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Hasegawa, Yuta; Onodera, Naoyuki; Asahi, Yuichi; Ina, Takuya; Imamura, Toshiyuki*; Idomura, Yasuhiro
Fluid Dynamics Research, 55(6), p.065501_1 - 065501_25, 2023/11
Times Cited Count：0 Percentile：0.01(Mechanics)We investigate the applicability of the data assimilation (DA) to large eddy simulations (LESs) based on the lattice Boltzmann method (LBM). We carry out the observing system simulation experiment of a two-dimensional (2D) forced isotropic turbulence, and examine the DA accuracy of the nudging and the local ensemble transform Kalman filter (LETKF) with spatially sparse and noisy observation data of flow fields. The advantage of the LETKF is that it does not require computing spatial interpolation and/or an inverse problem between the macroscopic variables (the density and the pressure) and the velocity distribution function of the LBM, while the nudging introduces additional models for them. The numerical experiments with 
grids and 10% observation noise in the velocity showed that the root mean square error of the velocity in the LETKF with 
observation points (
of the total grids) and 64 ensemble members becomes smaller than the observation noise, while the nudging requires an order of magnitude larger number of observation points to achieve the same accuracy. Another advantage of the LETKF is that it well keeps the amplitude of the energy spectrum, while only the phase error becomes larger with more sparse observation. From these results, it was shown that the LETKF enables robust and accurate DA for the 2D LBM with sparse and noisy observation data.
Hasegawa, Yuta; Onodera, Naoyuki; Asahi, Yuichi; Idomura, Yasuhiro
Dai-36-Kai Suchi Ryutai Rikigaku Shimpojiumu Koen Rombunshu (Internet), 5 Pages, 2022/12
This study implemented and tested the ensemble data assimilation (DA) of turbulent flows using the lattice Boltzmann method and the local ensemble transform Kalman filter (LBM-LETKF). The computational code was implemented fully on GPUs. The test was carried out for the 3D turbulent flow around a square cylinder with 
meshes and 32 ensemble members using 32 GPUs. The time interval of the DA in the test was a half of the period of the Kalman vortex shedding. The normalized mean absolute errors (NMAE) of the lift coefficient were 132%, 148%, and 13.2% for the non-DA case, the nudging case (a simpler DA algorithm), and the LETKF case, respectively. It was found that the LETKF achieved good DA accuracy even though the observation was not frequent enough for the small scale turbulence, while the nudging showed systematic delays in its solution, and could not keep the DA accurately.
Hasegawa, Yuta; Onodera, Naoyuki; Asahi, Yuichi; Idomura, Yasuhiro
Keisan Kogaku Koenkai Rombunshu (CD-ROM), 27, 4 Pages, 2022/06
We developed GPU implementation of ensemble data assimilation (DA) using the local ensemble transform Kalman filter (LETKF) with the lattice Boltzmann method (LBM). The performance test was carried out upto 32 ensembles of two-dimensional isotropic turbulence simulations using the D2Q9 LBM. The computational cost of the LETKF was less than or nearly equal to that of the LBM upto eight ensembles, while the former exceeded the latter at larger ensembles. At 32 ensembles, their computational costs per cycle were respectively 28.3 msec and 5.39 msec. These results suggested that further speedup of the LETKF is needed for practical 3D LBM simulations.
Hasegawa, Yuta; Onodera, Naoyuki; Asahi, Yuichi; Idomura, Yasuhiro
no journal, ,
We implemented an ensemble data assimilation called local ensemble transform Kalman Filter (LETKF) into the turbulent flow simulation based on Lattice Boltzmann Method (LBM). The code was implemented on GPU, using CUDA for the LBM, and cuBLAS/cuSOLVER libraries for the matrix calculation and eigenvalue decomposition in the LETKF. The data assimilation experiment was carried out on the two-dimensional isotropic turbulence. The experiment showed that the LETKF realized more accurate results compared with the nudging, which is a simple data assimilation scheme.
Hasegawa, Yuta; Idomura, Yasuhiro; Onodera, Naoyuki; Asahi, Yuichi
no journal, ,
The authors are developing a lattice Boltzmann method-local ensemble transformed Kalman filter (LBM-LETKF) to enable the ensemble data assimilation for turbulence with GPUs. The state vector (simulation variables) and observation vector (quantities that can be measured from experiments) have a significant impact on the performance of LETKF: as the state vector, the na
ve method uses a 27-elements vector composed of the LBM velocity distribution functions. However, it is also possible to use the 4-elements vector of macroscopic quantities composed of density and velocity. In this study, we compare the calculation accuracy and speed of the above two methods and select a state vector suitable for turbulence data assimilation.
Hasegawa, Yuta; Idomura, Yasuhiro; Onodera, Naoyuki
no journal, ,
Towards the digital twin of the wind environment of urban cities, the authors are developing the GPU-oriented efficient fluid dynamics and data assimilation code. We are implementing the lattice Boltzmann method (LBM), which is a fully explicit scheme and thus scalable for large-scale simulations, as a scheme to analyze fluid dynamics. The local ensemble transform Kalman filter (LETKF), which is widely used and applied to large-scale data assimilation with CPU-based supercomputers in the meteorological community, is adopted as a data assimilation method. In this presentation, we show the validation results of the LBM-LETKF against basic two-dimensional and three-dimensional turbulence systems, and discuss the accuracy of the data assimilation and the computing performance of the GPU implementation.
