A new, simple, and computationally efficient interface capturing scheme based on a diffuse interface approach is presented for simulation of compressible multiphase flows. Multi-fluid interfaces are represented using field variables (interface functions) with associated transport equations that are augmented, with respect to an established formulation, to enforce a selected interface thickness. The resulting interface region can be set just thick enough to be resolved by the underlying mesh and numerical method, yet thin enough to provide an efficient model for dynamics of well-resolved scales. A key advance in the present method is that the interface regularization is asymptotically compatible with the thermodynamic mixture laws of the mixture model upon which it is constructed. It incorporates first-order pressure and velocity non-equilibrium effects while preserving interface conditions for equilibrium flows, even within the thin diffused mixture region. We first quantify the improved convergence of this formulation in some widely used one-dimensional configurations, then show that it enables fundamentally better simulations of bubble dynamics. Demonstrations include both a spherical bubble collapse, which is shown to maintain excellent symmetry despite the Cartesian mesh, and a jetting bubble collapse adjacent a wall. Comparisons show that without the new formulation the jet is suppressed by numerical diffusion leading to qualitatively incorrect results.

The violent collapse of bubble clusters is thought to damage adjacent material in both engineering and biomedical applications. Yet the complexities of the root mechanisms have restricted theoretical descriptions to significantly simplified configurations. Reduced-physics models based upon either homogenization or arrays of idealized spherical bubbles do reproduce important gross cluster-scale features. However, these models neglect detailed local bubble-bubble interactions, which are expected to mediate damage mechanisms. To describe these bubble-scale interactions, we simulate the expansion and subsequent collapse of a hemispherical cluster of 50 bubbles adjacent to a plane rigid wall, explicitly representing both the asymmetric dynamics of each bubble within the cluster and the compressible-fluid mechanics of bubble-bubble interactions. Results show that the collapse propagates inward, as visualized in experiments, and that geometric focusing generates high impulsive pressures. This gross behaviour is nearly independent of the specific arrangement of bubbles within the cluster and matches predictions from the corresponding particle and homogenized models we consider. The peak pressure in the detailed simulations is associated with the centremost bubble, which causes a corresponding peak pressure on the nearby wall. However, the peak pressures in all cases are a small fraction -over a factor of ten times smaller in many cases -of those predicted in the corresponding reduced models. This is due to the enhanced focusing in the homogeneous model and the spherical constraint on each bubble in the particle models assessed. These would be important factors to consider in any subsequent predictions of wall damage based upon reduced models.

SUMMARY A ghost fluid Lattice Boltzmann method (GF‐LBM) is developed in this study to represent complex boundaries in Lattice Boltzmann simulations of fluid flows. Velocity and density values at the ghost points are extrapolated from the fluid interior and domain boundary via obtaining image points along the boundary normal inside the fluid domain. A general bilinear interpolation algorithm is used to obtain values at image points which are then extrapolated to ghost nodes thus satisfying hydrodynamic boundary conditions. The method ensures no‐penetration and no‐slip conditions at the boundaries. Equilibrium distribution functions at the ghost points are computed using the extrapolated values of the hydrodynamic variables, while non‐equilibrium distribution functions are extrapolated from the interior nodes. The method developed is general, and is capable of prescribing Dirichlet as well as Neumann boundary conditions for pressure and velocity. Consistency and second‐order accuracy of the method are established by running three test problems including cylindrical Couette flow, flow between eccentric rotating cylinders and flow over a cylinder in a confined channel. Copyright © 2011 John Wiley & Sons, Ltd.

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Tissue injury during therapeutic ultrasound or lithotripsy is thought, in cases, to be due to the action of cavitation bubbles. Assessing this and mitigating it is challenging since bubble dynamics in the complex confinement of tissues or in small blood vessels are challenging to predict. Simulations tools require specialized algorithms to simultaneously represent strong acoustic waves and shocks, topologically complex liquid-vapor phase boundaries, and the complex viscoelastic material dynamics of tissue. We discuss advances in a simulation tool for such situations. A single-mesh Eulerian solver is used to solve the governing equations. Special sharpening terms maintain the liquid-vapor interface in face of the finite numerical dissipation included in the scheme to accurately capture shocks. A recent enhancement to this formulation has significantly improved this interface capturing procedure, which is demonstrated for simulation of the Rayleigh collapse of a bubble. The solver also transports elastic stresses and can thus be used to assess the effects of elastic properties on bubble dynamics. A shock-induced bubble collapse adjacent to a model elastic tissue is used to demonstrate this and draw some conclusions regarding the injury suppressing role that tissue elasticity might play.