Simulation of spherical layered system compession by shock waves with allowance for radiative heat transfer in different approximation

Abstract

Numerical modeling is one of the basic tools to investigate physical phenomena that occur in materials compressed by shock waves. A study of the behavior of shock waves using simplified models is helpful in the analysis of more complex systems, for instance, in the problems of inertial thermonuclear fusion on laser facilities. Mathematical simulation of the nonstationary radiative heat transfer in a spectral kinetic statement is rather complicated because the system of equations is nonlinear and large in size. Generally, the kinetic transport equation is solved in 7D phase space, which requires huge computational resources. The initial system is often approximated under certain assumptions but this immediately causes questions as to whether the simplified model is applicable to particular calculations. In this study, several economic radiative heat transfer models were implemented in a 2D hydrodynamic code. Based on these models, test calculations were performed to simulate the compression of a layered spherical system by shock waves, taking into account radiative heat transfer. When the shock wave reaches the center of the sphere, it is focused and reflected. In the neighborhood of the focal point of a converging wave, temperature gradients increase; therefore, thermal conduction and radiation become the main mechanisms of energy dissipation to be considered when taking into account heat transfer. Maximum densities and temperatures at the center of the sphere and their average values in its regions were calculated. In addition, the time when shock and heat waves cross the sphere center was determined, and their behavior before and after focusing at the sphere center was estimated. It is shown that solutions to such problems can be found much faster and with adequate accuracy when applying simplified models.