Boundary conditions for the Navier-Stoke's equations at an artificial boundary intersecting a solid boundary

The problem where an artificial boundary intersects the surface of a solid body in hypersonic flow is investigated. The analysis is based on two fundamental observations. The first one is the compatibility at the corner. This means that the conditions along the wall must match the conditions along the artificial boundary such that no discontinuities are introduced. Boundary conditions with different degree of compatibility are derived and numerical experiments that confirm the analysis are performed. The second observation is that the linearization procedure, which is the basis for the construction of boundary conditions, must be carried out carefully. It is shown that if the linearization is made around a non-smooth solution new terms enter into the coefficient matrices for the first derivatives. This leads to new characteristic velocities such that two characteristics instead of one enter the domain at an outflow boundary.