An Immersed Volume Method for Large Eddy Simulation of compressible flows

Abstract

AbstractInthisworkatechniquefortreatingcomplexgeometriesinacompressiblecode using staggered non uniform cartesian gridsand finitedifferencemethodis developed. The new method developed is called Immersed Volume Method(IVM) and consists in the application (to each scalar of the Navier Stokesequations) of a finite volume method in the cartesian cells cutted by thecomplex surface geometry. Accurate description of the real three dimensionalgeometry inside the cell volume is preserved by means of triangulated surfacedescription (STL stereolithography) instead of approximating it by a plane.Since in the finite volume method, the geometric quantities of the cutted celllike face’s areas, volume, volume centroid, face’s areas centroids are needed,all these properties are evaluated by means of a specific code developed forthis goal. In the Navier-Stokes solver, the finite volume method is appliedto the cutted cells. The uxes are formulated using a modified version of theadvection upstream splitting method (AUSM) originally proposed by Liouand Steffen. The recontruction of the variables at the cell interfaces, is doneby means of a third order TVD (Total Variation Diminishing) interpolator.This choice is related to the future application of the method to combustorswith complex geometries, and so the limitation of numerical wiggles for the