Strong shocks in air blast lead to profound fluid-structure interaction (FSI) and structural damage and fragmentation. These complex phenomena in fluid/solid coupled systems pose considerable difficulties to conventional mesh-based numerical methods. In this work, an immersed Reproducing Kernel Particle Method (RKPM) framework is developed for modeling FSI problems in the shock regime. A variational multiscale approach is employed for the proposed immersed framework, termed variational multiscale immersed method (VMIM). The fine-scale solutions represent the residual of the coarse-scale equations, and the embedment of the fine-scale solutions results in a stabilized Petrov-Galerkin formulation, leading to increased accuracy and enhanced stability in the course-scale solutions. The proposed VMIM also exhibits a better convergence rate comparing to the conventional immersed method with comparable efficiency. The shock-enhanced meshfree algorithm is employed to ensure the enforcement of essential shock physics as well as to control the Gibbs phenomenon due to the shocks. The proposed immersed RKPM method allows an effective body-unfitted spatial discretization for the fluid/solid domains, suitable for the problem involves complex geometry. RKPM also naturally avoids computational challenges associated with low-quality meshes, allows efficient adaptive refinement and provides flexible control of continuity and locality in numerical approximations. Several numerical examples are examined to demonstrate the effectiveness of the proposed method for modeling FSI and air blast problems. To model shocks in fluids, a stabilized RKPM framework for modeling is developed. To capture essential shock physics and to avoid numerical oscillations, a Riemann-enriched smoothed flux divergence with an oscillation limiter is introduced under the stabilized conforming nodal integration (SCNI) framework \[1-2\]. Besides, a flux splitting approach is employed to avoid advection-induced instabilities in fluid modeling, and the Monotonic Upstream-Centered Scheme for Conservation Laws (MUSCL)-type oscillation limiter is employed to avoid over and undershooting of the numerical solution at shock front and to capture moving discontinuities with minimal diffusion \[3\]. The proposed methods, termed MUSCL-SCNI, have been applied to the shock tube problem, compressible flow with vortex, and explosive detonation. The proposed shock-enhanced immersed framework in modeling FSI is applied to the blast event modeling. The concrete block slab under the TNT explosion has been tested, and the satisfactory performance of the proposed method has been obtained. Good agreement has been achieved between the numerical results and experimental data.

References:

\[1\] Roth, M. J., Chen, J. S., Slawson, T. R., Danielson, K. D., “Stable and Flux-Conserved Meshfree Formulation to Model Shocks,” Computational Mechanics, Vol. 57, pp. 773–792, 2016.

\[2\] Roth, M. J., Chen, J. S., Danielson, K. D., Slawson, T. R., “Hydrodynamic Meshfree Method for High-Rate Solid Dynamics using a Rankine-Hugoniot Enhancement in a Riemann-SCNI Framework”, International Journal for Numerical Methods in Engineering, Vol. 108, pp. 1525–1549, 2016.

\[3\] Huang, T. H., Chen, J. S., Wei, H., Roth, M. J., Sherburn J. A., Bishop, J. E., Tupek, M. R., Fang, E. H. “A MUSCL-SCNI Approach for Meshfree Modeling of Shock Waves in Fluids,” Journal of Computational Particle Mechanics, Vol. 7, pp. 329–350, 2020.


A Variational Multiscale Immersed RKPM for Fluid-Structure Interaction in Air Blast

Division / Sponsors: 
Aerospace, Bioengineering, Applied Mechanics, Design Engineering Division, Advanced Energy Systems, Manufacturing Engineering Division, Noise Control and Acoustics, Nondestructive Evaluation, Diagnosis, and Prognosis (NDPD), Nuclear Engineering Division, Process Industries Division, Fluids Engineering, Heat Transfer, Materials, Microelectromechanical Systems, Safety Engineering and Risk Analysis, Computers & Information in Engineering


Paper Proceedings: https://asmedigitalcollection.asme.org/IMECE/IMECE2020/volume/84478

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