A hybrid scheme for the numerical simulation of shock/discontinuity problems

Mahmoudnejad, Niloufar; Hoffmann, Klaus A.

doi:10.1080/10618562.2011.632371

Cited by 6 publications

(1 citation statement)

References 44 publications

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“…A challenging problem in the numerical solution of fluid flows is the high accurate simulation of flows contain discontinuities such as shocks. The development of high-order shock-capturing schemes such as weighted essentially nonoscillatory (WENO) schemes [1,2] and their improved variations (such as WENO-M [3], WENO-Z [4] or WENO-AO [5,6]) and also the invention of various hybrid schemes (for instance, see [7][8][9][10][11][12]) are successful efforts in this regard. Another approach for simulation of shock containing flows, which has attracted less attention, is to use nondissipative high-order linear finite difference schemes along with a postprocessing dissipation, known as numerical filtering.…”

Section: Introductionmentioning

confidence: 99%

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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