Numerical N-S equation solver based on adaptive quadtree mesh

A numerical N-S equation solver is presented based on the adaptive quadtree mesh, in which the grid size can be automatically adjusted according to the value of vorticity. In this way, the grid resolution of the interested area can be enhanced without significant increase of the computational time. An unconditionally stable MacCormack numerical scheme is adopted in the model for the advection term and a modified central difference scheme is introduced for the discretization of the Poisson equation. A modified difference scheme is proposed for the viscous term in quadtree mesh frame. The computational results indicate that the numerical solution of the Poisson equation in the model is of second-order accuracy, and the numerical solution of velocity is beyond first-order accuracy. The velocity profile along the central axes in the example of the driven cavity flow agrees with that by Ghia. The drag coefficient and the lift coefficient in the example of flow over a circular cylinder are consistent with those of the experiment. The example of the driven cavity flow also shows that the computational time is effectively reduced by half with the adaptive mesh technique.