GPU-enabled ensemble data assimilation for mesh-refined lattice Boltzmann method

\nWe implemented the ensemble data assimilation (DA) method, the local ensemble transform Kalman filter (LETKF), into the mesh-refined lattice Boltzmann method (LBM) for turbulent flows. Both the LETKF and the mesh-refined LBM were fully implemented on GPUs, so that they are efficiently computed on modern GPU-based supercomputers. We examined the DA accuracy against the flow around a cylinder. The result showed that our method enabled accurate DA with spatially- and temporarily-sparse observation data; the error of the assimilated velocity field with the observation interval of τK/2 and the observation resolution D/16 (1.56% of the total computational grids) was smaller than the amplitude of the observation noise, where τK is the period of the Kármán vortex and D is diameter of the square cylinder.\n