Simulation of incompressible viscous flow on cartesian grid for arbitrary geometries composed of non-watertight polygon elements

A useful computational method was proposed for an incompressible viscous flow simulation around arbitrary geometries on a Cartesian grid system. This method has a remarkable feature that allows us to simulate the flow around geometries which are composed of non-watertight and incomplete polygon elements without any repair. The proposed method can reduce manpower drastically in the process of the mesh generation because the repair of the defective polygon elements can be eliminated. In this method, governing equations are discretized using the extrapolated velocity to satisfy the no-slip condition on the wall surface taking into account the distance between the polygons and the cell center on the Cartesian grid. Moreover, this approach has a higher accuracy of shape approximation compared with the voxel method. In this paper, four different cases were calculated to validate the proposed method. Firstly, the flow around an inclined plate thinner than the mesh size was calculated to show that this method can simulate the flow around the nonwatertight geometry. Additionally, in this case, the accuracy of shape approximation was compared between the proposed method and the voxel method. Sencondly and thirdly, flows around a circular cylinder (/?e=40, 100) were calculated to confirm the accuracy of solutions in the steady and unsteady flows. Finally, an internal flow in a curved duct was calculated to compare the solutions with other researcher's results including the experiment. Consequently, it was found that the proposed method could simulate the flow around the non-watertight geometry and this method had the reasonably good accuracy compared with the literature.