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

Abstract

In Physics and Fluid Mechanics, the Boundary Layer is a fluid layer in the neighborhood of a surface. This phenomena is important in many disciplines, mainly in aerodynamics. This paper presents a two-dimensional numerical simulation of this problem considering a incompressible laminar flux in steady state with non-slip condition. A adaptive mesh refinement is carried out by the Autonomous Leaves Graph (ALG) with finite volume discretizations. The Modified Hilbert Curve is implemented to traverse and provide the total ordering of the finite volumes that compose the domain. The numerical solution of the flat plate problem is compared with the Blasius Solution. Besides, flux simulations are presented around a airfoil NACA four digits. The results show evidences that the scheme is adequate in terms of performance and accuracy.