A numerical approach is developed for the simulation of fluid-structure interaction (FSI) problems and is applied to bubble collapse near a deformable wall, the phenomenon responsible for cavitation erosion. The present method is based on a partitioned coupling: The fluid flow is resolved in an in-house finite volume solver and structure dynamics are computed in FEniCS, an open-source finite element solver. Data communication between the two solvers and the space-time coupling of their respective solutions are handled by the coupling library preCICE. The novelty of the present strategy lies in the use of a penalization method to represent the solid body within the fluid solver, allowing the use of a fixed Cartesian grid for increased accuracy and reduced computational cost, as no remeshing is required for moving boundaries. Bubble collapse generates high-intensity shock waves that impact the surrounding wall, resulting in high equivalent stress in the material. When it exceeds the material yield strength, a cavitation pit forms. One-way and two-way coupling simulations are compared in order to demonstrate the need to consider strong coupling for this type of FSI problem. The influence of the initial bubble-wall distance on the resulting material damage is investigated.

This numerical study investigates the collapse of various arrangements of gas bubbles immersed in water in the vicinity of a rigid wall and impacted by a planar shock wave. Multiple bubble configurations, from 2 to 5 bubbles, are compared, focusing primarily on the pressure loads on the wall and the potential amplification in comparison with the single-bubble case. The three-dimensional simulations are performed using a massively parallel compressible diffuse interface solver. The effects of the grid resolution and the mass transfer term are discussed. The main characteristics of the flows are described, and the dynamic behaviors in pressure wave propagation are illustrated. A power-law is proposed for the evolution of the maximum pressure peak on the wall as a function of the density ratio of the bubble array. An amplification of a factor 30 is highlighted for a pyramidal arrangement.

A continuous forcing immersed boundary method (IBM) and a volume penalization method are investigated to simulate compressible viscous flows past an isothermal or adiabatic solid obstacle using a body non-conformal Cartesian grid. The present methods are validated on a large range of flow configurations such as incompressible and compressible flows (steady or unsteady) past isothermal or adiabatic solid obstacles. An adiabatic condition with implicit treatment of the source term is derived for the penalization method, taking advantage of the framework of the ghost-cell methods. Accuracy and computational cost of the methods are discussed. Three-dimensional supersonic flow configurations are carried out with the penalization method. The coupling between the porosity parameter and the different boundary conditions of the present penalization method is investigated in order to properly reproduce the wave reflection on a solid wall. Finally, a new penalization model is designed to improve the shock wave reflection on a solid surface while significantly reducing the computational cost compared to the previous porosity model.

. The aim of this work is to model compressible flows involving shock waves past a solid obstacle using a non-conformal mesh. An Immersed Boundary Method (IBM) with feedback forcing and a volume penalization method are considered and compared. Both methods are validated on various test-cases. Accuracy and computational cost are discussed

We review space and time discretizations of the Cahn-Hilliard equation which are energy stable. In many cases, we prove that a solution converges to a steady state as time goes to infinity. The proof is based on Lyapunov theory and on a Lojasiewicz type inequality. In a few cases, the convergence result is only partial and this raises some interesting questions. Numerical simulations in two and three space dimensions illustrate the theoretical results. Several perspectives are discussed.

SCB is an efficient fluid solver developed for computing two-phase compressible flows involving strong shocks and expansion waves. It solves a four-equation diffuse-interface model, which is derived from the five-equation model proposed by Kapila et al. The governing equations are discretized by a finite volume method with explicit time stepping. SCB uses a fully parallel environment via Message Passing Interfaces (MPI). With the fast growing number of heterogeneous computing platforms including disparate hardware architectures, it becomes nowadays necessary to develop hybrid parallelization strategies with a special care to portability. In this context, we present an heterogeneous computing framework based on MPI library and OpenACC. The choice of OpenACC is discussed. Performances, scalability and adaptability are illustrated through a series of tests on an heterogeneous architecture. Validations are proposed on various bubble collapses, in free-field or near a rigid wall. Comparisons are done with existing results and analytical solutions. Furthermore a stiff shock-induced bubble collapse demonstrates the capabilities and the high potential of the code.

