Assessment of a Two-Equation Turbulence Model in the High-Order Flux Correction Scheme

2016 ◽  
Author(s):  
Oisin Tong ◽  
Cole Blakely ◽  
Aaron J. Katz
Keyword(s):  
Turbulence Model ◽  
High Order ◽  
Flux Correction ◽  
Correction Scheme

Simulation of the Transitional Flow in a Low Pressure Gas Turbine Cascade With a High-Order Discontinuous Galerkin Method

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
A. Ghidoni ◽  
A. Colombo ◽  
S. Rebay ◽  
F. Bassi
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Time Integration ◽  
High Order ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Turbine Cascade ◽  
High Reynolds

In the last decade, discontinuous Galerkin (DG) methods have been the subject of extensive research efforts because of their excellent performance in the high-order accurate discretization of advection-diffusion problems on general unstructured grids, and are nowadays finding use in several different applications. In this paper, the potential offered by a high-order accurate DG space discretization method with implicit time integration for the solution of the Reynolds-averaged Navier–Stokes equations coupled with the k-ω turbulence model is investigated in the numerical simulation of the turbulent flow through the well-known T106A turbine cascade. The numerical results demonstrate that, by exploiting high order accurate DG schemes, it is possible to compute accurate simulations of this flow on very coarse grids, with both the high-Reynolds and low-Reynolds number versions of the k-ω turbulence model.

Time dispersion correction for arbitrarily even-order Lax-Wendroff methods and the application on full waveform inversion

Geophysics ◽  
2021 ◽  
pp. 1-89
Author(s):  
Zhiming Ren ◽  
Qianzong Bao ◽  
Bingluo Gu
Keyword(s):  
Waveform Inversion ◽  
Second Order ◽  
High Order ◽  
Full Waveform Inversion ◽  
Dispersion Correction ◽  
Equal Time ◽  
Full Waveform ◽  
Time Dispersion ◽  
Correction Scheme ◽  
Even Order

A second-order accurate finite-difference (FD) approximation is commonly used to approximate the second-order time derivative of wave equation. The second-order accurate FD scheme may introduce time dispersion in wavefield extrapolation. Lax-Wendroff methods can suppress such dispersion by replacing the high-order time FD error-terms with space FD error correcting terms. However, the time dispersion cannot be completely eliminated and the computation cost dramatically increases with increasing order of (temporal) accuracy. To mitigate the problem, we extend the existing time dispersion correction scheme for second- or fourth-order Lax-Wendroff method to a scheme for arbitrary even-order methods, which uses the forward and inverse time dispersion transform (FTDT and ITDT) to add and remove the time dispersion from synthetic data. We test the correction scheme using a homogeneous model and the Sigsbee2A model. Modeling examples suggest that the use of derived FTDT and ITDT pairs on high-order Lax-Wendroff methods can effectively remove time dispersion errors from high-frequency waves while using longer time steps than allowed in low-order Lax-Wendroff methods. We investigate the influence of the time dispersion on full waveform inversion (FWI) and show an anti-dispersion workflow. We apply the FTDT to source terms and recorded traces before inversion, resulting in that the source and adjoint wavefields contain equal time dispersion from source-side wave propagation, and the modeled and observed traces accumulate equal time dispersion from source- and receiver-side wave propagation. Inversion results reveal that the anti-dispersion workflow is capable of increasing the accuracy of FWI for arbitrary even-order Lax-Wendroff methods. Additionally, the high-order method can obtain better inversion results compared to the second-order method with the same anti-dispersion workflow.

A high-order Discontinuous Galerkin solver for the incompressible RANS and k–ω turbulence model equations

2014 ◽  
Vol 98 ◽  
pp. 54-68 ◽  
Author(s):  
F. Bassi ◽  
A. Ghidoni ◽  
A. Perbellini ◽  
S. Rebay ◽  
A. Crivellini ◽  
...  
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
High Order ◽  
Model Equations
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