Difference potential method for numerical solving Navier–Stokes equations

A technique for computing $2D$ plane viscous incompressible fluid flow is presented. Its foundation is the difference potential method (DPM), which allows to resolve by own means typical difficulties for this kind of problems associated with boundary conditions. The implicit difference scheme is written on the staggered grid of MAC-type. Time step restriction associated with calculating stability is directly proportional to the grid step and inversely proportional to the Reynolds number. The solution of difference problem on the upper time level is computed by direct technique (without iterations). The algorithm is effective for moderate values of Reynolds number: $\operatorname{Re}\leq1000$. Possibilities of the method are demonstrated on calculating flows in lid-driven cavities of various sections for Reynolds number up to 1600 on uniform rectangular grids $17\times17$, $33\times33$, $65\times65$ and $129\times129$ points.