A shock-detecting sensor for filtering of high-order compact finite difference schemes

Darian, Hossein Mahmoodi; Esfahanian, Vahid; Hejranfar, Kazem

doi:10.1016/j.jcp.2010.09.028

Cited by 28 publications

(20 citation statements)

References 49 publications

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“…The numerical filter equation in the conservative form is as follows :

{\overset{φ}{true}}_{j}^{n + 1} = φ_{j}^{n + 1} + \frac{normalΔt}{normalΔξ} ({\overset{F}{true}}_{j + 1 / 2} - {\overset{F}{true}}_{j - 1 / 2}),

in which Δ t is the time step and Δ ξ is the grid size in ξ ‐direction (the Δ ξ and Δ η is equal to 1). For a 2 m th‐order explicit linear filter (Appendix A), we have the following:

{\overset{F}{true}}_{j + 1 / 2}^{(m)} = {(- 1)}^{m - 1} ϵ^{(m)} {\overset{λ}{true}}_{ξ} {(normalΔ \nabla)}^{m - 1} normalΔ φ_{j},

where

{\overset{λ}{true}}_{ξ}

is the maximum characteristic velocity in the entire computational field.…”

Section: Methodsmentioning

confidence: 99%

“…Mahmoodi et al . designed a new sensor based on an order analysis, which uses an interpolation error scaled by a suitable value. The scaling is used to have dissipation proportional to the shock strength while minimizing the effects of the second‐order filter on the very small scales.…”

Section: Introductionmentioning

confidence: 99%

“…Numerical simulation of such flows is a challenge owing to conflicting requirements of numerical methods to be accurate enough to resolve the small scales of turbulence and at the same time to be robust enough to handle shock waves without generating spurious numerical noise.High-order total variation diminishing schemes, high-order extension of Godunov algorithm [3,4], the essentially non-oscillatory (ENO) [5][6][7][8][9], and weighted ENO (WENO) [10,11] schemes are developed in order to prevent the appearance of Gibbs oscillations in shocked flows as well as to enhance the shock-capturing ability in traditional methods. Among these schemes, assessment of these schemes for numerical simulation of compressible turbulent flows with shock waves shows that WENO schemes may play role as a reliable tool for DNS of compressible turbulent flows [12,13].In spite of their good shock-capturing capability of the aforementioned methods, their complicated algorithms, their high computational cost, and some other deficiencies motivated researchers to use high-order compact finite-difference schemes with a special type of shock-detecting sensor [14][15][16][17][18][19][20]. In other words, a shock-detecting sensor restricts the use of shock-capturing schemes in the vicinity of shocks and, hence, allows the dissipation to be applied only in the large gradient regions, that is, shocks while a spatial higher-order filter is applied to the smooth regions.…”

mentioning

confidence: 99%

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Numerical assessment of a shock‐detecting sensor for low dissipative high‐order simulation of shock–vortex interactions

Khoshab

Dehghan

Esfahanian

et al. 2014

Numerical Methods in Fluids

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SUMMARYConsidering the importance of high‐order schemes implementation for the simulation of shock‐containing turbulent flows, the present work involves the assessment of a shock‐detecting sensor for filtering of high‐order compact finite‐difference schemes for simulation of this type of flows. To accomplish this, a sensor that controls the amount of numerical dissipation is applied to a sixth‐order compact scheme as well as a fourth‐order two‐register Runge–Kutta method for numerical simulation of various cases including inviscid and viscous shock–vortex and shock–mixing‐layer interactions. Detailed study is performed to investigate the performance of the sensor, that is, the effect of control parameters employed in the sensor are investigated in the long‐time integration. In addition, the effects of nonlinear weighting factors controlling the value of the second‐order and high‐order filters in fine and coarse non‐uniform grids are investigated. The results indicate the accuracy of the nonlinear filter along with the promising performance of the shock‐detecting sensor, which would pave the way for future simulations of turbulent flows containing shocks. Copyright © 2014 John Wiley & Sons, Ltd.

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“…The numerical filter equation in the conservative form is as follows :

{\overset{φ}{true}}_{j}^{n + 1} = φ_{j}^{n + 1} + \frac{normalΔt}{normalΔξ} ({\overset{F}{true}}_{j + 1 / 2} - {\overset{F}{true}}_{j - 1 / 2}),

in which Δ t is the time step and Δ ξ is the grid size in ξ ‐direction (the Δ ξ and Δ η is equal to 1). For a 2 m th‐order explicit linear filter (Appendix A), we have the following:

{\overset{F}{true}}_{j + 1 / 2}^{(m)} = {(- 1)}^{m - 1} ϵ^{(m)} {\overset{λ}{true}}_{ξ} {(normalΔ \nabla)}^{m - 1} normalΔ φ_{j},

where

{\overset{λ}{true}}_{ξ}

is the maximum characteristic velocity in the entire computational field.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Numerical assessment of a shock‐detecting sensor for low dissipative high‐order simulation of shock–vortex interactions

Khoshab

Dehghan

Esfahanian

et al. 2014

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

show abstract

“…A combination of the second-and high-order linear filters can be used which acts as a second-order linear filter near discontinuities and behaves as a high-order linear filter in smooth regions [24][25][26].…”

Section: Numerical Dissipation Terms and Filtering Schemementioning

confidence: 99%

“…The interaction of a vortex with the stationary shock is a twodimensional test case which has been studied in several investigations i.e., describing the noise production phenomenon in a turbulent flow [24] or examining the performance of shock capturing methods [26]. Here, the fourth-order compact scheme with the sixth-order numerical dissipation term is used to compute this problem.…”

Section: Shock-vortex Interaction Problemmentioning

confidence: 99%

On application of high-order compact finite-difference schemes to compressible vorticity confinement method

Sadri

Hejranfar

Ebrahimi

2015

Aerospace Science and Technology

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Assessment of WENO schemes for multi‐dimensional Euler equations using GPU

Darian

Esfahanian

2014

Numerical Methods in Fluids

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SUMMARYThis paper presents a detailed study on the implementation of Weighted Essentially Non‐Oscillatory (WENO) schemes on GPU. GPU implementation of up to ninth‐order accurate WENO schemes for the multi‐dimensional Euler equations of gas dynamics is presented. The implementation detail is discussed in the paper. The computational times of different schemes are obtained and the speedups are reported for different number of grid points. Furthermore, the execution times for the main kernels of the code are given and compared with each other. The numerical experiments show the speedups for the WENO schemes are very promising especially for fine grids. Copyright © 2014 John Wiley & Sons, Ltd.

show abstract

A shock-detecting sensor for filtering of high-order compact finite difference schemes

Cited by 28 publications

References 49 publications

Numerical assessment of a shock‐detecting sensor for low dissipative high‐order simulation of shock–vortex interactions

Numerical assessment of a shock‐detecting sensor for low dissipative high‐order simulation of shock–vortex interactions

On application of high-order compact finite-difference schemes to compressible vorticity confinement method

Assessment of WENO schemes for multi‐dimensional Euler equations using GPU

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