO finite volume scheme using WENO-M nonlinear weights [24] for solving nonlinear hyperbolic equations.…”

Section: Introductionmentioning

confidence: 99%