Finite-volume WENO scheme for viscous compressible multicomponent flows

We develop a shock- and interface-capturing numerical method that is suitable for the simulation of multicomponent flows governed by the compressible Navier–Stokes equations. The numerical method is high-order accurate in smooth regions of the flow, discretely conserves the mass of each component, as well as the total momentum and energy, and is oscillation-free, i.e. it does not introduce spurious oscillations at the locations of shockwaves and/or material interfaces. The method is of Godunov-type and utilizes a fifth-order, finite-volume, weighted essentially non-oscillatory (WENO) scheme for the spatial reconstruction and a Harten–Lax–van Leer contact (HLLC) approximate Riemann solver to upwind the fluxes. A third-order total variation diminishing (TVD) Runge–Kutta (RK) algorithm is employed to march the solution in time. The derivation is generalized to three dimensions and nonuniform Cartesian grids. A two-point, fourth-order, Gaussian quadrature rule is utilized to build the spatial averages of the reconstructed variables inside the cells, as well as at cell boundaries. The algorithm is therefore fourth-order accurate in space and third-order accurate in time in smooth regions of the flow. We corroborate the properties of our numerical method by considering several challenging one-, two- and three-dimensional test cases, the most complex of which is the asymmetric collapse of an air bubble submerged in a cylindrical water cavity that is embedded in 10% gelatin

Shock-induced collapse of a bubble inside a deformable vessel

Shockwave lithotripsy repeatedly focuses shockwaves on kidney stones to induce their fracture, partially through cavitation erosion. A typical side effect of the procedure is hemorrhage, which is potentially the result of the growth and collapse of bubbles inside blood vessels. To identify the mechanisms by which shock-induced collapse could lead to the onset of injury, we study an idealized problem involving a preexisting bubble in a deformable vessel. We utilize a high-order accurate, shock- and interfacecapturing, finite-volume scheme and simulate the three-dimensional shock-induced collapse of an air bubble immersed in a cylindrical water column which is embedded in a gelatin/water mixture. The mixture is a soft tissue simulant, 10% gelatin by weight, and is modeled by the stiffened gas equation of state. The bubble dynamics of this model configuration are characterized by the collapse of the bubble and its subsequent jetting in the direction of the propagation of the shockwave. The vessel wall, which is defined by the material interface between the water and gelatin/water mixture, is invaginated by the collapse and distended by the impact of the jet. The present results show that the highest measured pressures and deformations occur when the volumetric confinement of the bubble is strongest, the bubble is nearest the vessel wall and/or the angle of incidence of the shockwave reduces the distance between the jet tip and the nearest vessel surface. For a particular case considered, the 40 MPa shockwave utilized in this study to collapse the bubble generated a vessel wall pressure of almost 450 MPa and produced both an invagination and distention of nearly 50% of the initial vessel radius on a O(10) ns timescale. These results are indicative of the significant potential of shock-induced collapse to contribute to the injury of blood vessels in shockwave lithotripsy

MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver

MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock–bubble interaction, and bubble dynamics. We present the 5- and 6-equation thermodynamically-consistent diffuse-interface models we use to handle such flows, which are coupled to high-order interface-capturing methods, HLL-type Riemann solvers, and TVD time-integration schemes that are capable of simulating unsteady flows with strong shocks. The numerical methods are implemented in a flexible, modular framework that is amenable to future development. The methods we employ are validated via comparisons to experimental results for shock–bubble, shock–droplet, and shock–water-cylinder interaction problems and verified to be free of spurious oscillations for material-interface advection and gas–liquid Riemann problems. For smooth solutions, such as the advection of an isentropic vortex, the methods are verified to be high-order accurate. Illustrative examples involving shock–bubble-vessel-wall and acoustic–bubble-net interactions are used to demonstrate the full capabilities of MFC

MFC: An open-source high-order multi-component, multi-phase, and multi-scale compressible flow solver

MFC is an open-source tool for solving multi-component, multi-phase, and bubbly compressible flows. It is capable of efficiently solving a wide range of flows, including droplet atomization, shock–bubble interaction, and bubble dynamics. We present the 5- and 6-equation thermodynamically-consistent diffuse-interface models we use to handle such flows, which are coupled to high-order interface-capturing methods, HLL-type Riemann solvers, and TVD time-integration schemes that are capable of simulating unsteady flows with strong shocks. The numerical methods are implemented in a flexible, modular framework that is amenable to future development. The methods we employ are validated via comparisons to experimental results for shock–bubble, shock–droplet, and shock–water-cylinder interaction problems and verified to be free of spurious oscillations for material-interface advection and gas–liquid Riemann problems. For smooth solutions, such as the advection of an isentropic vortex, the methods are verified to be high-order accurate. Illustrative examples involving shock–bubble-vessel-wall and acoustic–bubble-net interactions are used to demonstrate the full capabilities of MFC

