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

A comparative study on interface-capturing models and schemes to solve bubble dynamics and cavitation

In the context of simulation of bubble dynamics and cavitation, even the simple problem of the collapse of a spherical bubble is challenging to compute accurately with general, three-dimensional, interface-capturing schemes. Difficulties arise from both the physical model of the multicomponent fluid and the discretization scheme. Pathologies associated with each factor are identified and solutions to remedy specific issues are proposed

Investigation of the Energy Shielding of Kidney Stones by Cavitation Bubble Clouds during Burst Wave Lithotripsy

We conduct experiments and numerical simulations of the dynamics of bubble clouds nucleated on the surface of an epoxy cylindrical stone model during burst wave lithotripsy (BWL). In the experiment, the bubble clouds are visualized and bubble-scattered acoustics are measured. In the numerical simulation, we combine methods for modeling compressible multicomponent flows to capture complex interactions among cavitation bubbles, the stone, and the burst wave. Quantitative agreement is confirmed between results of the experiment and the simulation. We observe and quantify a significant shielding of incident wave energy by the bubble clouds. The magnitude of shielding reaches up to 80% of the total acoustic energy of the incoming burst wave, suggesting a potential loss of efficacy of stone comminution. We further discovered a strong linear correlation between the magnitude of the energy shielding and the amplitude of the bubble-scattered acoustics, independent of the initial size and the void fraction of bubble cloud within a range addressed in the simulation. This correlation could provide for real-time monitoring of cavitation activity in BWL

Interface Sharpening in Two-Phase Flows Based on Primitive Sub-Cell Reconstructions

The paper addresses a novel interface-capturing approach for two-phase flows governed by the five-equation diffuse interface model. To suppress the numerical diffusion of the interface, we introduce a primitive sub-cell reconstruction based on volume fractions in neighbouring cells. This reconstruction gives rise to a Riemann problem (CRP) with an additional contact discontinuity, so-called composite Riemann problem, which is stated on mixed cell faces. The CRP solution is used to calculate the numerical flux across cell faces of mixed cells with taking into account the interface reconstructed patterns. A hybrid HLLHLLC method is incorporated to approximate the solution of the CRP. The proposed approach is shown to effectively reduce the interface numerical diffusion without introducing spurious oscillations. Its performance and robustness is examined by 1D and 2D numerical tests

Near-surface dynamics of a gas bubble collapsing above a crevice

The impact of a collapsing gas bubble above rigid, notched walls is considered. Such surface crevices and imperfections often function as bubble nucleation sites, and thus have a direct relation to cavitation-induced erosion and damage structures. A generic configuration is investigated numerically using a second-order-accurate compressible multi-component flow solver in a two-dimensional axisymmetric coordinate system. Results show that the crevice geometry has a significant effect on the collapse dynamics, jet formation, subsequent wave dynamics, and interactions. The wall-pressure distribution associated with erosion potential is a direct consequence of development and intensity of these flow phenomena.Comment: 21 pages, 16 figures, submitted to the Journal of Fluid Mechanic