A Nitsche-based cut finite element method for a fluid--structure interaction problem

We present a new composite mesh finite element method for fluid--structure interaction problems. The method is based on surrounding the structure by a boundary-fitted fluid mesh which is embedded into a fixed background fluid mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The coupling between the embedded and background fluid meshes is enforced using a stabilized Nitsche formulation which allows us to establish stability and optimal order \emph{a priori} error estimates, see~\cite{MassingLarsonLoggEtAl2013}. We consider here a steady state fluid--structure interaction problem where a hyperelastic structure interacts with a viscous fluid modeled by the Stokes equations. We evaluate an iterative solution procedure based on splitting and present three-dimensional numerical examples.Comment: Revised version, 18 pages, 7 figures. Accepted for publication in CAMCo

Cavitation Induction by Projectile Impacting on a Water Jet

The present paper focuses on the simulation of the high-velocity impact of a projectile impacting on a water-jet, causing the onset, development and collapse of cavitation. The simulation of the fluid motion is carried out using an explicit, compressible, density-based solver developed by the authors using the OpenFOAM library. It employs a barotropic two-phase flow model that simulates the phase-change due to cavitation and considers the co-existence of non-condensable and immiscible air. The projectile is considered to be rigid while its motion through the computational domain is modelled through a direct-forcing Immersed Boundary Method. Model validation is performed against the experiments of Field et al. [Field, J., Camus, J. J., Tinguely, M., Obreschkow, D., Farhat, M., 2012. Cavitation in impacted drops and jets and the effect on erosion damage thresholds. Wear 290–291, 154–160. doi:10.1016/j.wear.2012.03.006. URL http://www.sciencedirect.com/science/article/pii/S0043164812000968 ], who visualised cavity formation and shock propagation in liquid impacts at high velocities. Simulations unveil the shock structures and capture the high-speed jetting forming at the impact location, in addition to the subsequent cavitation induction and vapour formation due to refraction waves. Moreover, model predictions provide quantitative information and a better insight on the flow physics that has not been identified from the reported experimental data, such as shock-wave propagation, vapour formation quantity and induced pressures. Furthermore, evidence of the Richtmyer-Meshkov instability developing on the liquid-air interface are predicted when sufficient dense grid resolution is utilised

Modelling the Interfacial Flow of Two Immiscible Liquids in Mixing Processes

This paper presents an interface tracking method for modelling the flow of immiscible metallic liquids in mixing processes. The methodology can provide an insight into mixing processes for studying the fundamental morphology development mechanisms for immiscible interfaces. The volume-of-fluid (VOF) method is adopted in the present study, following a review of various modelling approaches for immiscible fluid systems. The VOF method employed here utilises the piecewise linear for interface construction scheme as well as the continuum surface force algorithm for surface force modelling. A model coupling numerical and experimental data is established. The main flow features in the mixing process are investigated. It is observed that the mixing of immiscible metallic liquids is strongly influenced by the viscosity of the system, shear forces and turbulence. The numerical results show good qualitative agreement with experimental results, and are useful for optimisating the design of mixing casting processes

Stable cell-centered finite volume discretization for Biot equations

In this paper we discuss a new discretization for the Biot equations. The discretization treats the coupled system of deformation and flow directly, as opposed to combining discretizations for the two separate sub-problems. The coupled discretization has the following key properties, the combination of which is novel: 1) The variables for the pressure and displacement are co-located, and are as sparse as possible (e.g. one displacement vector and one scalar pressure per cell center). 2) With locally computable restrictions on grid types, the discretization is stable with respect to the limits of incompressible fluid and small time-steps. 3) No artificial stabilization term has been introduced. Furthermore, due to the finite volume structure embedded in the discretization, explicit local expressions for both momentum-balancing forces as well as mass-conservative fluid fluxes are available. We prove stability of the proposed method with respect to all relevant limits. Together with consistency, this proves convergence of the method. Finally, we give numerical examples verifying both the analysis and convergence of the method

Deformable Overset Grid for Multibody Unsteady Flow Simulation

A deformable overset grid method is proposed to simulate the unsteady aerodynamic problems with multiple flexible moving bodies. This method uses an unstructured overset grid coupled with local mesh deformation to achieve both robustness and efficiency. The overset grid hierarchically organizes the subgrids into clusters and layers, allowing for overlapping/embedding of different type meshes, in which the mesh quality and resolution can be independently controlled. At each time step, mesh deformation is locally applied to the subgrids associated with deforming bodies by an improved Delaunay graph mapping method that uses a very coarse Delaunay mesh as the background graph. The graph is moved and deformed by the spring analogy method according to the specified motion, and then the computational meshes are relocated by a simple one-to-one mapping. An efficient implicit hole-cutting and intergrid boundary definition procedure is implemented fully automatically for both cell-centered and cell-vertex schemes based on the wall distance and an alternative digital tree data search algorithm. This method is successfully applied to several complex multibody unsteady aerodynamic simulations, and the results demonstrate the robustness and efficiency of the proposed method for complex unsteady flow problems, particularly for those involving simultaneous large relative motion and self-deformation

Numerical approximation of poroelasticity with random coefficients using Polynomial Chaos and Hybrid High-Order methods

In this work, we consider the Biot problem with uncertain poroelastic coefficients. The uncertainty is modelled using a finite set of parameters with prescribed probability distribution. We present the variational formulation of the stochastic partial differential system and establish its well-posedness. We then discuss the approximation of the parameter-dependent problem by non-intrusive techniques based on Polynomial Chaos decompositions. We specifically focus on sparse spectral projection methods, which essentially amount to performing an ensemble of deterministic model simulations to estimate the expansion coefficients. The deterministic solver is based on a Hybrid High-Order discretization supporting general polyhedral meshes and arbitrary approximation orders. We numerically investigate the convergence of the probability error of the Polynomial Chaos approximation with respect to the level of the sparse grid. Finally, we assess the propagation of the input uncertainty onto the solution considering an injection-extraction problem.Comment: 30 pages, 15 Figure