Steady solver for incompressible Navier-Stokes equation with automated adaptive mesh refinement using FEniCS

Abstract

This study demonstrates steady incompressible flow over a cylinder section using the finite element method. An open-source framework was used to increase the accuracy of the results of the analysis. The Python-based open-source computing platform FEniCS was used for the problem formulation. The mesh generator used is Gmsh. FEniCS offers automated adaptive mesh refinement and higher-order elements of order three and higher, which produce more accurate results. These features are not available in most FEM software. The problem DFG benchmark 2D-1 in Featflow was analyzed using the open-source framework. The drag and lift coefficients and the pressure difference between the front and back of the cylinder were found and compared with the benchmark values. The results obtained prove that the proposed open-source framework is incredibly effective in solving fluid flow problems. The FEniCS code to perform this DFG 2D-1 benchmark analysis is given in this work. It shows the problem formulation, setting of boundary conditions, and the adaptive solver. Thus, the same open-source framework can be used to analyze any laminar incompressible flow by simply creating a different geometry and varying the flow characteristics and boundary conditions.