Toward Numerical Simulations of Compressible Multiphase Flows with Applications to Shockwave Lithotripsy and Richtmyer-Meskov Instability

Abstract

Multiphase flows are ubiquitous in nature and in engineering applications, and encompass a range of phenomena as diverse as the dynamics of bubble clouds, the ablation of human tissue by focused ultrasound, and the impact of ocean waves onto naval structures. Though numerical simulations have become common design and analysis tools in fluid dynamics, current multiphase flow algorithms are still in developmental stages, particularly when the flow is compressible.

In the present talk, a compressible multicomponent flow method is presented and applied to study the non-spherical collapse of gas bubbles in the context of shockwave lithotripsy, a medical procedure in which focused shockwaves are used to pulverize kidney stones. The dynamics of non-spherical bubble collapse are characterized, and the damage potential of the shockwaves emitted upon collapse is evaluated by tabulating the wall pressure. In addition, various properties are compared to available experiments and theory, showing good agreement. Furthermore, by using the present results as boundary conditions for simulations of elastic wave propagation within a kidney stone, a new stone comminution mechanism is proposed. Finally, the application of the current method is discussed for simulations of the Richtmyer-Meshkov instability, in which a shock interacts with a perturbed interface.