1st ICMC Workshop on Recent Advances in Computational Mechanics for Industry

Title: High-Fidelity Digital Twins: Detecting And Localizing Weaknesses In Structures

Abstract: Given that all materials exposed to the environment and/or undergoing loads eventually age and fail, the task of trying to detect and localize weaknesses in structures is common to many fields. To mention just a few: bridges, high-rise buildings, stadiums, airplanes, drones and missiles, turbines, launch pads and airport infrastructure, wind turbines, and satellites. Traditionally, manual inspection was the only way of carrying out this task, aided by ultrasound, X-ray, or vibration analysis techniques. The advent of accurate, abundant and cheap sensors, together with detailed, high-fidelity computational models in an environment of digital twins has opened the possibility of enhancing and automating the detection and localization of weaknesses in structures. The procedures proposed here are based on measured forces and displacements/strains, and formulate the determination of material properties (or weaknesses) as an optimization problem for the strength factor. These procedures belong to the more general class of inverse problems where structural properties are sought based on a desired cost functional. The use of adjoint formulations and smoothing of gradients to quickly localize damaged regions makes the problem tractable. In a subsequent step, techniques to minimize the number of load cases and sensors are proposed and tested. Several examples show the viability, accuracy and efficiency of the proposed methodology and its potential use for high fidelity digital twins.

Title: Mixed finite element methods in Elasticity—When inf-sup stability is not an option in practice

Abstract: In this talk we consider the finite element approximation of some mixed formulations of linear elasticity, namely, the displacement-pressure, the displacement-stress and the displacement-pressure-stress approaches. As for any mixed formulation, involving unknowns belonging to different functional spaces, the global inf-sup stability that ensures well posedness of the problem is a consequence of “little” inf-sup conditions that need to be satisfied between the interpolating spaces of the different unknowns. Approximations satisfying these conditions are sometimes difficult to implement, and even very rare, as in the case of the displacement-pressure-stress approach. The alternative is to modify the discrete problem by adding stabilisation terms to the Galerkin equations that yield stable approximations for any choice of the interpolating spaces.

Title: P-DNS: how to combine accuracy and efficiency to solve fluid mechanics problems in turbulent regimes. 

Abstract: This presentation introduces the pseudo-DNS method, a promising approach for simulating complex turbulent flows. It offers the accuracy of Direct Numerical Simulation (DNS) while maintaining computational costs similar to Reynolds-Averaged Navier-Stokes (RANS) methods, surpassing Large Eddy Simulation (LES) in accuracy. One key challenge in Computational Fluid Dynamics (CFD) is accurately simulating turbulent flows near walls, where fine meshes are typically required to capture steep velocity gradients. Properly evaluating viscous effects is crucial for predicting drag and lift forces, as it determines flow separation points, significantly impacting overall force predictions. The ultimate goal of this work is to simulate these forces accurately without relying on excessively fine meshes.

Title: Spatiotemporal dynamics of Amazonian rivers, importance for the Amazon basin sustainability

Abstract: Amazonian rivers present complex patterns from the Andes to their mouth in the Atlantic Ocean. The understanding of these patterns requires: 1) the application of remote sensing techniques to characterize the ancient and modern river planform dynamics, 2) the development of field measurements to understand the flow structure, sediments and morphological aspects, and 3) the development of hydrogeomorphological models that can reproduce the dynamics of the rivers at natural scales. Understanding of the dynamics of Amazonian rivers is vital to correlate them with existing biodiversity, with conservation plans and to minimize the impacts of anthropogenic activities.

Title: The Strength Of N-Simplex Vertex-Based Finite-Cell Methods

Abstract: Our starting point is the celebrated work of Courant published in 1943, in which the adventure of conforming piecewise linear finite elements – the so-called P1 FEM – began, as a powerful tool for the numerical solution of boundary value problems posed in N-dimensional domains of arbitrary shape. Nowadays it is probably the most popular finite-cell method defined upon a simplicial mesh, owing to its simplicity and low implementation cost, combined with an acknowledged reliability for handling a wide spectrum of mathematical models in Applied Science and Engineering. In the same category of methods, carrying the unknowns only at the mesh vertices, lies prominently the vertex- centered finite volume method, and also the linear discontinuous Galerkin method in some sense. However, for some types of models, specialists had been compelled to search for other alternatives, owing to a supposed lack of adequacy of vertex-based methods of the lowest order, such as the P1 FEM. Examples of problems, whose solution by these methods was long considered to fail, encompass the equations of incompressible viscous flow, the Maxwell’s equations of electro- magnetism and the system governing flow in porous media. It turns out that outstanding works – more particularly from the mid-eighties on –, showed that, as long as suitable formulations of these equations are employed, such methods do bring about a reliable possibility to solve them. In this talk we review how to reformulate some mathematical models in a way well-suited to vertex-based finite element methods, whose use otherwise would have to be discarded. In doing so we also highlight through a few examples, how judicious has been Gustavo Buscaglia’s choice along his brilliant career, to confine, to a large extent, his countless noteworthy contributions to the field of numerical simulations in Science and Technology, to vertex-based finite-cell methods.

