Stability of Finite Difference Discretizations of Multi-Physics Interface Conditions (Communications in Computational Physics, 2018)
We consider multi-physics computations where the Navier-Stokes equationsof compressible fluid flow on some parts of the computational domain are coupled tothe equations of elasticity on other parts of the computational domain. The differentsubdomains are separated by well-defined interfaces. We consider time accurate computations resolving all time scales. For such computations, explicit time stepping isvery efficient. We address the issue of discrete interface conditions between the twodomains of different physics that do not lead to instability, or to a significant reductionof the stable time step size. Finding such interface conditions is non-trivial.We discretize the problem with high order centered difference approximations withsummation by parts boundary closure. We derive L2 stable interface conditions for thelinearized one dimensional discretized problem. Furthermore, we generalize the interface conditions to the full non-linear equations and numerically demonstrate theirstable and accurate performance on a simple model problem. The energy stable interface conditions derived here through symmetrization of the equations contain theinterface conditions derived through normal mode analysis by Banks and Sjögreenin [8] as a special case.