Computation of compressible fluid flow

Abstract

A Cartesian method for steady compressible Euler computations is presented. The proposed method combines the advantages of the conventional Cartesian method and the gridless method while avoiding their shortcomings. A standard finite-volume method is used over the bulk of the computational domain while the gridless method is employed at solid boundaries. This resulted in a flexible and efficient method for complex geometry problems. Two types of cloud points are used for boundary implementation. One is set up to compute Euler fluxes, whereas the other is for boundary conditions implementation and surface value determination. Numerous 2-D test cases involving flow over a single airfoil and flow over multi-component objects are computed. The results compare well with referenced body-fitted curvilinear grid solutions and converge well for the wide range of Mach numbers tested. The formulation is general and is easily extensible to three dimensions. Some preliminary three-dimensional results are presented.