This paper presents a numerical study of the strong loads caused by the collapse of an air bubble immersed in water in the vicinity of a wall and impacted by a normal shock wave. Simulations are performed using an efficient parallel fully compressible two-phase solver based on a homogeneous mixture model. Different configurations are investigated by varying the distance of the initial bubble to the wall. Comparisons are done with exiting results and with two-dimensional simulations highlighting large discrepancies on the computed pressure peaks. The computations show that the stand-off distance has significant effects on the collapse dynamics and the maximum wall pressure leading to potential wall damage. A power-law is proposed for the evolution of the maximum pressure peak as a function of the stand-off distance. Finally, a twin-bubble collapse is computed illustrating collective effects and the amplification of pressure peak at the wall.

We present high-performance and high-accuracy numerical simulations of quantum turbulence modelled by the Gross–Pitaevskii equation for the time-evolution of the macroscopic wave function of the system. The hydrodynamic analogue of this model is a flow in which the viscosity is absent and all rotational flow is carried by quantized vortices with identical topological line-structure and circulation. Numerical simulations start from an initial state containing a large number of quantized vortices and follow the chaotic vortex interactions leading to a vortex-tangle turbulent state. The Gross–Pitaevskii equation is solved using a parallel (MPI-OpenMP) code based on a pseudo-spectral spatial discretization and second order splitting for the time integration. We define four quantum-turbulence simulation cases based on different methods used to generate initial states: the first two are based on the hydrodynamic analogy with classical Taylor–Green and Arnold–Beltrami–Childress vortex flows, while the other two methods use a direct manipulation of the wave function by generating a smoothed random phase field, or seeding random vortex-ring pairs. The dynamics of the turbulent field corresponding to each case is analysed in detail by presenting statistical properties (spectra and structure functions) of main quantities of interest (energy, helicity, etc.). Some general features of quantum turbulence are identified, despite the variety of initial states. Numerical and physical parameters of each case are presented in detail by defining corresponding benchmarks that could be used to validate or calibrate new Gross–Pitaevskii codes. The efficiency of the parallel computation for a reference case is also reported.

We study the numerical solution to two-phase problems using a four-equations model. In particular we focus the present study on HLLC numerical flux approximation and its extensions. These numerical methods are tested on expansion tube cases with a final goal of constructing higher order hybrid numerical tool for solving the problem of bubble collapsing by a shock wave.

This paper presents a numerical study of the interaction between a planar shock wave moving in air with a helium gas bubble. Simulations are performed using a one-fluid inviscid compressible code with different models: a four-equation model, a five-equation model and a multicomponent one. Comparisons are done with experimental data.

Purpose The purpose of this paper is to quantify the relative importance of the multiphase model for the simulation of a gas bubble impacted by a normal shock wave in water. Both the free-field case and the collapse near a wall are investigated. Simulations are performed on both two- and three-dimensional configurations. The main phenomena involved in the bubble collapse are illustrated. A focus on the maximum pressure reached during the collapse is proposed. Design/methodology/approach Simulations are performed using an inviscid compressible homogeneous solver based on different systems of equations. It consists in solving different mixture or phasic conservation laws and a transport-equation for the gas volume fraction. Three-dimensional configurations are considered for which an efficient massively parallel strategy was developed. The code is based on a finite volume discretization for which numerical fluxes are computed with a Harten, Lax, Van Leer, Contact (HLLC) scheme. Findings The comparison of three multiphase models is proposed. It is shown that a simple four-equation model is well-suited to simulate such strong shock-bubble interaction. The three-dimensional collapse near a wall is investigated. It is shown that the intensity of pressure peaks on the wall is drastically increased (more than 200 per cent) in comparison with the cylindrical case. Research limitations/implications The study of bubble collapse is a key point to understand the physical mechanism involved in cavitation erosion. The bubble collapse close to the wall has been addressed as the fundamental mechanism producing damage. Its general behavior is characterized by the formation of a water jet that penetrates through the bubble and the generation of a blast wave during the induced collapse. Both the jet and the blast wave are possible damaging mechanisms. However, the high-speed dynamics, the small spatio-temporal scales and the complicated physics involved in these processes make any theoretical and experimental approach a challenge. Practical implications Cavitation erosion is a major problem for hydraulic and marine applications. It is a limiting point for the conception and design of such components. Originality/value Such a comparison of multiphase models in the case of a strong shock-induced bubble collapse is clearly original. Usually models are tested separately leading to a large dispersion of results. Moreover, simulations of a three-dimensional bubble collapse are scarce in the literature using such fine grids.