Commun. Comput. Phys., 13 (2013), pp. 386-410.

Stability of Finite Difference Discretizations of Multi-Physics Interface Conditions

Bjorn Sjogreen 1*, Jeffrey W. Banks 1

1 Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, CA 94551, USA.

Received 28 July 2011; Accepted (in revised version) 7 February 2012
Available online 28 June 2012


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. We discretize the problem with high order centered difference approximations with summation by parts boundary closure. We derive L^2 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 Sjogreen in [8] as a special case.

AMS subject classifications: 65M06, 65M12, 74F10

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Key words: Fluid-structure interaction, finite difference method, summation by parts, multi-physics interface condition.

*Corresponding author.
Email: (B. Sjogreen), (J. W. Banks)

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