Title: Coupling dimensionally-heterogeneous models in hemodynamics simulations

Abstract: This presentation will discuss advanced methods for effectively coupling flow models of different dimensions. The approach was initially developed to address challenges in computational hemodynamics, but it can also be applied to other areas of physics and engineering. The focus will be on addressing transient non-linear problems, such as those encountered in modeling blood flow in the cardiovascular system. The proposed methodology involves breaking down a coupled 3D-1D-0D closed-loop model of the cardiovascular system into separate representations for the 3D (specific vessels), 1D (systemic arteries/peripheral vessels), and 0D (venous/cardiac/pulmonary circulation) models.

Title: Homogeneous Shear Turbulence and Application to Cavitation Inception

Abstract: We study the behavior of homogeneous shear turbulence (HST) in the context of cavitation inception for computational fluid dynamics. A SGS cavitation inception model attempts to represent thhe unresolved turbulence with a canonical turbulent flow. HST is the simplest self-sustained form of turbulence that produces physically realistic flows. We perform DNS of HST at Taylor microscale Reynolds numbers in the range 50 < Re < 250, and study the resulting pressure statistics.  For all Re conditions we seed and transport bubbles with sizes R < 0.2 l, and study the Lagrangian pressure statistics. The pressure histories for each bubble are used to solve the Rayleigh-Plesset equation under different reference pressures, resulting in a cavitation rate for each condition, which is used to produce a cavitation inception model. The model is evaluated for the ducted propeller P5757. It is concluded that HST exhibits higher pressure transients than homogeneous isotropic turbulence for the same Re, also reaching lower pressures and producing higher cavitation rates and higher cavitation inception numbers.

Title: Dispersion of Aerosols, Particles, and Pollutants: The Role of Turbulent Fluctuations

Abstract: Potential sources of hazardous pollutants are numerous. In natural systems, these include volcanic eruptions, sand and dust storms, and other phenomena; in human activities, pollution arises from industrial processes, transportation, and human-emitted particles (such as sneezing and coughing), as well as catastrophic events like chemical and nuclear plant failures. Effective management of these issues requires accurately modeling dispersion processes, which are predominantly influenced by turbulent transport. Numerical simulations provide invaluable insights into this complex phenomenon, addressing the nonlinear nature of turbulent flows and their complex interaction with inertial particles. This talk will discuss the research on the turbulent transport of particles in jet flows, conducted by a consortium of Brazilian and French researchers under the expert guidance of Professor Gustavo Buscaglia, demonstrating how advanced computational mechanics can impact our understanding of both environmental and industrial pollutants.

Title: Dimensionality Reduction and Reduced-Order Models in Viscoelastic Fluid Flow

Abstract: A key aspect of constructing effective Reduced-Order Models lies in the application of dimensionality reduction methods, which extract meaningful reduced coordinates from high-dimensional data. Our study emphasizes the importance of selecting the right dimensionality reduction technique not only for accurate data representation but also for facilitating the development of ROMs. In particular, we highlight how nonlinear methods contribute to enhanced reconstructions, which are critical for the subsequent application of ROM techniques like Sparse Identification of Nonlinear Dynamics (SINDy). These methods enable more efficient parametric reductions in viscoelastic flows, offering significant improvements over traditional linear approaches like Proper Orthogonal Decomposition.

Title: Formulation, analysis and numerical solution of optimization subproblems in DDCM

Abstract: One possible realization for the new computing paradigm called Data-Driven Computational Mechanics (DDCM) relies on the formulation of a topological optimization problem that seeks to optimally assign experimental constitutive data to subdomains of the physical body under consideration, also to be determined as a part of the problem’s solution, while satisfying, in a weak sense, equilibrium, compatibility and boundary conditions. This topological optimization problem is, in general, very difficult to analyze, due to the functional/topological aspects involved, and extremely expensive to solve, due to its NP-hardness. Therefore, as a first step, we are going to set the focus on a collection of optimization subproblems that arises when the active data set and its corresponding active domain partition are fixed and given in advance. These nonlinear optimization subproblems can be formulated either on a single domain combined with a data extension by simple functions or on a smooth domain partition with simple data assignment over each subdomain. Moreover, by adopting two/three primal fields and one/two dual fields, we identify four main formulations for the realization of DDCM. Upon linearization, it can be shown that all optimization subproblems are well posed, and after further analysis, all of them turn to be equivalent. To show the potential of the formulations proposed and their numerical treatment by means of the finite element method, we investigate two concrete examples, i.e., the fluid flow in a porous media and the linear elasticity problem, but this time in their data-driven form.

Title:  A Methodology for Rigid Body and Fluid Interactions

Abstract: This work introduces a novel computational approach to simulate the complex dynamics of numerous rigid bodies interacting with each other and with a Newtonian fluid. The proposed methodology represents rigid bodies as a collection of four or more interconnected particles. Quaternions are employed for efficient internal calculations.

