Design and verification methodology of boundary conditions for finite volume schemes

• We propose a unifying framework for boundary condition implementation.
• We provide a new verification technique for general boundary conditions.
• Our verification method detects ill-posed or unstable boundary conditions.
• Physical insight is necessary to devise consistent boundary conditions.

Despite the critical importance of resolving flow at or near domain boundaries, boundary condition formulations are often implemented in an ad hoc fashion. The purpose of this work is to provide a general framework for the implementation and, importantly, the verification of boundary conditions for node- and cell-centered finite volume schemes. These conditions may include any combination of Dirichlet conditions, Neumann conditions, extrapolation, and the conservation equations themselves. Specific conditions for inviscid walls, inflow, and outflow are systematically tested using manufactured and exact solutions to assess well-posedness and stability. The procedures in this work provide a method for the verification of complex boundary conditions as well as shed physical insight for different problem configurations.