A simplified new multigrid algorithm of lattice Boltzmann method for steady states

In the present paper, a new strategy of multigrid method is introduced to accelerate the convergence speed of numerical simulations via lattice Boltzmann method. Based on the popular V-cycle multigrid algorithm, a simplified multigrid algorithm is presented and validated through the simulations of the classic lid-driven cavity flow for steady states. The novelty of the present algorithm resides in the construction of the information transferring process, in which, for a full cycle, the numerical simulation starts on the coarse mesh, transferring to medium mesh and then streams to the fine mesh through a prolongation operator. Afterwards, instead of using a restriction operator, the fluid information jumps back directly from the fine mesh to the coarse mesh via an assignment operator. The accuracy and efficiency of the simplified new algorithm are validated by comparing the results obtained when employing the classic V-cycle multigrid algorithm and the traditional lattice Boltzmann method with uniform Cartesian grid.