Simple smoothness indicator WENO-Z scheme for hyperbolic conservation laws

Rathan, Samala; Gande, Naga Raju; Bhise, Ashlesha A.

doi:10.1016/j.apnum.2020.06.006

Cited by 21 publications

(12 citation statements)

References 33 publications

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“…Remark 1. Now, if the Gaussian RBF is considered as another infinitely smooth RBF basis in Equation (15), by following the same procedure we have that…”

Section: Hermite Rbf-eno/weno Methods In 1d Casementioning

confidence: 99%

“…For this reason, designing efficient, accurate, and robust numerical schemes to solve these equations is a significant issue, and as expected, many researchers and practitioners have become interested in this field 4‐10 . Accordingly, in recent decades, many high‐order numerical schemes to solve equations in the form (1) have been developed 11‐15 . It should be noted that due to the high efficiency of WENO schemes, today these methods have been employed and expanded to solve other equations such as the Hamilton–Jacobi 3,16‐20 and the degenerate parabolic equations 21‐26 .…”

Section: Introductionmentioning

confidence: 99%

“…[4][5][6][7][8][9][10] Accordingly, in recent decades, many high-order numerical schemes to solve equations in the form (1) have been developed. [11][12][13][14][15] It should be noted that due to the high efficiency of WENO schemes, today…”

Section: Introductionmentioning

confidence: 99%

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A finite difference Hermite RBF‐WENO scheme for hyperbolic conservation laws

Abedian

2022

Numerical Methods in Fluids

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One of the best ideas for controlling the Gibbs oscillations in hyperbolic conservation laws is to apply weighted essentially non‐oscillatory (WENO) schemes. The traditional WENO and Hermite WENO (HWENO) schemes are based on the polynomial interpolation. In this research, a non‐polynomial HENO and HWENO finite difference scheme in order to enhance the local accuracy and convergence is proposed. The idea of the reconstruction in HWENO schemes is derived from traditional WENO schemes, with the difference that in traditional WENO schemes only function values are evolved and used, while in HWENO schemes both the values of the function and the first derivative of the function are evolved in time and used. The Hermite radial basis functions (RBFs) interpolation offers the flexibility to control the local error by optimizing the free parameter. The numerical results demonstrate that the developed Hermite RBF‐ENO and RBF‐WENO schemes enhance the local accuracy and give sharper solution profile than the Hermite ENO and WENO schemes based on the polynomial interpolation.

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“…Remark 1. Now, if the Gaussian RBF is considered as another infinitely smooth RBF basis in Equation (15), by following the same procedure we have that…”

Section: Hermite Rbf-eno/weno Methods In 1d Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A finite difference Hermite RBF‐WENO scheme for hyperbolic conservation laws

Abedian

2022

Numerical Methods in Fluids

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“…Subsequently, various new global smoothness indicators have been proposed by researchers to enhance the numerical performance of the WENO-Z scheme. [18][19][20][21][22][23][24][25][26][27] The mapping function associated with the weight function can improve the accuracy of the WENO-M scheme for low-order critical points. In this paper, the WENO-Z scheme is improved by using a weight-independent mapping function.…”

Section: Introductionmentioning

confidence: 99%

High‐resolution mapping type WENO‐Z schemes for solving compressible flow

Tang,

2024

Numerical Methods in Fluids

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SummaryThis paper presents a new WENO‐Z scheme (WENO‐MZ) that incorporates a mapping function to enhance the weights of the less smooth sub‐stencils. The mapping function uses an innovative approach to modify the weight ratio of the less smooth sub‐stencil to the smooth stencil. In addition, we present the WENO‐MD scheme, which is a further development of the WENO‐MZ scheme that incorporates a modifier function. The WENO‐MD scheme shows improvements over the WENO‐MZ scheme by achieving an improved optimal order at critical points in higher orders and by increasing the proportion of less smooth sub‐stencils. Theoretical and numerical experiments have shown that the newly developed methods have improved shock capture capabilities and resolution compared to WENO‐JS, WENO‐Z, WENO‐M, WENO‐D, and WENO‐AIM, and also lead to significant computational time savings compared to WENO‐M and WENO‐AIM.

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“…And they developed a class of structurally simple fifth-order WENO-Z schemes. In addition, Castro [19], Don [20], Liu [21], Wang [22], Peng [23], Mulet [24,25,26], Hu [27], Russo [28,29,30], Rathan [31] and Huang [32] have successively developed various high order WENO-Z type schemes based on Borges'.…”

Section: Introductionmentioning

confidence: 99%

A smoothness indicators free third-order weighted ENO scheme for gas-dynamic Euler equations

Tang

2023

Comp. Appl. Math.

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To improve the shock-capturing capability of the third-order WENO scheme and enhance its computational efficiency, in this paper, we designed a new WENO scheme independent of the local smooth factor, WENO-SIF. The weight functions of the WENO-SIF scheme are segmentation functions of the sub-stencils, which can guarantee it achieves the desired accuracy at the high-order critical points. During the calculation, WENO-SIF need not calculate the smoothing factor, which can effectively reduce the computational consumption. The new WENO-SIF is compared with WENO-JS and other WENO schemes for numerical experiments at one-and two-dimensional benchmark problems with a suitable choice of λ = 0.13. The results show the WENO scheme can further improve the resolution of WENO-JS, achieve the optimal accuracy at high-order critical points, and significantly reduce computational consumption.

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Simple smoothness indicator WENO-Z scheme for hyperbolic conservation laws

Cited by 21 publications

References 33 publications

A finite difference Hermite RBF‐WENO scheme for hyperbolic conservation laws

A finite difference Hermite RBF‐WENO scheme for hyperbolic conservation laws

High‐resolution mapping type WENO‐Z schemes for solving compressible flow

A smoothness indicators free third-order weighted ENO scheme for gas-dynamic Euler equations

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