UC San Diego

In the extreme event such as air-blast or explosion, strong shocks lead to severe damage and fragmentation in structures. Despite the considerable effort made in recent years, reliable numerical prediction of fragmentation processes in materials and solids under blast loading or shock wave remains challenging. The conventional mesh-based methods (e.g., finite element method (FEM)) are ineffective due to large deformation-induced mesh distortion issues and exhibit non-convergent solutions in fracture problems. The meshfree method, such as reproducing kernel particle method (RKPM), naturally avoids computational difficulties associated with low-quality meshes, allows efficient adaptive refinement, and provides flexible control of smoothness and locality in numerical approximations.

The objective of this work is to develop a computational framework for effective modeling of shock dynamics in fluids and fluid-structure interactive systems. In this work, a stabilized RKPM framework for modeling shock waves in fluids is first 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. 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. The proposed methods, termed MUSCL-SCNI, have been applied to the shock tube problem, compressible flow with vortex, and explosive detonation.

Next, an immersed RKPM formulation is developed for an effective body-unfitted spatial discretization of subdomains in heterogeneous materials and fluid structure interaction (FSI) problems involving complex geometries. RKPM naturally avoids computational challenges associated with low-quality meshes, allows efficient adaptive refinement, and provides flexible control of continuity and locality in the numerical approximations. A variational multiscale immersed method (VMIM) is proposed, where the solution fields are decoupled into coarse- and fine-scales, and the fine-scale solution represents the residual of the coarse-scale equations. Under VMIM, the coupling between different subdomains is done through a volumetric constraint, and the embedment of the fine-scale solution into coarse-scale equations yields a stabilized Galerkin formulation with enhanced stability and accuracy. The proposed method is first applied to modeling heterogeneous materials. It is then further extended to shock wave modeling in the FSI systems, where the meshfree algorithm based on MUSCL-SCNI is employed for ensured stability. Finally, the proposed VMIM is applied to air-blast events simulations.