Data assimilation of two-dimensional isotropic turbulence by lattice Boltzmann method and local ensemble transform Kalman filter (LBM-LETKF)

Hasegawa, Yuta   ; Onodera, Naoyuki   ; Asahi, Yuichi   ; Idomura, Yasuhiro   

We implemented and investigated the data assimilation (DA) of two-dimensional isotropic turbulence using the lattice Boltzmann method and the local ensemble transform Kalman filter (LBM-LETKF). We carried out the numerical experiment with 256 grids, 256 or less observation points, 10% root mean square (RMS) observation noise in the velocity observation, and 4, 16, or 64 ensemble members. The numerical experiment showed that the accuracy of the LETKF was better than the nudging DA with both dense and sparse observation. The lack of observation points caused the numerical instability in the LETKF, but such a numerical instability can be suppressed by increasing the number of ensemble members. In the sparse observation case (88 observation points) with 64 ensemble members, the root means squared error (RMSE) of the velocity in the LBM-LETKF was smaller than the RMS of the observation noise, while the nudging DA required 3232 observation points to obtain the same accuracy. Overall, the LETKF with sufficiently large number of ensemble members was highly accurate and robust, thus, the LETKF was a good choice for the DA of turbulent flows using the LBM.