For the case of fluid-structure interactions (FSI) with or without free-surfaces or for the case of fluid with moving internal interfaces (multi-fluids), it is well known that in the explicit integrations, the time-step to be used in the solution is stable only for time-step smaller than two critical values: the Courant-Friedrichs-Lewy (CFL) number and the Fourier number. The first one is concerning with the convective terms and the second one with the diffusive ones. Both numbers must be less than one to have stable algorithms. For convection dominant problems the condition CFL<1 becomes crucial and limit the use of explicit methods or outdistance its to be efficient. On the other hand, implicit integrations using Eulerian formulations are restricted in the time-step size due to the lack of convergence of the non-linear terms. Both time integrations, explicit or implicit are, in most cases, limited to CFL no much larger than one.

In this lecture we will present a Particle Method to solve coupled problems like FSI or multi-fluid problems that use in all the domain (solid and fluid) a Lagrangian formulation with explicit or implicit time integration without the CFL<1 restriction. This allows large time-steps, independent of the spatial discretization, having equal or better precision that an Eulerian integration.

The proposal will be tested numerically for FSI and multi-fluid flows problems using the Particle Finite Element Method second generation (PFEM2). The results show than this Particle Method is largely more efficient compared as well in accuracy as in computing time with other more standard Eulerian formulations.

The talk will review recent activities on topology optimization of thermofluidic problems within the TopOpt group. On the parameterization side we discuss pros and cons between element-based (fictitious domain) and boundary tracking topology optimization formulations as well as comparisons between Finite Element and Lattice Boltzman formulations. On the application side we discuss recent applications within systematic design of active and passive (natural convection) cooling devices, heat exchangers, as well as simplified models for fire-protection of structures. 

In this presentation, the modelling, simulation and visualization methods are presented for tsunami waves. The stabilized finite element methods are employed for 2D and 3D tsunami simulations based on the shallow water equation, Boussinesq equation and Navier-Stokes equation. In order to realize an efficient tsunami simulation, a combination method using 2D and 3D models is presented. We also propose a visualization system linked to the evacuation simulation using virtual reality technology to understand the power of tsunami and the importance of the evacuation. The present modelling, simulation and visualization methods are shown to be useful tools to realize the high quality computing for large scale tsunami simulation. 

On one hand, we will talk about how to deal in a parallel element-based environment with multiphysics simulations that involve interface coupling, e.g., fluid-structure interaction. Our approach is based on the partition of topological meshes, and ghost element information, in order to define locally the degrees of freedom and the unknowns that must be communicated among processors.

On the other hand, we will discuss how we deal with the resulting multiphysics (non)linear systems. We have two different approaches to the problem: block preconditioning and monolithic solvers. Block preconditioning techniques are interesting in the sense that they allow us to decouple complex multiphysics problems into simpler (probably) one physics simulations. However, in order for block preconditioners to be effective, we must define effective approximation of Schur complement systems, which can be a complicated (and very heuristic) task. We will show how we have implemented complex (recursive) block preconditioning strategies in FEMPAR using abstract definitions of operators, and how this framework has been applied to different multiphysics solvers.

We will also discuss how we can reach sustained scalability up to large core-counts (about 400,000 cores in a BG/Q). Our in-house numerical linear algebra solvers are based on multilevel domain decomposition techniques, and their very efficient practical implementations based on overlapped and asynchronous techniques. We will consider two different approaches, the first one being a combination of block-preconditioning and multilevel domain decomposition, whereas the second one will be a truly monolithic domain decomposition approach.

Many multiphysics simulations are also multiscale, and the use of adaptively refined meshes can reduce even orders of magnitude the computational cost of simulations with respect to uniformly refined meshes. The possibility to reach extremely scalable adaptive multiphysics solvers would open the door to unprecedented simulations of challenging problems that are out of reach nowadays. In this sense, we will show how we are dealing with scalable adaptive solvers in FEMPAR, via a combination of the p4est library for parallel mesh refinement and dynamic load balancing in our element-based framework. Further, we will show how we modify our solvers to deal with nonconforming meshes through interfaces, and the effect of cheap space-filling curve partitions on solver robustness. 

We propose in this work a monolithic formulation where the complete problem is written in a fully Eulerian framework and the phases (fluid, solid,…) are separated by a level set function. The obtained system is solved using stabilized finite element methods. We combine this approximation with time-dependent anisotropic mesh adaptation to ensure accurate capturing of the discontinuities at the interfaces.

Different use of the levelset function ranging from, grain growth models for the evolutions of microstructure or void disclosure induced by forming operations, to the heat treatment of immersed metallic-alloys inside three-dimensional industrial furnaces will be presented. The advantages and the encountered numerical issues as well as the ongoing investigations related to these formulations will be discussed. 

Four examples of the model application for analysing transient chemo-hygro-thermo-mechanical processes in porous building materials are presented and discussed. The first example concerns the salt crystallization during drying of a wall made of concrete or ceramic brick, causing degradation of surface layer due to development of crystallization pressure. The second one deals with calcium leaching from a concrete wall due to chemical attack of pure water, exposed to gradients of temperature and pressure. The third one describes cracking of concrete element, caused by development of expanding products of ASR. The fourth example concerns freezing and thawing of a wet concrete wall in variable temperature and relative humidity.

Since 2008, our group, in cooperation with colleagues from Germany, Italy, Russia, Poland, Belgium, and Iceland, has been deeply involved in overcoming this challenge, by more deeply studying the X-ray physics underlying Computed Tomography: we developed increasingly mature methods to retrieve, from the grey value-defined voxel characteristics given in CT images, the actually underlying physical property, called X-ray attenuation coefficient. The latter contains information on the chemical composition of the material making up the considered voxel, and combining this information with known chemical characteristics of the material class making up the scanned object, gives access to important microstructural information inside the voxel, such as microporosity, or contents of known chemical substances. The latter then enter, as input values, experimentally validated micromechanical formulations representing the material inside the voxel, so as to reliably determine the voxel’s mechanical properties. Corresponding CT-to-mechanics conversion schemes will be presented in appropriate detail, with applications ranging from various ceramics and polymer-ceramic composites used in tissue engineering, to organs made up of the natural material bone.