Computation of the flow field around arbitrary three-dimensional body geometry using Cartesian grid

Abstract

A finite difference method for the simulation using Cartesian grid is developed. As the body boundary is not necessarily located on the grid points, finite difference formulation near the boundary is critically important. The distance from the adjacent stencils to the body boundary is integrated into the finite difference formulation to satisfy the body boundary conditions. From the stability analysis, it is proved that the mid-term in the dissipation term should be treated implicitly to avoid the severe diffusion number condition. The artificial dissipation term based on the reconstruction that uses a virtual center point gives the most accurate solution near the body boundary. As for the pressure boundary condition, the internal pressure is defined by the least square method to satisfy all the differential calculus along the normal vector to the body boundary should be zero as much as possible around the stencil.