A hybrid Cartesian grid and gridless method for compressible flows

A hybrid Cartesian grid and gridless method is presented to compute unsteady compressible flows for complex geometries. In this method, a Cartesian grid is used as baseline mesh to cover the computational domain, while the boundary surfaces are addressed using a gridless method. This hybrid method combines the efficiency of a Cartesian grid method and the flexibility of a gridless method for the complex geometries. The developed method is used to compute a number of test cases to validate the accuracy and efficiency of the method. The numerical results obtained indicate that the use of this hybrid method leads to a significant improvement in performance over its unstructured grid counterpart for the time-accurate solution of the compressible Euler equations. An overall speed-up factor of about eight and a saving in storage requirements about one order of magnitude for a typical three-dimensional problem in comparison with the unstructured grid method are demonstrated.