For linear initial boundary value problems (IBVPs), the number and type of boundary conditions are independent of the solution. For nonlinear IBVPs, the number and type of boundary conditions varies depending on the particular diagonalization of the boundary term. This raises a number of questions that are addressed in this note. We consider the compressible Euler equations, take the derived boundary term and reformulate it using congruence matrix analysis. This reformulation ensures that the number and placement of boundary conditions for the nonlinear Euler equations are consistent with the ones from the corresponding linearized equations.
Winters et al. (Fri,) studied this question.