1,017 research outputs found

    Monolith: a monolithic pressure-viscosity-contact solver for strong two-way rigid-rigid rigid-fluid coupling

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    We propose Monolith, a monolithic pressure-viscosity-contact solver for more accurately, robustly, and efficiently simulating non-trivial two-way interactions of rigid bodies with inviscid, viscous, or non-Newtonian liquids. Our solver simultaneously handles incompressibility and (optionally) implicit viscosity integration for liquids, contact resolution for rigid bodies, and mutual interactions between liquids and rigid bodies by carefully formulating these as a single unified minimization problem. This monolithic approach reduces or eliminates an array of problematic artifacts, including liquid volume loss, solid interpenetrations, simulation instabilities, artificial "melting" of viscous liquid, and incorrect slip at liquid-solid interfaces. In the absence of solid-solid friction, our minimization problem is a Quadratic Program (QP) with a symmetric positive definite (SPD) matrix and can be treated with a single Linear Complementarity Problem (LCP) solve. When friction is present, we decouple the unified minimization problem into two subproblems so that it can be effectively handled via staggered projections with alternating LCP solves. We also propose a complementary approach for non-Newtonian fluids which can be seamlessly integrated and addressed during the staggered projections. We demonstrate the critical importance of a contact-aware, unified treatment of fluid-solid coupling and the effectiveness of our proposed Monolith solver in a wide range of practical scenarios.This work was supported in part by the Natural Sciences and Engineering Research Council of Canada (Grant RGPIN-04360-2014)

    FrictionalMonolith: A Monolithic Optimization-based Approach for Granular Flow with Contact-Aware Rigid-Body Coupling

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    We propose FrictionalMonolith, a monolithic pressure-friction-contact solver for more accurately, robustly, and efficiently simulating two-way interactions of rigid bodies with continuum granular materials or inviscid liquids. By carefully formulating the components of such systems within a single unified minimization problem, our solver can simultaneously handle unilateral incompressibility and implicit integration of friction for the interior of the continuum, frictional contact resolution among the rigid bodies, and mutual force exchanges between the continuum and rigid bodies. Our monolithic approach eliminates various problematic artifacts in existing weakly coupled approaches, including loss of volume in the continuum material, artificial drift and slip of the continuum at solid boundaries, interpenetrations of rigid bodies, and simulation instabilities. To efficiently handle this challenging monolithic minimization problem, we present a customized solver for the resulting quadratically constrained quadratic program that combines elements of staggered projections, augmented Lagrangian methods, inexact projected Newton, and active-set methods. We demonstrate the critical importance of a unified treatment and the effectiveness of our proposed solver in a range of practical scenarios.Natural Sciences and Engineering Research Council of Canada, Grant RGPIN-2021-02524

    Lagrangian FE methods for coupled problems in fluid mechanics

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    This work aims at developing formulations and algorithms where maximum advantage of using Lagrangian finite element fluid formulations can be taken. In particular we concentrate our attention at fluid-structure interaction and thermally coupled applications, most of which originate from practical “real-life” problems. Two fundamental options are investigated - coupling two Lagrangian formulations (e.g. Lagrangian fluid and Lagrangian structure) and coupling the Lagrangian and Eulerian fluid formulations. In the first part of this work the basic concepts of the Lagrangian fluids, the so-called Particle Finite Element Method (PFEM) [1], [2] are presented. These include nodal variable storage, mesh re-construction using Delaunay triangulation/tetrahedralization and alpha shape-based method for identification of the computational domain boundaries. This shall serve as a general basis for all the further developments of this work.Postprint (published version

    Reactive Flows in Deformable, Complex Media

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    Many processes of highest actuality in the real life are described through systems of equations posed in complex domains. Of particular interest is the situation when the domain is changing in time, undergoing deformations that depend on the unknown quantities of the model. Such kind of problems are encountered as mathematical models in the subsurface, material science, or biological systems.The emerging mathematical models account for various processes at different scales, and the key issue is to integrate the domain deformation in the multi-scale context. The focus in this workshop was on novel techniques and ideas in the mathematical modelling, analysis, the numerical discretization and the upscaling of problems as described above

