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An Introduction to the Lattice Grid

The collocated grid and the staggered grid have been heavily implemented for calculations of Navier-Stokes equations. In this work, we present a new conservative lattice grid for solving incompressible flows with the finite-volume method. The name “lattice” is to reflect the pattern of this grid. For example, in the case of 2-D incompressible flows, every node for a velocity vector is surrounded by four pressure nodes, and every pressure node is surrounded by four nodes for a velocity vector. As in the staggered grid, local conservations can be conveniently imposed on the lattice grid. This is illustrated through a simulation of the shear-driven cavity flow with an exact factorization technique on the new grid. In the same numerical example, the compact velocity cell is introduced to simplify the application of boundary conditions. In addition, the developing channel flow, a transient flow of the modified Stokes first problem with the exact solution, and a transient pulsatile channel flow with the exact solution are calculated. Good results are obtained, based on a compressed general-purpose Krylov-subspace iterative solver, GPBiCG(m,l).