Equivalence Conditions for Finite Volume / Element Discretizations in Cylindrical Coordinates

Abstract. A novel numerical technique for the solution of the compressible flow equations over unstructured grids in a cylindrical reference is presented. The proposed approach is based on a mixed finite volume / finite element method. Equivalence conditions relating the finite volume and the finite element metrics in cylindrical coordinates are derived. Numerical simulations of the explosion and implosion problems for inviscid compressible flows are carried out to evaluate the correctness of the numerical scheme. For the implosion problem, numerical simulations include also the effect of the presence of cylindrical obstacles in the flow field, which have been recently proposed as a mean to modify the shape of a cylindrical converging shock to increase the shock front stability in experimental studies on the sonoluminescence effect. Spherical shock waves are also considered and the modification to the shock geometry due to the presence of a spherical obstacle is evaluated numerically and compared to its cylindrical counterpart.