DNS 1-2 Computational Details: Difference between revisions
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== Computational approach == | == Computational approach == | ||
The computations are performed using [http://pyfr.org PyFR] version 1.12.0, a python based framework for solving advection-diffusion type problems using the Flux Reconstruction approach of Huynh. The details of the numerical approach are available [https://www.sciencedirect.com/science/article/pii/S0010465514002549 here]. | The computations are performed using [http://pyfr.org PyFR] version 1.12.0, a python based framework for solving advection-diffusion type problems using the Flux Reconstruction approach of Huynh. The details of the numerical approach are available [https://www.sciencedirect.com/science/article/pii/S0010465514002549 here]<ref name="witherden2014">'''F.D. Witherden, A.M. Farrington and P.E. Vincent''', PyFR: An open source framework for solving advection–diffusion type problems on streaming architectures using the flux reconstruction approach, Computer Physics Communications, 185 (3028-2040), 2014</ref>. | ||
<!-- Provide an overview of the numerical method/setup used for the computation of the DNS or | <!-- Provide an overview of the numerical method/setup used for the computation of the DNS or | ||
LES database. This includes a description of the spatial and temporal discretisation, order | LES database. This includes a description of the spatial and temporal discretisation, order | ||
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== Spatial and temporal resolution, grids == | == Spatial and temporal resolution, grids == | ||
The domain is discretised into <math>62\times29\times60</math> hexahedral elements. For a polynomial order of 5, this yields 174 solution points in the transverse direction and about <math>23\times10^6</math> in total. The grid is uniform in the spanwise and streamwise directions, but clustered near the walls in transverse direction.Iyer et al. (2019) observed that the grid resolution and polynomial order used in these calculations are sufficient enough to guarantee mesh independence of velocity statistics. | The domain is discretised into <math>62\times29\times60</math> hexahedral elements. For a polynomial order of 5, this yields 174 solution points in the transverse direction and about <math>23\times10^6</math> in total. The grid is uniform in the spanwise and streamwise directions, but clustered near the walls in transverse direction. Iyer et al. (2019)<ref name="iyer2019">'''A. Iyer, F. D. Witherden, S. I. Chernyshenko and P. E. Vincent''', Identifying eigenmodes of averaged small-amplitude perturbations to turbulent channel flow, Journal of Fluid Mechanics, 875 (758-780), 2019</ref> observed that the grid resolution and polynomial order used in these calculations are sufficient enough to guarantee mesh independence of velocity statistics. | ||
An explicit RK45 scheme is used to advance the solution in time. The order of accuracy of the solution changes as a function of time, as discussed in | An explicit RK45 scheme is used to advance the solution in time. The order of accuracy of the solution changes as a function of time, as discussed in Witherden et al. (2014)<ref name="witherden2014"/>. The grid used for the simulations is available on the [http://kbwiki-data.s3-eu-west-2.amazonaws.com/DNS-1/2/Channel_180/Channel-180.pyfrm ERCOFTAC database]. | ||
<!-- Discuss the resolution of the simulation. If possible, relate it to the spectral accuracy. Indicate the | <!-- Discuss the resolution of the simulation. If possible, relate it to the spectral accuracy. Indicate the | ||
dependence of the formal accuracy of the code to the quality of the mesh. Discuss the procedure for the a priori estimation of the grid resolution. Finally, provide the grids used for the study. --> | dependence of the formal accuracy of the code to the quality of the mesh. Discuss the procedure for the a priori estimation of the grid resolution. Finally, provide the grids used for the study. --> | ||
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approach in Introduction.--> | approach in Introduction.--> | ||
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===== References ===== | |||
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Revision as of 14:09, 6 October 2021
Computational Details
Computational approach
The computations are performed using PyFR version 1.12.0, a python based framework for solving advection-diffusion type problems using the Flux Reconstruction approach of Huynh. The details of the numerical approach are available here[1].
Spatial and temporal resolution, grids
The domain is discretised into hexahedral elements. For a polynomial order of 5, this yields 174 solution points in the transverse direction and about in total. The grid is uniform in the spanwise and streamwise directions, but clustered near the walls in transverse direction. Iyer et al. (2019)[2] observed that the grid resolution and polynomial order used in these calculations are sufficient enough to guarantee mesh independence of velocity statistics.
An explicit RK45 scheme is used to advance the solution in time. The order of accuracy of the solution changes as a function of time, as discussed in Witherden et al. (2014)[1]. The grid used for the simulations is available on the ERCOFTAC database.
Computation of statistical quantities
PyFR computes volumetric time average quantities by accumulating averages every 50 time steps over a prescribed time period, which is 100 time units for the channel flow simulations. The average calculation is started after 3000 convective time unit in windowed mode. The outputs from the different averaging windows are then combined together.
In the case of channel flow, averages are further reduced to one-dimensional data by spatial averaging in the homogeneous streamwise and spanwise directions.
References
- ↑ 1.0 1.1 F.D. Witherden, A.M. Farrington and P.E. Vincent, PyFR: An open source framework for solving advection–diffusion type problems on streaming architectures using the flux reconstruction approach, Computer Physics Communications, 185 (3028-2040), 2014
- ↑ A. Iyer, F. D. Witherden, S. I. Chernyshenko and P. E. Vincent, Identifying eigenmodes of averaged small-amplitude perturbations to turbulent channel flow, Journal of Fluid Mechanics, 875 (758-780), 2019
Contributed by: Arun Soman Pillai, Lionel Agostini — Imperial College London
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