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From the same paper as the previous 3 slides.
The implosion of a submerged, gas-filled structure is a transient, high-speed, fluid-structure interaction problem characterized by ultrahigh compressions, shock waves, large structural displacements and deformations, and self- contact. Hence, the development of a computational approach for this problem is a formidable challenge. It requires incorporating in the computations material failure models, capturing the precise effects on the pressure peaks of many factors such as the rate of structural collapse, and accounting for the various interactions between the external fluid, the nonlinear structure, and the internal gas. Recently, a coupled fluid-structure computational framework that carefully addresses these challenges was presented in Farhat et al. [2012] and Wang et al. [2011, 2012].
The semi-discrete fluid and structure subsystems are time-integrated by an Eulerian version of the second-order implicit-explicit staggered time-integrator described in Farhat et al. [2010]. In this coupled time-discretization algorithm, the semi-discrete fluid subsystem is time-integrated using the second-order three-point implicit backward difference formula and the semi-discrete structural subsystem is time-integrated using the second-order central difference scheme. This state-of-the-art loosely-coupled time-integrator was proved to deliver second-order time-accuracy and shown to possess excellent numerical stability properties thanks to its carefully designed coupling mechanisms.
The computational framework summarized above was implemented in the massively parallel AERO Suite of Codes (Farhat et al. [2003], Geuzaine et al. [2003]). It was also verified and validated for several large-scale, highly nonlinear applications associated with marine and aerospace engineering (e.g., see Wang et al. [2011, 2012]). It is applied here to simulate the implosion experiment displayed here.
References:
Farhat, C., Gerbeau, J.-F., Rallu, A., 2012. FIVER: A finite volume method based on exact two-phase Riemann problems and sparse grids for multi-material flows with large density jumps. J. Comput. Physics 231, 6360-6379.
Wang, K., Rallu, A., Gerbeau J.-F., Farhat C., 2011. Algorithms for interface treatment and load computation in embedded boundary methods for fluid and fluid-structure interaction problems. Int’l J. Num. Methods Fluids 67, 1175–1206.
Wang, K., Gretarsson, J., Main, A., and Farhat, C., 2012. Computational algorithms for tracking dynamic fluid-structure interfaces in embedded boundary methods. Int’l J. Num. Methods Fluids 70, 515–535.
Farhat, C., Geuzaine, P., Brown G., 2003. Application of a three-field nonlinear fluid-structure formulation to the prediction of the aeroelastic parameters of an F-16 fighter. Comput. Fluids 32, 3–29.
Geuzaine, P., Brown, G., Harris, C. and Farhat, C., 2003. Aeroelastic dynamic analysis of a full F-16 configuration for various flight conditions. AIAA J. 41, 363-371.
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