Some Applications Of High-order Finite Volume WENO Schemes To The Numerical Simulation Of Radiation Hydrodynamics

Fusion energy is a new emerging energy source that is abundant, safe, envi-ronmentally acceptable, and potentially economical. Inertial confinement is oneapproach to achieve the controlled fusion. However, the inertial confinement fusion(ICF) implosions are related to the multi-material, compressible fluids with largedeformation. The implosion includes, but not limited to, the strong shock, thehydrodynamic instabilities, and high density ratio interface．A simulation of thesehighly nonlinear and unusually complicated problems is a well-known difculty inmathematics and physics．In physics, the governing equations of the ICF implosionare the radiation hydrodynamic equations, which consist of nonlinear hyperbolicequations, parabolic equations and algebraic equations in mathematics. The gov-erning equations have the properties of strong nonlinearity and stifness, and multiscale. In this research, some typical applications of high-order finite volume WENOschemes in the ICF implosion simulation are investigated. The main steps in oursimulation are as follows．First, the radiation hydrodynamics equation system issplit into the Euler equation and the radiation conduction equation. Then the Eulerfluid equations are solved by the high-order finite volume WENO schemes in onetime step to obtain state variables of next time such as density, velocity and uncor-rected total energy. Finally, the radiation heat conduction equation is solved by thesecond order diference scheme and the corrected total energy is calculated from thenew temperature.The high order FV-WENO schemes is first applied to solving the issues of thehigh density ratio and of the interactions between strong shock waves and contacteddiscontinuity, which are very common in ICF implosion. Results with non-oscillationand high resolution are obtained. The proposed method exhibits the suitabilityfor the simulation of the ICF implosion. Second, combined with the second-orderdiference scheme for the multi-fluid radiation heat conduction equation and thefifth-order FV-WENO scheme for the Euler equations, a Euler fluid software forsimulating the spherical symmetry ICF implosion by the radiation drive is estab- lished. Some ICF implosion experiments is simulated using the developed softwareand reliable results are obtained. The computation speed of our soft is increase bymany times in compared to other reported Euler fluid software. Therefore,the largeamount of quick and repeated numerical experiments can be run in our software,which plays a vital role in the design of ICF ignition target.