TY - JOUR
T1 - Stability of Finite Difference Discretizations of Multi-Physics Interface Conditions
AU - Björn Sjögreen & Jeffrey W. Banks
JO - Communications in Computational Physics
VL - 2
SP - 386
EP - 410
PY - 2013
DA - 2013/02
SN - 13
DO - http://doi.org/10.4208/cicp.280711.070212a
UR - https://global-sci.org/intro/article_detail/cicp/7227.html
KW - 
AB - <p style="text-align: justify;">We consider multi-physics computations where the Navier-Stokes equations
of compressible fluid flow on some parts of the computational domain are coupled to
the equations of elasticity on other parts of the computational domain. The different
subdomains are separated by well-defined interfaces. We consider time accurate computations resolving all time scales. For such computations, explicit time stepping is
very efficient. We address the issue of discrete interface conditions between the two
domains of different physics that do not lead to instability, or to a significant reduction
of the stable time step size. Finding such interface conditions is non-trivial.<br/>We discretize the problem with high order centered difference approximations with
summation by parts boundary closure. We derive L<sup>2&nbsp;</sup>stable interface conditions for the
linearized one dimensional discretized problem. Furthermore, we generalize the interface conditions to the full non-linear equations and numerically demonstrate their
stable and accurate performance on a simple model problem. The energy stable interface conditions derived here through symmetrization of the equations contain the
interface conditions derived through normal mode analysis by Banks and Sjögreen
in [8] as a special case.</p>