Numerical Simulation Model on Irreversibility of Shock-Wave Process

Longhao Huang, Marquette University


The objective of this research is to develop a better understanding of the irreversibilities associated with the shock compaction of matter, especially as a result of impact. Due to complex shock processes, experimentation alone cannot fix the material state, since properties such as internal energy, entropy as well as the shock process are not measurable. Thus, in addition to experimentation, analytical and numerical methods are also used to completely characterize the shock process, although they are restricted by underlying constitutive assumptions. Instead of using artificial irreversibility, such as artificial viscosity to simplify and stabilize the numeric shock model, this work will directly incorporate and solve the correct constitutive relations that describe the sources of irreversibility. Shock wave processes in gas and water are simulated and two equations of state (EOS) are discussed. For a one-dimensional shock wave in gas, results from simulations at two different non-dimensional scales utilizing two different EOS are comparable to the idealized analytical solution and experimental data. Besides, the Mie-Grüneisen (M-G) equation of state, which has been used for solids, is extended to study gas and liquid. The value of Mie-Grüneisen constant, which is a function of atom oscillator frequency and specific volume, is hard to detect from experiment. Based on statistical mechanics, a relationship between the gas Mie-Grüneisen constant and specific heat ratio is derived analytically, which makes Mie-Grüneisen EOS available for gas. The M-G constant is also derived from shock jump condition and Mie-Grüneisen EOS for water and a sensitivity analysis is done based on the simulation result.