900 research outputs found
An adaptive fixed-mesh ALE method for free surface flows
In this work we present a Fixed-Mesh ALE method for the numerical simulation of free surface flows capable of using an adaptive finite element mesh covering a background domain. This mesh is successively refined and unrefined at each time step in order to focus the computational effort on the spatial regions where it is required. Some of the main ingredients of the formulation are the use of an Arbitrary-Lagrangian–Eulerian formulation for computing temporal derivatives, the use of stabilization terms for stabilizing convection, stabilizing the lack of compatibility between velocity and pressure interpolation spaces, and stabilizing the ill-conditioning introduced by the cuts on the background finite element mesh, and the coupling of the algorithm with an adaptive mesh refinement procedure suitable for running on distributed memory environments. Algorithmic steps for the projection between meshes are presented together with the algebraic fractional step approach used for improving the condition number of the linear systems to be solved. The method is tested in several numerical examples. The expected convergence rates both in space and time are observed. Smooth solution fields for both velocity and pressure are obtained (as a result of the contribution of the stabilization terms). Finally, a good agreement between the numerical results and the reference experimental data is obtained.Postprint (published version
An effective preconditioning strategy for volume penalized incompressible/low Mach multiphase flow solvers
The volume penalization (VP) or the Brinkman penalization (BP) method is a
diffuse interface method for simulating multiphase fluid-structure interaction
(FSI) problems in ocean engineering and/or phase change problems in thermal
sciences. The method relies on a penalty factor (which is inversely related to
body's permeability ) that must be large to enforce rigid body velocity
in the solid domain. When the penalty factor is large, the discrete system of
equations becomes stiff and difficult to solve numerically. In this paper, we
propose a projection method-based preconditioning strategy for solving volume
penalized (VP) incompressible and low-Mach Navier-Stokes equations. The
projection preconditioner enables the monolithic solution of the coupled
velocity-pressure system in both single phase and multiphase flow settings. In
this approach, the penalty force is treated implicitly, which is allowed to
take arbitrary large values without affecting the solver's convergence rate or
causing numerical stiffness/instability. It is made possible by including the
penalty term in the pressure Poisson equation. Solver scalability under grid
refinement is demonstrated. A manufactured solution in a single phase setting
is used to determine the spatial accuracy of the penalized solution.
Second-order pointwise accuracy is achieved for both velocity and pressure
solutions. Two multiphase fluid-structure interaction (FSI) problems from the
ocean engineering literature are also simulated to evaluate the solver's
robustness and performance. The proposed solver allows us to investigate the
effect of on the motion of the contact line over the surface of the
immersed body. It also allows us to investigate the dynamics of the free
surface of a solidifying meta
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 “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
A fully coupled regularized mortar-type finite element approach for embedding one-dimensional fibers into three-dimensional fluid flow
The present article proposes a partitioned Dirichlet-Neumann algorithm, that
allows to address unique challenges arising from a novel mixed-dimensional
coupling of very slender fibers embedded in fluid flow using a regularized
mortar-type finite element discretization. The fibers are modeled via
one-dimensional (1D) partial differential equations based on geometrically
exact nonlinear beam theory, while the flow is described by the
three-dimensional (3D) incompressible Navier-Stokes equations. The arising
truly mixed-dimensional 1D-3D coupling scheme constitutes a novel approximate
model and numerical strategy, that naturally necessitates specifically tailored
solution schemes to ensure an accurate and efficient computational treatment.
In particular, we present a strongly coupled partitioned solution algorithm
based on a Quasi-Newton method for applications involving fibers with high
slenderness ratios that usually present a challenge with regard to the
well-known added mass effect. The influence of all employed algorithmic and
numerical parameters, namely the applied acceleration technique, the employed
constraint regularization parameter as well as shape functions, on efficiency
and results of the solution procedure is studied through appropriate examples.
Finally, the convergence of the two-way coupled mixed-dimensional problem
solution under uniform mesh refinement is demonstrated, a comparison to a 3D
reference solution is performed, and the method's capabilities in capturing
flow phenomena at large geometric scale separation is illustrated by the
example of a submersed vegetation canopy
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
Efficient split-step schemes for fluid–structure interaction involving incompressible generalised Newtonian flows
Blood flow, dam or ship construction and numerous other problems in biomedical and general engineering involve incompressible flows interacting with elastic structures. Such interactions heavily influence the deformation and stress states which, in turn, affect the engineering design process. Therefore, any reliable model of such physical processes must consider the coupling of fluids and solids. However, complexity increases for non-Newtonian fluid models, as used, e.g., for blood or polymer flows. In these fluids, subtle differences in the local shear rate can have a drastic impact on the flow and hence on the coupled problem. There, existing (semi-) implicit solution strategies based on split-step or projection schemes for Newtonian fluids are not applicable, while extensions to non-Newtonian fluids can lead to substantial numerical overhead depending on the chosen fluid solver. To address these shortcomings, we present here a higher-order accurate, added-mass-stable fluid–structure interaction scheme centered around a split-step fluid solver. We compare several implicit and semi-implicit variants of the algorithm and verify convergence in space and time. Numerical examples show good performance in both benchmarks and an idealised setting of blood flow through an abdominal aortic aneurysm considering physiological parameters
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