Fundamentals of Aerodynamics 2025, 01: Laminar Boundary Layers

For incompressible flow over a flat plate, there is a formalism, the "Blasius Solution". It assumes a 0 angle of attack with constant flow pressures. It utilizes the Blasius equation for differential equations: 2f''' + ff'' = 0, applied to the stream functions u, v. For compressible flow, i.e. at low Mach numbers with constant density, the quantities need to be derived with energy equations in mind, which results in separate differential equations for from the wave equations and from the enthalpy equations. At the stagnation point, the flow velocity is zero, but the flow condition at the edge of the stagnation point boundary layer are given by inviscid flow solutions. Shear stress at the wall and stagnation points is also zero by continuity. Heat transfer scales by geometry

For arbitrary bodies, the solutions must of course be numerical. The standard method for the general case is the "finite-difference solution" applied to

via following approximations after tiling the flow volume.