Finite-volume scheme for the solution of integral boundary layer equations

• Finite volume formulation for solution of steady conservation laws.
• Rotational invariant formulation applicable to unstructured meshes.
• Stabilizing up-wind scheme applicable to mixed-hyperbolic systems.
• Solution of three-dimensional integral boundary layer equations.

An unstructured-mesh finite-volume formulation for the solution of systems of steady conservation laws on embedded surfaces is presented. The formulation is invariant to the choice of local tangential coordinate systems and is stabilized by a novel up-winding scheme applicable also to mixed-hyperbolic systems. The formulation results in a system of non-linear equations which is solved by a quasi-Newton method. While the finite volume scheme is applicable to a range of conservation laws, it is here implemented for the solution of the integral boundary layer equations, as a first step in developing a fully coupled viscous-inviscid interaction method. For validation purposes, integral boundary layer quantities computed using a minimal set of three-dimensional turbulent integral boundary layer equations are compared to experimental data and an established computer code for two-dimensional problems. The validation shows that the proposed formulation is stable, yields a well-conditioned global Jacobian, is conservative on curved surfaces and invariant to rotation as well as convergent with regard to mesh refinement.