An immersed volume method for Large Eddy Simulation of compressible flows using a staggered-grid approach

This article suggests a new and efficient method, called Immersed Volume Method (IVM) to compute compressible viscous flows with complex stationary geometries using finite difference codes with a staggered cartesian grid formulation. A background cartesian mesh is generated for each staggered variable and a finite volume approach is adopted in the layer near the immersed boundaries according to the well known cut cell method. Accurate description of the real three-dimensional geometry inside the cut cell volume is preserved by means of a triangulated surface description instead of approximating it by a plane. The overall spatial accuracy of the base solver (2nd order in this article) is preserved by means of high order flux reconstruction in the cut cells. In particular, the code adopted here to test the suggested technique adopts a 2nd order centered scheme in space and 3rd order Runge–Kutta scheme in time. The code is parallelized using domain decomposition and message passing interface. The robustness and accuracy of the method is proved simulating, at first, a laminar flow past a sphere at R e = 50 , 200 , 250 , then a turbulent nonreacting flow past a sphere with a sting at R e = 51 500 and a turbulent premixed, stoichiometric CH 4 / air flame anchored by means of a cubic bluff body at R e = 3200 , both adopting the Large Eddy Simulation approach. Numerical results are compared with available experimental data.