Finite Volume adaptive mesh refinement based on graph applied to the Boundary Layer Problem

In physics and fluid mechanics, the boundary layer is the fluid layer in the immediate vicinity of a bounding surface. It is important in many aerodynamic problems. This work presents a numerical simulation of the two-dimensional laminar boundary-layer problem considering a steady incompressible flow with no-slip condition on the surface. The adaptive mesh refinement is performed by Autonomous Leaves Graph in the Finite Volume solution. A modified Hilbert curve algorithm is used to connect and provide the ordering of the graph nodes. Initially, the numerical solution for the flat plate problem is compared to its analytical solution, namely Blasius solution. Next, simulations of the flux around a NACA airfoil shape are presented. Computer experiments show that an adaptive mesh refinement using Autonomous Leaves Graph with the modified Hilbert curve ordering is appropriate for an aerodynamic problem. Finally, results illustrate that the method provides a good trade-off between speed and accuracy.