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Detailed CVFEM Algorithm for Three Dimensional Advection-diffusion Problems

E. Tombarević1, V. R. Voller2, I. Vušanović1

University of Montenegro, Faculty of Mechanical Engineering.
University of Minnesota, Department of Civil Engineering.

Computer Modeling in Engineering & Sciences 2013, 96(1), 1-29.


The Control Volume Finite Element Method (CVFEM) combines the geometric flexibility of the Finite Element Method (FEM) with the physical intuition of the Control Volume Method (CVM). These two features of the CVFEM make it a very powerful tool for solving heat and fluid flow problems within complex domain geometries. In solving problems in the two-dimensional domains the development of the CVFEM has been well documented. For the three-dimensional problems, while there is extensive reporting on the details of the numerical approximation, there is relatively sparse information on important issues related to data structure and interpolation. Here, in the context of a general 3D advection-diffusion problem, a step-by-step derivation of the CVFEM is provided. Significant emphasis is placed on clearly defining an appropriate geometric data structure and detailing the key elements required to arrive at the final discrete equation. The performance and operation of the resulting 3D CVFEM scheme is highlighted by comparing its predictions against existing analytical solutions.


Cite This Article

Tombarević, E., Voller, V. R., Vušanović, I. (2013). Detailed CVFEM Algorithm for Three Dimensional Advection-diffusion Problems. CMES-Computer Modeling in Engineering & Sciences, 96(1), 1–29.

cc This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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