Multi-Level quasi-Newton methods for the partitioned simulation of fluid-structure interaction

In previous work of the authors, Fourier stability analyses have been performed of Gauss-Seidel iterations between the flow solver and the structural solver in a partitioned fluid-structure interaction simulation. These analyses of the flow in an elastic tube demonstrated that only a number of Fourier modes in the error on the interface displacement are unstable. Moreover, the modes with a low wave number are most unstable and these modes can be resolved on a coarser grid. Therefore, a new class of quasi-Newton methods with more than one grid level is introduced. Numerical experiments show a significant reduction in run time

Mesh update techniques for free-surface flow solvers using spectral element method

This paper presents a novel mesh-update technique for unsteady free-surface Newtonian flows using spectral element method and relying on the arbitrary Lagrangian--Eulerian kinematic description for moving the grid. Selected results showing compatibility of this mesh-update technique with spectral element method are given

Existence of global strong solutions to a beam-fluid interaction system

We study an unsteady non linear fluid-structure interaction problem which is a simplified model to describe blood flow through viscoleastic arteries. We consider a Newtonian incompressible two-dimensional flow described by the Navier-Stokes equations set in an unknown domain depending on the displacement of a structure, which itself satisfies a linear viscoelastic beam equation. The fluid and the structure are fully coupled via interface conditions prescribing the continuity of the velocities at the fluid-structure interface and the action-reaction principle. We prove that strong solutions to this problem are global-in-time. We obtain in particular that contact between the viscoleastic wall and the bottom of the fluid cavity does not occur in finite time. To our knowledge, this is the first occurrence of a no-contact result, but also of existence of strong solutions globally in time, in the frame of interactions between a viscous fluid and a deformable structure

Three-dimensional CFD simulations with large displacement of the geometries using a connectivity-change moving mesh approach

This paper deals with three-dimensional (3D) numerical simulations involving 3D moving geometries with large displacements on unstructured meshes. Such simulations are of great value to industry, but remain very time-consuming. A robust moving mesh algorithm coupling an elasticity-like mesh deformation solution and mesh optimizations was proposed in previous works, which removes the need for global remeshing when performing large displacements. The optimizations, and in particular generalized edge/face swapping, preserve the initial quality of the mesh throughout the simulation. We propose to integrate an Arbitrary Lagrangian Eulerian compressible flow solver into this process to demonstrate its capabilities in a full CFD computation context. This solver relies on a local enforcement of the discrete geometric conservation law to preserve the order of accuracy of the time integration. The displacement of the geometries is either imposed, or driven by fluid–structure interaction (FSI). In the latter case, the six degrees of freedom approach for rigid bodies is considered. Finally, several 3D imposed-motion and FSI examples are given to validate the proposed approach, both in academic and industrial configurations

New Challenges in Grid Generation and Adaptivity for Scientific Computing

This volume collects selected contributions from the “Fourth Tetrahedron Workshop on Grid Generation for Numerical Computations”, which was held in Verbania, Italy in July 2013. The previous editions of this Workshop were hosted by the Weierstrass Institute in Berlin (2005), by INRIA Rocquencourt in Paris (2007), and by Swansea University (2010). This book covers different, though related, aspects of the field: the generation of quality grids for complex three-dimensional geometries; parallel mesh generation algorithms; mesh adaptation, including both theoretical and implementation aspects; grid generation and adaptation on surfaces – all with an interesting mix of numerical analysis, computer science and strongly application-oriented problems

Stability analysis of second-order time accurate schemes for ALE-FEM

In this work we will introduce and analyze the Arbitrary Lagrangian Eulerian formulation for a model problem of a scalar advection-diffusion equation defined on a moving domain. Moving from the results illustrated in our previous work [J. Num. Math. 7 (1999) 105], we will consider first and second-order time advancing schemes and analyze how the movement of the domain might affect accuracy and stability properties of the numerical schemes with respect to their counterpart on fixed domains. Theoretical and numerical results will be presented, showing that stability properties are not, in general, preserved, while accuracy is maintained. (C) 2004 Elsevier B.V. All rights reserved

MgB2 superconducting thin films with a transition temperature of 39 Kelvin

We report the growth of high-quality c-axis-oriented epitaxial MgB2 thin films by using a pulsed laser deposition technique. The thin films grown on (1`1 0 2) Al2O3 substrates show a Tc of 39 K. The critical current density in zero field is ~ 6 x 10^6 A/cm2 at 5 K and ~ 3 x 10^5 A/cm^2 at 35 K, suggesting that this compound has great potential for electronic device applications, such as microwave devices and superconducting quantum interference devices. For the films deposited on Al2O3, X-ray diffraction patterns indicate a highly c-axis-oriented crystal structure perpendicular to the substrate surface.Comment: 3 pages and 3 figure

Landslide run-out simulations with depth-averaged models and integration with 3D impact analysis using the Material Point Method

Landslides pose a significant threat to human safety and the well-being of com- munities, making them one of the most challenging natural phenomena. Their potential for catastrophic consequences, both in terms of human lives and economic impact, is a major con- cern. Additionally, their inherent unpredictability adds to the complexity of managing the risks associated with landslides. It is crucial to continuously monitor areas susceptible to landslides. In situ detection systems like piezometers and strain gauges play a vital role in accurately mon- itoring internal pressures and surface movements in the targeted areas. Simultaneously, satel- lite surveys contribute by offering detailed topographic and elevation data for the study area. However, relying solely on empirical monitoring is insufficient for ensuring effective manage- ment of hazardous situations, especially in terms of preventive measures. This study provides advanced simulations of mudflows and fast landslides using particle depth-averaged methods, specifically employing the Material Point Method adapted for shallow water (Depth Averaged Material Point Method). The numerical method has been parallelized and validated through benchmark tests and real-world cases. Furthermore, the investigation extends to coupling the depth-averaged formulation with a three-dimensional one in order to have a detailed description of the impact phase of the sliding material on barriers and membranes. The multidimensional approach and its validation on real cases provide a robust foundation for a more profound and accurate understanding of the behavior of mudflows and fast landslides

An unfitted formulation for the interaction of an incompressible fluid with a thick structure via an XFEM/DG approach

A numerical procedure that combines an extended finite element formulation and a discontinuous Galerkin technique is presented, with the final aim of providing an effective tool for the simulation of three-dimensional (3D) fluid-structure interaction problems. In this work we consider a thick structure immersed in a fluid. We describe the numerical models and discuss the specific implementation issues arising in three dimensions. Finally, 3D numerical results are provided to show the effectiveness of the approach

Time-discrete higher order ALE formulations: a priori error analysis

We derive optimal a priori error estimates for discontinuous Galerkin (dG) time discrete schemes of any order applied to an advection-diffusion model defined on moving domains and written in the Arbitrary Lagrangian Eulerian (ALE) framework. Our estimates hold without any restrictions on the time steps for dG with exact integration or Reynolds' quadrature. They involve a mild restriction on the time steps for the practical Runge-Kutta-Radau methods of any order. The key ingredients are the stability results shown earlier in Bonito et al. (Time-discrete higher order ALE formulations: stability, 2013) along with a novel ALE projection. Numerical experiments illustrate and complement our theoretical results.</p