科研成果详情

It was shown previously (Shan, 2010) that the lattice weights of the lattice Boltzmann method are the solutions to an optimization problem subjecting to a set of linear equality and inequality constraints. Here, a solution strategy is developed and complete solutions for such optimization problem are obtained in one-, two-, and three-dimensions up to 9th order. In addition to recovering the well-known lattices, a number of high-order lattices are also discovered for the first time. These lattices can be used to construct high-order lattice Boltzmann schemes for non-equilibrium flow simulation.