High order conservative differencing for viscous terms and the application to vortex-induced vibration flows

Shen, Yiqing; Zha, Gecheng; Chen, Xiangying

doi:10.1016/j.jcp.2009.08.004

Cited by 70 publications

(11 citation statements)

References 52 publications

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“…The time-dependent, compressible Reynolds-averaged Navier-Stokes equations are formulated in a generalized coordinate system. The 5th order weighted essentially nonoscillatory (WENO) scheme [15] is used to discretize the inviscid components, while the 4th order central differencing [16] is employed for the viscous terms. Time integration is achieved by dual-time stepping with sufficient sub-iterative convergence, which results in a second-order accuracy.…”

Section: Methodsmentioning

confidence: 99%

An Entropy-Assisted Shielding Function in DDES Formulation for the SST Turbulence Model

Zhou

Zhao

Shi

2017

Entropy

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Abstract:The intent of shielding functions in delayed detached-eddy simulation methods (DDES) is to preserve the wall boundary layers as Reynolds-averaged Navier-Strokes (RANS) mode, avoiding possible modeled stress depletion (MSD) or even unphysical separation due to grid refinement. An entropy function f s is introduced to construct a DDES formulation for the k-ω shear stress transport (SST) model, whose performance is extensively examined on a range of attached and separated flows (flat-plate flow, circular cylinder flow, and supersonic cavity-ramp flow). Two more forms of shielding functions are also included for comparison: one that uses the blending function F 2 of SST, the other which adopts the recalibrated shielding function f d_cor of the DDES version based on the Spalart-Allmaras (SA) model. In general, all of the shielding functions do not impair the vortex in fully separated flows. However, for flows including attached boundary layer, both F 2 and the recalibrated f d_cor are found to be too conservative to resolve the unsteady flow content. On the other side, f s is proposed on the theory of energy dissipation and independent on from any particular turbulence model, showing the generic priority by properly balancing the need of reserving the RANS modeled regions for wall boundary layers and generating the unsteady turbulent structures in detached areas.

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Section: Methodsmentioning

confidence: 99%

An Entropy-Assisted Shielding Function in DDES Formulation for the SST Turbulence Model

Zhou

Zhao

Shi

2017

Entropy

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“…In the current work since there is no shock in the flow, the ǫ = 0.3 is used. The viscous terms are discretized by a fully conservative fourth-order accurate finite central differencing scheme suggested by Shen et al [16,17].…”

Section: The 5th Order Weno Schemementioning

confidence: 99%

Simulation of Airfoil Stall Flows Using IDDES with High Order Schemes

Yang

Zha

2016

46th AIAA Fluid Dynamics Conference

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The IDDES(Improved Delayed Detached Eddy Simulation) turbulence modeling is validated with the flat plate boundary layer and is used to investigate the stall flows of NACA0012 airfoil. The spatially filtered unsteady 3D Navier-Stokes equations are solved using a 5th order WENO reconstruction with a low diffusion E-CUSP scheme for the inviscid fluxes and a conservative 4th order central differencing for the viscous terms. Validation and comparison of 3D flat plate flows are conducted at different Mach numbers, Reynolds numbers and mesh sizes using the Spalart-Allmaras(S-A) model, DES97, DDES and IDDES. The study indicates that the IDDES is accurate to predict the velocity profile in the turbulent boundary layer regardless of the mesh size, whereas model stress depletion and log layer mismatch are observed in the DES97 and DDES computations.Stalled flows of the NACA0012 airfoil at four different angle of attacks of 5 • , 17 • , 45 • , 60 • are simulated to investigate the capability of the IDDES to resolve massive separated turbulent flow structures. At high angle of attack(AoA), the airfoil lift and drag coefficients calculated by IDDES are much more accurate than those of the URANS results using S-A turbulence model. The S-A model over-predicts the drag coefficient by about 30%, whereas the IDDES accurately predicts the drag coefficient. For the massive separated flows, more realistic voritcal and spanwise flow structures are resolved by the IDDES simulation.

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“…The computation domain is taken to be OEx; y D OE0; 200 OE 20; 20. The inflow is specified with a hyperbolic tangent profile, The fourth-order central difference scheme [20] is used for the viscous terms. The uniform grids with the same grid number of 321 81 in [19] are used.…”

Section: Shock/shear Layer Interactionmentioning

confidence: 99%

Multistep weighted essentially non‐oscillatory scheme

Shen

Liu

Yang

2014

Numerical Methods in Fluids

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SUMMARYA fifth-order accurate multistep weighted essentially non-oscillatory (WENO) scheme is constructed in this paper. Different from the traditional WENO schemes, which are designed to have (2r 1/th order accuracy in the smooth regions directly from r candidate stencils, the new scheme is constructed through (r 1/ weighting steps. In each step, only two neighboring stencils are used to construct the intermediate fluxes (or the final flux), which are only one order higher than the fluxes obtained from the previous step. Henrick's mapping function is used in each step to satisfy the sufficient condition of fifth-order convergence for a fifth-order WENO scheme; hence, the new scheme is fifth-order accurate in smooth regions. The distinctive advantage of the new scheme is that it can improve the accuracy by one order higher than the traditional WENO schemes at transition points (connecting a smooth region and a discontinuity point); and hence, it improves the accuracy in the regions near discontinuities. Numerical examples show that the new scheme is robust and is less dissipative than the traditional fifth-order WENO schemes.

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High order conservative differencing for viscous terms and the application to vortex-induced vibration flows

Cited by 70 publications

References 52 publications

An Entropy-Assisted Shielding Function in DDES Formulation for the SST Turbulence Model

An Entropy-Assisted Shielding Function in DDES Formulation for the SST Turbulence Model

Simulation of Airfoil Stall Flows Using IDDES with High Order Schemes

Multistep weighted essentially non‐oscillatory scheme

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