Boundary Conditions for Hyperbolic Systems of Equations on Curved Domains

Our focus in this paper is on the fundamental system of partial differential equation with boundary conditions (the continuous problem) that all types of numerical methods must respect. First, a constant coefficient hyperbolic system of equations which turns into a variable coefficient system of equations by transforming to a non-cartesian domain is considered. We discuss possible formulations of time-dependent boundary conditions leading to well-posed or strongly well-posed problems. Next, we re-use the previous theoretical derivations for the problem with boundary conditions applied at the wrong position and/or with an incorrect normal (a typical result with a less than perfect mesh generator). Possible error sources are discussed and a crude error estimate is derived.