An efficient low‐dissipative WENO filter scheme

Kang, Lei; Lee, Chun‐Hian

doi:10.1002/fld.2555

Cited by 2 publications

(4 citation statements)

References 24 publications

(52 reference statements)

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“…In [14,20,33] to produce a filter flux, the flux of a central (nondissipative) scheme is subtracted from a shock-capturing scheme:…”

Section: Hybrid Weno5 Filtermentioning

confidence: 99%

“…Sjogreen and Yee in a series of papers [14][15][16] used nonlinear filtering approach to simulate several flows with shocks. Further works on this approach are the works carried out by Bogey et al [17], Visbal et al [18], Mahmoodi et al [19] and Kang et al [20]. Recently, Kotov et al [21][22][23][24] and also Yee and Sjogreen [25][26][27] developed nonlinear filtering approach for DNS and LES applications.…”

Section: Introductionmentioning

confidence: 99%

“…Using this modification, we expect to obtain solutions that are more accurate. Note that the dissipative part of a WENO scheme is simply obtained by removing the convective part of the scheme which is different from the idea used in [14,20,33]. Among various WENO schemes, we choose the classic WENO scheme [1,2] and the recently developed WENO-AO scheme (WENO scheme with adaptive order) [5,6] for the introduced hybrid WENO5 filter.…”

Section: Introductionmentioning

confidence: 99%

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Numerical experiments on a hybrid WENO5 filter for shock‐capturing

Darian

Bozorgpour

Shafaee

2019

Numerical Methods Partial

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In the present paper, a hybrid filter is introduced for high accurate numerical simulation of shock-containing flows. The fourth-order compact finite difference scheme is used for the spatial discretization and the third-order Runge-Kutta scheme is used for the time integration. After each time-step, the hybrid filter is applied on the results. The filter is composed of a linear sixth-order filter and the dissipative part of a fifth-order weighted essentially nonoscillatory scheme (WENO5). The classic WENO5 scheme and the WENO5 scheme with adaptive order (WENO5-AO) are used to form the hybrid filter. Using a shock-detecting sensor, the hybrid filter reduces to the linear sixth-order filter in smooth regions for damping high frequency waves and reduces to the WENO5 filter at shocks in order to eliminate unwanted oscillations produced by the nondissipative spatial discretization method. The filter performance and accuracy of the results are examined through several test cases including the advection, Euler and Navier-Stokes equations. The results are compared with that of a hybrid second-order filter and also that of the WENO5 and WENO5-AO schemes. KEYWORDS compact finite-difference schemes, high-order methods, hybrid filter, shock sensor, shock-capturing schemes, weighted essentially nonoscillatory schemes Numer Methods Partial Differential Eq. 2019;35:2375-2406. wileyonlinelibrary.com/journal/num

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“…In [14,20,33] to produce a filter flux, the flux of a central (nondissipative) scheme is subtracted from a shock-capturing scheme:…”

Section: Hybrid Weno5 Filtermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Numerical experiments on a hybrid WENO5 filter for shock‐capturing

Darian

Bozorgpour

Shafaee

2019

Numerical Methods Partial

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“…One can also clearly see from Figure 6b that the predicted wave shape remains almost unchanged. The linear advection equation u t þ u x ¼ 0 is also solved under the following initial condition [27][28][29][30]:…”

Section: One-dimensional Verification Studiesmentioning

confidence: 99%

Development of a symplectic and phase error reducing perturbation finite-difference advection scheme

Zhi

Sheu³

2016

Numerical Heat Transfer, Part B: Fundamentals

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The aim of this work is to develop a new scheme for solving the pure advection equation. This scheme formulated within the perturbation finite-difference context not only conserves symplecticity but also preserves the numerical dispersion relation equation. The employed symplectic integrator of secondorder accuracy in time enables calculation of a long-time accurate solution in the sense that the Hamiltonian is conserved at all times. The generalized highorder spatially accurate perturbation difference scheme optimizes numerical phase accuracy through the minimization of the difference between the numerical and exact dispersion relation equations. Our proposed new class of phase error reducing perturbation difference schemes can in addition locally capture discontinuities underlying the concept of applying a shope/flux limiter. The high-order spatial accuracy can be recovered in a smooth region. Besides the Fourier analysis of the discretization errors, anisotropy and dispersion analyses are both conducted on the dispersion-relation and symplecticity-preserving pure advection scheme to shed light on the distinguished nature of the proposed scheme. Numerical tests are carried out and the results compare well with the exact solutions, demonstrating the efficiency, accuracy, and the discontinuity-resolving ability using the proposed class of high-resolution perturbation finite-difference schemes. ARTICLE HISTORY

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An efficient low‐dissipative WENO filter scheme

Cited by 2 publications

References 24 publications

Numerical experiments on a hybrid WENO5 filter for shock‐capturing

Numerical experiments on a hybrid WENO5 filter for shock‐capturing

Development of a symplectic and phase error reducing perturbation finite-difference advection scheme

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