Abstract
Smoothed Particle Hydrodynamics (SPH) is typically used for the simulation of shock propagation through solid media, commonly observed during hypervelocity impacts. Although schemes for impacts into monolithic structures have been studied using SPH, problems occur when multimaterial structures are considered. This study begins from a variational framework and builds schemes for multiphase compressible problems, coming from different density estimates. Algorithmic details are discussed and results are compared upon three one-dimensional Riemann problems of known behavior.
Highlights
The Smoothed Particle Hydrodynamics (SPH) numerical method is widely used for the solution of a broad range of shock propagation problems [20]
For hypervelocity impacts into inhomogeneous materials, it is commonly noted that SPH schemes produce large errors when shocks propagate through material interfaces [5, 15, 25, 26]
Three fully compressible SPH schemes have been developed from a standard SPH variational framework and three different SPH density estimates; they all embed a wellknown density - smoothing length - kernel coupling
Summary
The Smoothed Particle Hydrodynamics (SPH) numerical method is widely used for the solution of a broad range of shock propagation problems [20]. For hypervelocity impacts into inhomogeneous materials, it is commonly noted that SPH schemes produce large errors when shocks propagate through material interfaces [5, 15, 25, 26]. Most hypervelocity impact studies with SPH opt for a homogenization of the inhomogeneous structure [7, 6, 26, 30] and neglect reflections and transmissions which occur whenever a shock encounters a material interface [9, 31]. In order to find a treatment coherent to this SPH framework, one needs to recognize that shock propagation through inhomogeneous materials is effectively a multiphase problem; discontinuities appear in density and material parameters. Two questions arise: whether shock propagation through inhomogeneous solids is possible within this general SPH framework; and subsequently which scheme is the most suitable. The behavior of each scheme is analyzed with three one-dimensional tests: an isothermal impact into a material of purely discontinuous density profile, the classical shock-tube benchmark test [21, 28, 29] and an isentropic equivalent of the first test
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