A Second-Order Godunov Method for Wave Problems in Coupled Solid-Water-Gas Systems

We present a second-order Godunov method for computing unsteady, one-dimensional wave problems with fracture and cavitation in coupled solid?water?gas systems. The method employs a hydro-elasto-plastic body, the Tait equation, and the ideal gas law for solid, water, and gaseous phases, respectively, and models both fractures and cavities as vacuum zones with distinct borders. The numerical approach utilizes a Lagrangian formulation in conjunction with local solid?water?gas-vacuum Riemann problems, which have unique solutions and can be solved efficiently. The various phases are treated in a unified manner and no supplementary interface conditions are necessary for tracking material boundaries. Calculations are carried out for Riemann problems, wave propagation and reflection in a water?rock?air system, and spallation and cavitation in an explosion?steel?water?gas system. It is shown that the Godunov method has high resolution for shocks and phase interfaces, clearly resolves elastic and plastic waves, and successfully describes onset and propagation of fracture and cavitation zones.

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