A novel weighting switch function for uniformly high‐order hybrid shock‐capturing schemes

Peng, Jun; Shen, Yiqing

doi:10.1002/fld.4285

Cited by 15 publications

(5 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Fig.1 illustrates θ with different values of parameters. Detailed analysis of this function can be found in [27]. Here, we take:…”

Section: Adaptive Weno-z Methodsmentioning

confidence: 99%

See 1 more Smart Citation

An adaptive characteristic-wise reconstruction WENO-Z scheme for gas dynamic euler equations

Peng¹,

Zhai²,

Ni³

et al. 2019

Computers & Fluids

Self Cite

View full text Add to dashboard Cite

Due to its excellent shock-capturing capability and high resolution, the WENO scheme family has been widely used in varieties of compressive flow simulation. However, for problems containing strong shocks and contact discontinuities, such as the Lax shock tube problem, the WENO scheme still produces numerical oscillations. To avoid such numerical oscillations, the characteristic-wise construction method should be applied. Compared to component-wise reconstruction, characteristic-wise reconstruction leads to much higher computational cost and thus is not suitable for large scale simulation such as direct numerical simulation of turbulence. In this paper, an adaptive characteristic-wise reconstruction WENO-Z scheme, i.e. the AdaWENO-Z scheme, is proposed to improve the computational efficiency of the characteristic-wise reconstruction method. By defining shared smoothness functions, shared smoothness indicators as well as shared WENO weights are firstly introduced to reduce the computational cost of the componentwise reconstruction procedure and to define a global switch function capable of detecting discontinuity. According to the given switch function, the new scheme performs characteristic-wise reconstruction near discontinuities and switches to component-wise reconstruction for smooth regions. Several one dimensional and two dimensional numerical tests are performed to validate and evaluate the AdaWENO-Z scheme. Numerical results show that AdaWENO-Z maintains essentially non-oscillatory flow field near discontinuities as with the characteristic-wise reconstruction method. Besieds, compared to the component-wise reconstruction method, AdaWENO-Z is about 20% to 40% faster which indicates its excellent efficiency.

show abstract

“…Fig.1 illustrates θ with different values of parameters. Detailed analysis of this function can be found in [27]. Here, we take:…”

Section: Adaptive Weno-z Methodsmentioning

confidence: 99%

“…(22). Taking the properties of the non-linear weights α ± k,G into consideration (see [4,6,27] for more details), we have:…”

Section: Adaptive Weno-z Methodsmentioning

confidence: 99%

An adaptive characteristic-wise reconstruction WENO-Z scheme for gas dynamic euler equations

Peng¹,

Zhai²,

Ni³

et al. 2019

Computers & Fluids

Self Cite

View full text Add to dashboard Cite

show abstract

“…By combining the Roe scheme with the HLL scheme in different directions and different flux components, they concluded that schemes that directly restricted instability source were more stable than other hybrid schemes. Peng and Shen 30 presented a new weighting switch function and the seventh‐order hybrid compact‐reconstruction WENO scheme (HCCS). Several numerical tests revealed that the scheme had lower dissipation, less computational cost, and higher robustness than the seventh‐order WENO scheme.…”

Section: Introductionmentioning

confidence: 99%

A stable hybrid Roe scheme on triangular grids

Phongthanapanich

2020

Numerical Methods in Fluids

View full text Add to dashboard Cite

Numerical shock instability is a common problem for shock‐capturing methods that try to resolve contact and shear waves with minimal diffusion. Most flux‐difference splitting and the AUSM family of schemes produce the carbuncle phenomenon on both structured and unstructured grids. The original Roe scheme is well known to generate shock anomalies and can lead to nonentropic weak solutions to the Euler equations. A simple and robust approach for healing these numerical instabilities is to apply the hybrid technique incorporated with an efficient weighting switch function to control the amount of dissipation in the vicinity of shock waves. This article proposes a simple, robust, and accurate hybrid Roe scheme (Roe+ scheme) by hybridizing the Roe scheme and the modified AUSMV+ scheme. A new normalized pressure/density‐based weighting switch function is proposed and applied to the scheme to minimize the numerical dissipation and maintain the robustness of the hybridization. The linearized discrete analysis is performed to evaluate the proposed scheme according to the perturbation damping mechanism of an odd–even decoupling problem. The resulting recursive equations indicate that the hybridized mechanism damps all perturbations effectively. Finally, several numerical examples demonstrated that the Roe+ scheme provides an accurate, robust, and carbuncle‐free solution on both structured and unstructured triangular grids.

show abstract

“…In this paper, we propose a new adaptive method to improve the performance of TENO. Based on the shock-sensor developed in [49], an novel adaptive function for C T is introduced. The new method maintains the low dissipation property of TENO for smooth fields and significantly improves its shock-capturing capability at a low price.…”

Section: Introductionmentioning

confidence: 99%

An efficient targeted ENO scheme with local adaptive dissipation for compressible flow simulation

Peng,

Li,

Shen

et al. 2020

Preprint

Self Cite

View full text Add to dashboard Cite

High fidelity numerical simulation of compressible flow requires the numerical method being used to have both stable shock-capturing capability and high spectral resolution. Recently, a family of Targeted Essentially Non-Oscillatory (TENO) schemes are developed to fulfill such requirements. Although TENO has very low dissipation for smooth flow, it introduces a cutoff value C T to maintain the non-oscillatory shock-capturing property. C T is problem depended and therefore needs adjustments by trial and error for different problems. As C T actually controls the dissipation property of TENO, the choice of C T for better shockcapturing capability always means higher dissipation. To overcome this, in this paper, a local adaptive method is proposed for the choice of C T . By introducing a novel adaptive function based on the WENO smoothness indicators, C T is dynamically adjusted form 1.0×10.0 −10 for lower dissipation to 1.0×10.0 −4 for better capturing of shock according to the smoothness of the reconstruction stencil. Numerical results of the new method are compared with those of the original TENO method and the TENO-A method (Fu et al., JCP, 2017). It reveals that the new method is capable of better suppressing numerical oscillations near discontinuities while maintaining the low dissipation property of TENO at lower extra computational cost.

show abstract

A novel weighting switch function for uniformly high‐order hybrid shock‐capturing schemes

Cited by 15 publications

References 46 publications

An adaptive characteristic-wise reconstruction WENO-Z scheme for gas dynamic euler equations

An adaptive characteristic-wise reconstruction WENO-Z scheme for gas dynamic euler equations

A stable hybrid Roe scheme on triangular grids

An efficient targeted ENO scheme with local adaptive dissipation for compressible flow simulation

Contact Info

Product

Resources

About