DNS 1-2 Computational Details: Difference between revisions
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=DNS Channel Flow= | |||
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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 & 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. An explicit RK45 scheme is used to advance the solution in time. The order of accuracy of the solution changes a function of time, as discussed in | 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 & 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. The resolution is also sufficient to accurately capture the linear dependence of <math>u^+</math> on <math>y^+</math> and the log law as seen in the figure. There is also good agreement in the inner, transition and outer layers with the results of Moser et al. <ref name="moser99"> ''R. D. Moser, J. Kim, J. & N. N. Mansour'', Direct numerical simulation of turbulent channel flow up to <math>Re_\tau=590</math>, Physics of Fluids, 11 (4), 1999</ref> (hereafter, MKM1999) that is shown in the same [[lib:DNS_1-2_computational_#fig2|figure]]. The dashed lines represent the linear (blue) and log-law (green) variation of velocity with respect to <math>y^+</math>. The velocity profile in semi-log scale is given in [[lib:DNS_1-2_quantification_#figure2|figure 3]]. | ||
<div id="fig2"></div> | |||
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|''Figure 2:'' Averaged streamwise velocity profile in the turbulent channel compared with the results of Moser et al. (1999) | |||
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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. --> | ||
== Computation of statistical quantities == | == 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. | 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. For the channel flow, PyFR accumulates the average fields <math>(\bar{u},\bar{p},\overline{\frac{du}{dx}},\ldots)</math>, second-order correlations <math>(\overline{uv},\overline{up},\overline{u\frac{dp}{dx}},\ldots)</math> and third-order correlations <math>(\overline{uuu},\ldots)</math> in the aforementioned process. These statistics are then averaged in the streamwise and spanwise directions. From these statistical quantities, the individual terms in the turbulent stress budget equations are computed. Wall-normal gradients of the averaged quantities are calculated using a cubic spline interpolation. | ||
<!--- Describe how the averages and correlations are obtained from the instantaneous results and how | <!--- Describe how the averages and correlations are obtained from the instantaneous results and how | ||
terms in the budget equations are computed, in particular if there are differences to the proposed | terms in the budget equations are computed, in particular if there are differences to the proposed | ||
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|authors=Arun Soman Pillai, Lionel Agostini | |authors=Arun Soman Pillai, Lionel Agostini, Peter Vincent | ||
|organisation=Imperial College London | |organisation=Imperial College London | ||
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Latest revision as of 09:33, 5 January 2023
DNS Channel Flow
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. The resolution is also sufficient to accurately capture the linear dependence of on and the log law as seen in the figure. There is also good agreement in the inner, transition and outer layers with the results of Moser et al. [3] (hereafter, MKM1999) that is shown in the same figure. The dashed lines represent the linear (blue) and log-law (green) variation of velocity with respect to . The velocity profile in semi-log scale is given in figure 3.
|
| Figure 2: Averaged streamwise velocity profile in the turbulent channel compared with the results of Moser et al. (1999) |
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. For the channel flow, PyFR accumulates the average fields , second-order correlations and third-order correlations in the aforementioned process. These statistics are then averaged in the streamwise and spanwise directions. From these statistical quantities, the individual terms in the turbulent stress budget equations are computed. Wall-normal gradients of the averaged quantities are calculated using a cubic spline interpolation.
- ↑ 1.0 1.1 F.D. Witherden, A.M. Farrington & 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 & P. E. Vincent, Identifying eigenmodes of averaged small-amplitude perturbations to turbulent channel flow, Journal of Fluid Mechanics, 875 (758-780), 2019
- ↑ R. D. Moser, J. Kim, J. & N. N. Mansour, Direct numerical simulation of turbulent channel flow up to , Physics of Fluids, 11 (4), 1999
Contributed by: Arun Soman Pillai, Lionel Agostini, Peter Vincent — Imperial College London
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