Characteristic boundary conditions using ghost cells (GC-CBC) for high-order finite volume simulations of multicomponent Euler gas equations handling near-zero/sonic velocities

Characteristic boundary conditions (CBC) have become standard in the simulation of compressible fluids to impose target values smoothly and control the level of acoustic reflections. While classical CBC methods evolve discrete boundary values in time, structured finite volume codes typically rely on ghost cells to close the numerical scheme (GC-CBC). Within characteristic equations, this requires to use the normal boundary gradient instead of the time derivative to fill the ghost cells at a fixed time. Since this gradient involves the inverse of the characteristic speeds, the present analysis shows that the ghost cell values may blow up near zero and sonic velocities, leading to nonphysical ghost states. To overcome this intrinsic issue, which has not been addressed in previous works, original implementation strategies are presented to stabilize the numerical simulations. The GC-CBC framework is generalized to high-order numerical finite volume methods for multicomponent Euler equations with thermodynamically complex gases. The order of accuracy associated with the boundary condition is also thoroughly assessed, and shown to depend both on the order of the extrapolation polynomial and the number of inner cells used to compute the outgoing waves. The present contribution paves the way for an implementation in a general open-source framework with dynamic mesh adaptation and error control through multi-resolution analysis.