Direct numerical simulation of the interaction of a laser -induced plasma with isotropic turbulence

In this work, numerical simulations have been used to study laser–induced breakdown in air and interaction of a laser–induced plasma with isotropic turbulence. A parallel compressible Navier–Stokes solver has been developed for the purpose. The solver uses Fourier spectral spatial derivatives, a skew–symmetric representation of the nonlinear terms to suppress aliasing error and a fourth order Runge–Kutta explicit time integration scheme for time advancement. A predictor corrector based shock capturing scheme (Yee et al. 1999) is used to capture strong shock waves obtained as a result of laser energy deposition. A non–linear limiter (Ducross et al. 1999) is used to prevent excessive dissipation of the background turbulence. A logarithmic formulation for the continuity equation is used to stabilize the solution in regions of very low density in the plasma core. Three different models for air with increasing levels of physical complexity are used in the simulations. Both the solution and the corrector step are suitably extended for high temperature flows using data for thermodynamic and transport properties of air (Boulos et al. 1994) under equilibrium conditions. A formal derivation for the above extension is presented. Spherical energy deposition is studied as a model problem to understand some aspects of laser–induced breakdown. A spherically symmetric shock wave is observed to form and propagate into the background. The shock wave is very strong at initial times but in time its intensity decreases due to the radial nature of the problem. Shock formation and propagation is described based on pressure gradients developed in the flow. Shock radius evolution in time is compared to the strong shock solution (Taylor 1950, Sedov 1959) and found to agree well at short times but deviate towards the acoustic limit at longer times. A symmetric reverse flow is observed behind the shock front and is explained based on conservation of mass. Laser–induced breakdown in air is studied using all three simulation models. Evolution of the resulting flow field is classified into formation of a shock wave, its propagation into the background and subsequent collapse of the plasma core. Each phase is studied in detail. Formation and propagation of the shock wave is explained