Numerical dissipation control in an adaptive WCNS with a new smoothness indicator

Zhao, Guoyan; Sun, Mingbo; Xie, Songbai; Wang, Hongbo

doi:10.1016/j.amc.2018.01.019

Cited by 8 publications

(6 citation statements)

References 28 publications

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“…Moreover, in this numerical case, expected symmetries are lost in all solutions. Similar behaviors were also found in references Shi et al (2003); Zhao et al (2018). A thorough investigation into the occurrence of symmetry breaking was carried out by Fleischmann et al (2019) in their recent work.…”

Section: Configurationsupporting

confidence: 80%

A multi-resolution weighted compact nonlinear scheme for hyperbolic conservation laws

Zhang

Wang

Zhang

2020

International Journal of Computational Fluid Dynamics

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A typical weighted compact nonlinear scheme (WCNS) uses a convex combination of several low-order polynomials approximated over selected candidate stencils of same width, achieving non-oscillatory interpolation near discontinuities and high order accuracy for smooth solutions. In this paper, we present a new multi-resolution fifth-order WCNS by making use of the information of polynomials on three nested central spatial sub-stencils having first-, third-and fifth-order accuracy, respectively. The new scheme is capable of obtaining high-order spatial interpolation in smooth regions, and it is characterized by the feature of gradually degrading from fifth-order down to first-order accuracy as large stencils deemed to be crossing strong discontinuities. The advantages of the present scheme include the superior resolution for highwavenumber fluctuations and the flexibility of implementing different numerical flux functions.

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Section: Configurationsupporting

confidence: 80%

A multi-resolution weighted compact nonlinear scheme for hyperbolic conservation laws

Zhang

Wang

Zhang

2020

International Journal of Computational Fluid Dynamics

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“…where the boxed eigen vectors are placed at the first two positions to make sure that the summation of them is computed first. Hence, the symmetry property regarding x-and y-axis can be preserved by either adjusting the order of the summation of matrix-vector product as shown in (38) or re-arranging the eigen matrices as (39).…”

Section: Local Characteristic Decompositionmentioning

confidence: 99%

“…To conclude this subsection regarding the transformation between conservative variables and characteristic variables, we state the two crucial points to enforce the solution symmetry, 1) to add a bracket and modify the summation order as (38) or arrange the eigenvectors matrices as (39) to ensure the axis-symmetry property, and 2) to add a bracket to (42) and ( 43) for diagonal symmetry-preserving.…”

Section: Local Characteristic Decompositionmentioning

confidence: 99%

“…i) Change the order of summation in the transformation from the characteristic variables to the conservative variables, using (38) or (39);…”

Section: Hllc Riemann Solvermentioning

confidence: 99%

“…As a result, the numerical solution may lose spatial symmetry even started from a symmetrical setup. It is commonly observed that highresolution simulations with fine meshes usually lead to undesirable asymmetrical numerical results [34,35,36,37,13,38,39,40,33,41,42,26] in application problems that possess physical symmetry in solution structures, such as the Rayleigh-Taylor instability (RTI) and the symmetric implosion benchmark problems. The symmetry-breaking results might not be visible in simulations with significant numerical dissipation, and have not been seen as a serious problem in the past.…”

Section: Introductionmentioning

confidence: 99%

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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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High-order maximum-principle-preserving and positivity-preserving weighted compact nonlinear schemes for hyperbolic conservation laws

Tang

Song

Zhang

2019

Appl. Math. Mech.-Engl. Ed.

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Numerical dissipation control in an adaptive WCNS with a new smoothness indicator

Cited by 8 publications

References 28 publications

A multi-resolution weighted compact nonlinear scheme for hyperbolic conservation laws

A multi-resolution weighted compact nonlinear scheme for hyperbolic conservation laws

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

High-order maximum-principle-preserving and positivity-preserving weighted compact nonlinear schemes for hyperbolic conservation laws

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