Development of explicit and conservative schemes for Lattice Boltzmann equations with adaptive streaming

The Lattice Boltzmann Method (LBM) has several limitations for velocity and temperature. One can consider distribution function in moving frame to overcome these limitations as in PonD. In PonD, values of distribution functions are streamed from off-lattice points, so value estimation is needed. It leads to the implicit and non-conservative numerical scheme. Earlier, for the one-dimensional case, the approach of moments prediction was found, which leads to an explicit and conservative numerical scheme. We apply this approach to the two-dimensional and three-dimensional cases in this work. Requirements to interpolation stencil, quadrature, and Hermite polynomial expansion which guarantee moment matching, conservation, and exact calculation, were studied. The resulting schemes were implemented and tested on several tasks.