Finite element/volume solution to axisymmetric conservation laws

Authors:
A. Guardone;L. Vigevano
Affiliations:
Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa 34, 20158 Milano, Italy;Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano, Via La Masa 34, 20158 Milano, Italy
Venue:
Journal of Computational Physics
Year:
2007

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Abstract

Conservation laws in axisymmetric geometries are discretized for the first time according to the node-pair framework of Selmin [Comput. Methods Appl. Mech. Eng. 102 (1993) 107-138]. A relation is found linking the node-pair finite element discretization to the finite volume scheme, opening the way to the use of standard finite volume stabilization techniques and high-resolution schemes in the computation of axisymmetric problems. By construction, the treatment of the axis is naturally built-in inside the basic structural elements of the spatial discretization. Numerical results are presented and compared to the exact solution for scalar advection in a source flow, considering both continuous and discontinuous initial profiles. Numerical simulations of compressible flows include the complex dynamical interaction and propagation of waves in a shock-tube experiment and the steady flow at the exit of under-expanded and sonic nozzles. Numerical results are found to agree fairly well with experimental data, demonstrating the validity of the proposed approach.