A new method is presented for the explicit Eulerian finite difference computation of shock capturing problems involving multiple resolved material phases in three dimensions. We solve separately for each phase the equations of fluid dynamics or solid mechanics, using as interface boundary conditions artificially extended representations of the individual phases. For fluids we use a new 3D spatially unsplit implementation of the piecewise parabolic (PPM) method of Colella and Woodward. For solids we use the 3D spatially unsplit Eulerian solid mechanics method of Miller and Colella. Vacuum and perfectly incompressible obstacles may also be employed as phases.A separate problem is the time evolution of material interfaces, which are represented by planar segments constructed with a volume-of-fluid method. The volume fractions are advanced in time using a second-order 3D spatially unsplit advection routine with a velocity field determined by solution of interface-normal two-phase Riemann problems. From the Riemann problem solutions we also determine crossinterface momentum and energy fluxes.The volume fractions in mixed cells may be arbitrarily small, which would ordinarily make the Courant-Friedrichs-Lewy time step stability limit arbitrarily small as well. We overcome this limitation using the mass-redistribution formalism to conservatively redistribute generalized mass in the neighborhood of the split cells. 3D EULERIAN SHOCK CAPTURING METHOD 27We present an application of this method to an explosion contained in a metal can: a reactive fluid (approximating PBX 9404) is encased within an elastic-plastic solid (approximating copper) surrounded by vacuum. Our implementation is in parallel, and with adaptive mesh refinement. c 2002 Elsevier Science (USA)

We present an explicit second-order-accurate Godunov finite difference method for the solution of the equations of solid mechanics in one, two, and three spatial dimensions. The solid mechanics equations are solved in nonconservation form, with the novel application of a diffusion-like correction to enforce the gauge condition that the deformation tensor be the gradient of a vector. Physically conserved flow variables (e.g., mass, momentum, and energy) are strictly conserved; only the deformation gradient field is not. Verification examples demonstrate the accurate capturing of plastic and elastic shock waves across approximately five computational cells. 2D and 3D results are obtained without spatial operator splitting.

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