Combined finite volume and finite element method for convection-diffusion-reaction equation

A combined finite volume and finite element method is presented for solving the unsteady scalar convection-diffusion-reaction equation in two dimensions. The finite volume method is used to discretize the convection-diffusion-reaction equation. The higher-order reconstruction of unknown quantities at the cell faces is determined by Taylor’s series expansion. To arrive at an explicit scheme, the temporal derivative term is estimated by employing the idea of local expansion of unknown along the characteristics. The concept of the finite element technique is applied to determine the gradient quantities at the cell faces. Robustness and accuracy of the method are evaluated by using available analytical and numerical solutions of the two-dimensional pure-convection, convection-diffusion and convection-diffusion-reaction problems. Numerical test cases have shown that the method does not require any artificial diffusion to improve the solution stability. This paper was recommended for publication in revised form by Associate Editor Dongshin Shin Pramote Dechaumphai received his B.S. degree in Industrial Engineering from Khon-Kaen University, Thailand, in 1974, M.S. degree in Mechanical Engineering from Youngstown State University, USA in 1977, and Ph.D. in Mechanical Engineering from Old Dominion University, USA in 1982. He is currently a Professor of Mechanical Engineering at Chulalongkorn University, Bangkok, Thailand. His research interests are numerical methods, finite element method for thermal stress and computational fluid dynamics analysis. Sutthisak Phongthanapanich received his B.S. degree in Mechanical Engineering from Chiangmai University, Thailand in 1990. He then received his M.S., and Ph.D. degrees in Mechanical Engineering from Chulalongkorn University, Thailand in 2002, and 2006, respectively. He is a Lecturer of Mechanical Engineering Technology at King Mongkut’s University of Technology North Bangkok, Bangkok, Thailand. His research interests are finite element method, finite volume method, mesh generation and adaptation, and shock wave dynamics.