Euler Solution Using Cartesian Grid with Least Squares Technique

Abstract

Abstract subdomains exist. They include methods using unstructured meshes, body-fitted curvilinear meshes, and Cartesian meshes. This paper discusses an approach that uses “gridless ” or “meshless ” methods to address the boundary or interface while standard structured grid methods are used everywhere else. The present method uses the Cartesian grid to specify and distribute the computational points on the boundary surface but not to define the geometrical properties. Euler fluxes for the neighbors of cut cells are computed using the gridless method involving a local least-squares curve fit to a “cloud ” of grid points. The boundary conditions implemented on the surface points are automatically satisfied in the process of evaluating the surface values