Immersed Boundary Method Using Ghost Cells in a Three-Dimensional Case

Abstract

When solving numerically gas dynamics problems, one often encounters difficulties in processing regions with complex geometry. Generating consistent computational grids for such areas may be a complex task. The immersed boundary method avoids these problems. The use of this method makes it possible to carry out calculations for bodies with complex geometry, even using structured Cartesian grids. This article discusses an approach to the implementation of the immersed boundary method using ghost cells, that is, those cells in which the calculation of gas-dynamic quantities is required only in order to carry out calculations for neighboring grid cells. Usually these ghost cells do not belong to the computational domain; they can be located completely or almost completely inside the streamlined object. The calculation of gas-dynamic parameters for ghost cells in the three-dimensional case is performed using approximation using data from nearby cells of the computational grid, as well as taking into account the approximation of the boundary conditions. In this article, when calculating the flow around a body, the Neumann boundary condition is considered. The article presents formulas for calculating the scalar and vector gas-dynamic characteristics of a ghost cell based on three points in space with known characteristics and one point on the surface of the streamlined object, at which the boundary condition is approximated. The described approach was verified in the three-dimensional case, in which the computational domain is represented by a rectangular uniform Cartesian grid, and the streamlined object is described by an unstructured surface grid, the cells of which are triangles.

Keywords

• immersed boundary method
• flow around bodies with complex geometry
• ghost cells
• approximation of scalar and vector quantities