Hybrid finite compact‐WENO schemes for shock calculation

Shen, Yiqing; Yang, Guowei

doi:10.1002/fld.1286

Cited by 53 publications

(30 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In those smooth zones, a bi-diagonal compact scheme avoiding flux contamination at discontinuties due to the standard compact scheme is suggested. The scheme is hence called finite compact difference scheme [19,20].…”

Section: The Finite Compact Differencing Schemementioning

confidence: 99%

See 1 more Smart Citation

Generalized finite compact difference scheme for shock/complex flowfield interaction

Shen

Zha

2011

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

Section: The Finite Compact Differencing Schemementioning

confidence: 99%

“…In [19,20], the global compact difference scheme (18) is divided into multiple smooth zones by discontinuities. In those smooth zones, a bi-diagonal compact scheme avoiding flux contamination at discontinuties due to the standard compact scheme is suggested.…”

Section: The Finite Compact Differencing Schemementioning

confidence: 99%

Generalized finite compact difference scheme for shock/complex flowfield interaction

Shen

Zha

2011

Journal of Computational Physics

Self Cite

View full text Add to dashboard Cite

“…Combined with the TVD of ENO limiters, a set of high resolution finite compact (FC) difference schemes with only bi-diagonal matrix inversion are constructed [19,20]. Some of the above methods need to calculate the preliminary fluxes first by using a standard compact scheme [12,13,14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Comparisons of High Order Hybrid Schemes Using a Parameter-free Discontinuity Detector

Shen

Zha

Yang

et al. 2012

42nd AIAA Fluid Dynamics Conference and Exhibit

Self Cite

View full text Add to dashboard Cite

In order to simulate accurately the interaction of shock wave/complex flows, hybrid schemes combining the compact scheme and weighted essentially non-oscillatory(WENO) scheme are beneficial, especially the high order low diffusion schemes used in smooth regions. There are two key issues, one is how to detect the discontinuity, the other is how to choose the high order low diffusion scheme to ensure the accuracy, robustness and efficiency. In this paper, several high order schemes are combined with the fifth order WENO scheme by using the discontinuity detector proposed by Shen and Zha(Y. Shen, G.Zha, J. Compu. Phys., 2011, 230:4419-4436) and compared numerically.

show abstract

“…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

View full text Add to dashboard Cite

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

show abstract

Hybrid finite compact‐WENO schemes for shock calculation

Cited by 53 publications

References 30 publications

Generalized finite compact difference scheme for shock/complex flowfield interaction

Generalized finite compact difference scheme for shock/complex flowfield interaction

Comparisons of High Order Hybrid Schemes Using a Parameter-free Discontinuity Detector

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

Contact Info

Product

Resources

About