Bilateral restrictions between particles are enforced using iterative penalization, while unilateral restrictions, such as collisions between rigid bodies and walls, are handled through a penalization approach. The interaction between the rigid bodies and the fluid is modeled using an embedded technique. To efficiently determine if a fluid cell intersects a rigid body, an Approximate Nearest Neighbor Tree algorithm is employed. This information is then used to calculate penalization terms and, consequently, the forces acting on the rigid bodies.

The  library offers a versatile framework for simulating a wide range of rigid body systems, including complex arrays of bodies, links, moorings, and contacts with surfaces. All elements within the simulation, including rigid bodies, are represented as particles. Rigid bodies are modeled as arrays of four or more particles arranged to match the desired mass and inertia moments. Fixed distances between particles maintain the body’s rigidity, and the overall system dynamics are solved as a system of Differential-Algebraic Equations.

Title:  Computational Mechanics in Northern Patagonia, mid-80s to present

Abstract: I will present a summary of the activities of the Computational Mechanics Group at the Bariloche Atomic Center, from our first steps in the discipline (in the mid-80s of the last century) to the present. The presentation will range from those heroic times – programming recursive algorithms in FORTRAN IV and requesting reprints of papers by (not-e) mail – to the present day, with extensive software libraries widely available and the possibility of holding virtual meetings with colleagues regardless of the geographical location.

Title: Conservative formulations for the simulation of fluid-structure interaction in cavitated hydrodynamic journal bearings

Abstract: This talk presents the results obtained through the implementation of a novel model developed from first principles that allows characterizing the pressure field of a liquid–gas lubricant mixture avoiding the reported instabilities with the time derivative of the mixture density. The model is applied to cavitation in hydrodynamic bearings with a focus on accuracy, stability and conservativeness. The formulation also relies on a coupled transport equation describing the evolution of the liquid fraction, ensuring mass conservation. High resolution schemes are used for the spatial treatment of the advection and a temporal discretization based on the Strang splitting method, enabling second-order convergence in both space and time. This model is applied to study cases with gaseous, vaporous or pseudo-cavitation in three state-of-art problems: surfaces texturing optimization, textures and temperature interaction and solid-fluid resonance phenomena. In the first problem changes in depth, shape and quantity of textures are explored to enhance the pumping effect present in Chevron type textures. The texture study also accounts for the simultaneous effects of cavitation and temperature increase due to friction, a topic rarely addressed in the literature. Finally the time evolution of an unidimensional elastic rotor is studied using a coupled Finite Element Method solver in co-simulation with the journal bearing tool to represent the shaft-bearing assembly. Shaft instabilities are triggered by unbalanced discs and masses using linear and non-linear models for the hydrodynamic bearings. The Oil Whirl and Oil Whip instabilities are correctly captured showing the potential of the simulation tool.

Title: Multi-phase modeling and simulation of air-water flows for hydraulic structures

Abstract: Air-water flows are very important in both natural and man-made situations. Although significant progress has been achieved in the last decades, there still is a rather long road in order to have a definite, widely-agreed menu of options to simulate these flows; further, our understanding is still rather limited. Two-phase flows constitute a multi-scale problem in which the small scales associated to the bubble scale contribute to the macro-behavior of the flow. This issue requires either a detailed resolution of those scales, or the use of indirect approaches which take into account that strong dependence. In this presentation, we introduce a framework for the multiscale modeling of air entrainment in hydraulic structures. First, we devote time to present Scale-Resolving Simulations (SRSs), which we started in 2015-2017, we continued in 2020, and we evolved to a larger extent very recently for the simulation of flow past stepped spillways – an archetypical hydraulic structure. The SRS model applies the Spalart-Allmaras-Detached Eddy Simulation model, and no sub-grid model is included for the dispersed air phase. Then, we turn to a Reynolds-Averaged Navier-Stokes (RANS) approach for the same flow. The RANS model proposes a three-phase mixture formulation and a turbulence closure for the turbulent stresses, recently published in the CMAME. A criterion using a balance between a disturbing energy and stabilizing energy allows for determining the regions where air is entrained or detrained; this has been found to produce good results for stepped spillways as well as (amazingly) impinging jets. Very interestingly, the RANS model provides information about air concentration as well as the level of bulking, which causes notable numerical shortcomings in many other models. Both methodologies show very good agreement with the experimental data. Naturally, the SRS model comes at a more substantial computational cost. Future lines of research for both types of models are discussed during the presentation.

Title: Some Computational Mechanics Problems Inspired by Metal 3D Printing

Abstract: Metal 3D printing processes require complex multi-physics models involving both fluids and solids to describe them and give rise to novel optimization problems. In this presentation I will describe a few “new” computational mechanics problems inspired by advances in this technology. These include the problems of: (a) designing a liquid metal jetting nozzle to increase the jetting frequency, (b) optimizing the path a laser should follow when printing a part to accomplish a goal, such as minimizing distortion or maximizing in-situ tempering, and (c) optimizing the material distribution in multi-material printing to smoothly vary the material at each point of a part.