An Eulerian method for computation of multimaterial impact with ENO shock-capturing and sharp interfaces

Abstract

A technique is presented for the numerical simulation of high-speed multimaterial impact. Of particular interest is the interaction of solid impactors with targets. The computations are performed on a fixed Cartesian mesh by casting the equations governing material deformation in Eulerian conservation law form. The advantage of the Eulerian setting is the disconnection of the mesh from the boundary deformation allowing for large distortions of the interfaces. Eigenvalue analysis reveals that the system of equations is hyperbolic for the range of materials and impact velocities of interest. High-order accurate ENO shock-capturing schemes are used along with interface tracking techniques to evolve sharp immersed boundaries. The numerical technique is designed to tackle the following physical phenomena encountered during impact: (1) high velocities of impact leading to large deformations of the impactor as well as targets; (2) nonlinear wave-propagation and the development of shocks in the materials; (3) modeling of the constitutive properties of materials under intense impact conditions and accurate numerical calculation of the elasto-plastic behavior described by the models; (4) phenomena at multiple interfaces (such as impactor–target, target–ambient and impactor–ambient), i.e. both free surface and surface–surface dynamics. Comparison with Lagrangian calculations is made for the elasto-plastic deformation of solid material. The accuracy of convex ENO scheme for shock capturing, with the Mie–Gruneisen equation of state for pressure, is closely examined. Good agreement of the present finite difference fixed grid results is obtained with exact solutions in 1D and benchmarked moving finite element solutions for axisymmetric Taylor impact.