1,017 research outputs found
Monolith: a monolithic pressure-viscosity-contact solver for strong two-way rigid-rigid rigid-fluid coupling
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
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
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 âreal-lifeâ 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
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
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
A consistent linearisation has been carried out for a monolithic solution procedure of a poroelastic medium with fluidâtransporting fractures, including a comprehensive assessment of the convergence behaviour. The fracture has been modelled using a subâgrid 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 NonâUniform Rational BâSplines as interpolants vs Lagrangian polynomials. To increase the generality of the results, Newtonian as well as nonâNewtonian (powerâlaw) 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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Multiscale thermo-hydro-mechanical-chemical coupling effects for fluid-infiltrating crystalline solids and geomaterials: theory, implementation, and validation
Extreme climate change and demanding energy resources have led to new geotechnical engineering challenges critical for sustainable development and resilient infrastructure of our society. Applications such as geological disposal of nuclear waste and carbon dioxide, artificial ground freezing, and hydraulic fractures all require an in-depth understanding of the thermo-hydro-mechanical coupling mechanisms of geomaterials subjected to various environmental impact. This dissertation presents a multiphysical computational framework dedicated to address the issues related to those unconventional applications.
Our objective is not only incorporating multiphysical coupling effects at the constitutive laws, but also taking into account the nonlocal effects originated from the flow of pore-fluid, thermal convection and diffusion among solid and fluid constituents, and crystallization and recrystallization of crystals in the pore space across length scales. By considering these coupling mechanisms, we introduce a single unified model capable of predicting complex thermo-hydro-mechanical responses of geological and porous media across wide spectra of temperature, confining pressure and loading rate.
This modeling framework applies to two applications, i.e., the freezing and thawing of frozen soil and the modeling of anisotropic crystal plasticity/fracture response of rock salt. Highlights of the key ingredients of the models cover the stabilization procedure used for the multi-field finite element, the return mapping algorithm for crystal plasticity, the micromorphic regularization of the Modified Cam-Clay model, and the strategy for enhancing computational efficiency of solvers, such as pre-conditioner, adaptive meshing, and internal variable mapping. By introducing the multiphysical coupling mechanisms explicitly, our computational geomechanics model is able to deliver more accurate and consistent results without introducing a significant amount of additional material parameters.
In a parallel effort, we analyze the impact of thermo-hydro-mechanical (THM) coupling effects on the dynamic wave propagation and strain localization in a fully saturated softening porous medium. The investigation starts with deriving the characteristic polynomial corresponding to the governing equations of the THM system. The theoretical analysis based on the AbelâRuffini theorem reveals that the roots of the characteristic polynomial for the THM problem cannot be expressed algebraically. Our analysis concludes that the rate-dependence introduced by multiphysical coupling may not regularize the THM governing equations when softening occurs
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