Simulation of Shock-Induced Bubble Collapse with Application to Vascular Injury in Shockwave Lithotripsy

Shockwave lithotripsy is a noninvasive medical procedure wherein shockwaves are repeatedly focused at the location of kidney stones in order to pulverize them. Stone comminution is thought to be the product of two mechanisms: the propagation of stress waves within the stone and cavitation erosion. However, the latter mechanism has also been implicated in vascular injury. In the present work, shock-induced bubble collapse is studied in order to understand the role that it might play in inducing vascular injury. A high-order accurate, shock- and interface-capturing numerical scheme is developed to simulate the three-dimensional collapse of the bubble in both the free-field and inside a vessel phantom. The primary contributions of the numerical study are the characterization of the shock-bubble and shock-bubble-vessel interactions across a large parameter space that includes clinical shockwave lithotripsy pressure amplitudes, problem geometry and tissue viscoelasticity, and the subsequent correlation of these interactions to vascular injury. Specifically, measurements of the vessel wall pressures and displacements, as well as the finite strains in the fluid surrounding the bubble, are utilized with available experiments in tissue to evaluate damage potential. Estimates are made of the smallest injurious bubbles in the microvasculature during both the collapse and jetting phases of the bubble's life cycle. The present results suggest that bubbles larger than 1 μm in diameter could rupture blood vessels under clinical SWL conditions

Numerical simulation of bubble dynamics in deformable vessels

The growth and collapse of cavitation bubbles has been implicated as a potential damage mechanism leading to the rupture of blood vessels in shock wave lithotripsy (SWL) [Bailey et al., in The Fifth International Symposium on Cavitation, Osaka, Japan (2003)]. While this phenomenon has been investigated numerically, the resulting simulations have often assumed some degree of symmetry and have often failed to include a large number of influential physics, such as viscosity, compressibility, surface tension, phase change, and fluid‐structure interactions (FSI). We present here our efforts to explore the role that cavitation bubbles play in the rupture of blood vessels in SWL and to improve upon the current state of the numerical approach. We have developed a 3‐D, high‐order accurate, shock‐ and interface‐capturing, multicomponent flow algorithm that accounts for the effects of surface tension and FSI. The preliminary results for the case of a bubble collapse, induced by a shock wave lithotripter pulse and occurring inside a deformable vessel, are presented

Effects of Polydispersity in Bubbly Flows

This thesis concerns the dynamics of bubbly flows with a distribution of equilibrium bubble sizes. The main goal is to formulate the physical and numerical models of continuum bubbly flows that enable us to efficiently compute the average mixture dynamics. Numerical simulations are conducted to quantify the effects of bubble size distributions on the averaged dynamics for several model flows. First, the ensemble-averaged conservation laws for polydisperse bubbly flows are derived. One-way-coupled flow computations are conducted to illustrate that the different-sized bubbles can oscillate with different frequencies. The resulting phase cancellations can be regarded as an apparent damping of the averaged dynamics of polydisperse flows. A high-order-accurate finite-volume method is then developed to compute the flow, paying special attention to issues of wave dispersion and stiffness. Next, computations of one-dimensional shock propagation through bubbly liquids are performed. The numerical experiments reveal that the bubble size distribution has a profound impact on the averaged shock structure. If the distribution is sufficiently broad, the apparent damping due to the phase cancellations can dominate over the single-bubble-dynamic dissipation (due to thermal, viscous, and compressibility effects) and the averaged shock dynamics become insensitive to the individual bubble dynamics. One-dimensional cloud cavitation caused by fluid-structure interaction is also solved to investigate the collapse of cavitation clouds with both monodisperse and polydisperse nuclei. The phase cancellations among the cavitation bubbles with broad nuclei size distributions are found to eliminate violent cloud collapse in the averaged dynamics. Finally, shock propagation through a bubbly liquid-filled, deformable tube is considered. The quasi-one-dimensional conservation law that takes into account structural deformation is formulated and steady shock relations are derived. The results are compared to water-hammer experiments; the present shock theory gives better agreement with the measured wave speeds than linear theory. This indicates that the gas-phase nonlinearity needs to be included to accurately predict the propagation speeds of finite-amplitude waves in a deformable tube filled with a bubbly liquid.