    Lagrangian FE methods for coupled problems in fluid mechanics

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    Lagrangian finite element methods emerged in fluid dynamics when the deficiencies of the Eulerian methods in treating free surface flows (or generally domains undergoing large shape deformations) were faced. Their advantage relies upon natural tracking of boundaries and interfaces, a feature particularly important for interaction problems. Another attractive feature is the absence of the convective term in the fluid momentum equations written in the Lagrangian framework resulting in a symmetric discrete system matrix, an important feature in case iterative solvers are utilized. Unfortunately, the lack of the control over the mesh distortions is a major drawback of Lagrangian methods. In order to overcome this, a Lagrangian method must be equipped with an efficient re-meshing tool. This work aims at developing formulations and algorithms where maximum advantage of using Lagrangian finite element fluid formulations can be taken. In particular we concentrate our attention at fluid-structure interaction and thermally coupled applications, most of which originate from practical “real-life” problems. Two fundamental options are investigated - coupling two Lagrangian formulations (e.g. Lagrangian fluid and Lagrangian structure) and coupling the Lagrangian and Eulerian fluid formulations. In the first part of this work the basic concepts of the Lagrangian fluids, the so-called Particle Finite Element Method (PFEM) [1], [2] are presented. These include nodal variable storage, mesh re-construction using Delaunay triangulation/tetrahedralization and alpha shape-based method for identification of the computational domain boundaries. This shall serve as a general basis for all the further developments of this work. Next we show how an incompressible Lagrangian fluid can be used in a partitioned fluid-structure interaction context. We present an improved Dirichlet-Neumann strategy for coupling the incompressible Lagrangian fluid with a rigid body. This is finally applied to an industrial problem dealing with the sea-landing of a satellite capsule. In the following, an extension of the method is proposed to allow dealing with fluid-structure problems involving general flexible structures. The method developed takes advantage of the symmetry of the discrete system matrix and by introducing a slight fluid compressibility allows to treat the fluid-structure interaction problem efficiently in a monolithic way. Thus, maximum benefit from using a similar description for both the fluid (updated Lagrangian) and the solid (total Lagrangian) is taken. We show next that the developed monolithic approach is particularly useful for modeling the interaction with light-weight structures. The validation of the method is done by means of comparison with experimental results and with a number of different methods found in literature. The second part of this work aims at coupling Lagrangian and Eulerian fluid formulations. The application area is the modeling of polymers under fire conditions. This kind of problem consists of modeling the two subsystems (namely the polymer and the surrounding air) and their thermomechanical interaction. A compressible fluid formulation based on the Eulerian description is used for modeling the air, whereas a Lagrangian description is used for the polymer. For the surrounding air we develop a model based upon the compressible Navier-Stokes equations. Such choice is dictated by the presence of high temperature gradients in the problem of interest, which precludes the utilization of the Boussinesq approximation. The formulation is restricted to the sub-sonic flow regime, meeting the requirement of the problem of interest. The mechanical interaction of the subsystems is modeled by means of a one-way coupling, where the polymer velocities are imposed on the interface elements of the Eulerian mesh in a weak way. Thermal interaction is treated by means of the energy equation solved on the Eulerian mesh, containing thermal properties of both the subsystems, namely air and polymer. The developments of the second part of this work do not pretend to be by any means exhaustive; for instance, radiation and chemical reaction phenomena are not considered. Rather we make the first step in the direction of modeling the complicated thermo-mechanical problem and provide a general framework that in the future can be enriched with a more detailed and sophisticated models. However this would affect only the individual modules, preserving the overall architecture of the solution procedure unchanged. Each chapter concludes with the example section that includes both the validation tests and/or applications to the real-life problems. The final chapter highlights the achievements of the work and defines the future lines of research that naturally evolve from the results of this work

    A convergence study of monolithic simulations of flow and deformation in fractured poroelastic media

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    A consistent linearisation has been carried out for a monolithic solution procedure of a poroelastic medium with fluid‐transporting fractures, including a comprehensive assessment of the convergence behaviour. The fracture has been modelled using a sub‐grid scale model with a continuous pressure across the fracture. The contributions to the tangential stiffness matrix of the fracture have been investigated to assess their impact on convergence. Simulations have been carried out for different interpolation orders and for Non‐Uniform Rational B‐Splines as interpolants vs Lagrangian polynomials. To increase the generality of the results, Newtonian as well as non‐Newtonian (power‐law) fluids have been considered. Unsurprisingly, a consistent linearisation invariably yields a quadratic convergence, but comes at the expense of a loss of symmetry and recalculation of the contribution of the interface to the stiffness matrix at each iteration. When using a linear line search however, the inclusion of only those terms of the interface stiffness which result in a symmetric and constant tangential stiffness matrix is sufficient to obtain a stable and convergent iterative process
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