Simulating laser-fluid coupling and laser-induced cavitation using embedded boundary and level set methods

Abstract

A computational method for simulating thermal cavitation induced by long-pulsed laser is presented. This method accounts for the absorption of laser light by a liquid, the formation of vapor bubbles due to localized heating, and the dynamics of the bubbles and the surrounding liquid. The physical model combines the Euler equations for a compressible inviscid two-phase fluid flow, a reduced form of the radiative transfer equation for laser radiation, and a local thermodynamic model of vaporization. The Euler equations are solved using the FInite Volume method with Exact two-phase Riemann solvers (FIVER). Following this method, numerical fluxes across phase boundaries are computed by constructing and solving one-dimensional bimaterial Riemann problems. The paper focuses on numerical methods for coupling the laser and fluid governing equations and tracking the vapor bubbles. An embedded boundary finite volume method is proposed to solve the laser radiation equation on the same mesh created for the Euler equations, which usually does not resolve the boundary and propagation directions of the laser beam. To impose boundary conditions, ghost nodes outside the laser domain are populated by mirroring and interpolation techniques. The existence and uniqueness of solution are proved for the two-dimensional case, leveraging the special geometry of the laser domain. The order of accuracy of the method is also proved, and verified using numerical tests. A method of latent heat reservoir is proposed to predict the onset of vaporization, which accounts for the accumulation and release of latent heat. A unique challenge associated with long-pulsed laser is that the dynamics of vapor bubbles is driven not only by the inertia of the bubble nuclei, but also by the continuation of vaporization. In this work, the localized level set method is employed to track the bubble surface, and a method of local correction and reinitialization is proposed to account for continuous phase transitions. Several numerical tests are presented to verify the convergence of these methods. Two realistic simulations of laser-induced cavitation are presented at the end, showing that the computational method is able to capture the key phenomena in these events, including non-spherical bubble expansion, shock waves, and the “Moses effect”.