Solution of Darcy-Brinkman-Forchheimer Equation for Irregular Flow Channel by Finite Elements Approach

Abstract

The finite element method of solution with curved triangles to solve the three-dimensional, fully-developed Darcy-Brinkman-Forchheimer flow equation in channel with curved side is solved using quasi-linearization and Gauss-Seidel iteration method. Exhaustive numerical computation and numerical experimentation reveals the parameters' influence on the velocity distributions. A salient feature of the method adopted in the present paper is that it ensures that the errors are almost equally distributed among all the nodes. It is found that the irregular cross-section channel with upward concave boundary decelerates the flow. Numerical experimentation involved different order curved triangular elements and extensive computation revealed that the quintic order curved triangular element yields the desired solution to an accuracy of 10-5. The finite element method is found to be very effective in capturing boundary and inertia effects in the three-dimensional, fully-developed flow through porous media. Further, it prevails with regards to giving the required answer for vast estimations of Forchheimer number when shooting technique fails to do as such. The technique can be effortlessly utilized in some other sporadic cross-area channel.