Development of a mixed control volume - Finite element method for the advection-diffusion equation with spectral convergence

作者：Piller M^*; Stalio E

来源：Computers & Fluids, 2011, 40(1): 269-279.

DOI：10.1016/j.compfluid.2010.09.026

• Advection-diffusion equation
• Matrix conditioning
• hp-Convergence
• Quadrature free method
• CVFEM

In this paper we attack the problem of devising a finite volume method for computational fluid dynamics and related phenomena which can deal with complex geometries while attaining high-orders of accuracy and spectral convergence at a reasonable computational cost. As a first step towards this end, we propose a control volume finite element method for the solution of the advection-diffusion equation. The numerical method and its implementation are carefully tested in the paper where h- and p-convergence are checked by comparing numerical results against analytical solutions in several relevant test-cases. The numerical efficiency of a selected set of operations implemented is estimated by operation counts, ill-conditioning of coefficient matrices is avoided by using an appropriate distribution of interpolation points and control-volume edges.

• 出版日期2011-1