7,377 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
Optimal control in ink-jet printing via instantaneous control
This paper concerns the optimal control of a free surface flow with moving
contact line, inspired by an application in ink-jet printing. Surface tension,
contact angle and wall friction are taken into account by means of the
generalized Navier boundary condition. The time-dependent differential system
is discretized by an arbitrary Lagrangian-Eulerian finite element method, and a
control problem is addressed by an instantaneous control approach, based on the
time discretization of the flow equations. The resulting control procedure is
computationally highly efficient and its assessment by numerical tests show its
effectiveness in deadening the natural oscillations that occur inside the
nozzle and reducing significantly the duration of the transient preceding the
attainment of the equilibrium configuration
A partition of unity approach to fluid mechanics and fluid-structure interaction
For problems involving large deformations of thin structures, simulating
fluid-structure interaction (FSI) remains challenging largely due to the need
to balance computational feasibility, efficiency, and solution accuracy.
Overlapping domain techniques have been introduced as a way to combine the
fluid-solid mesh conformity, seen in moving-mesh methods, without the need for
mesh smoothing or re-meshing, which is a core characteristic of fixed mesh
approaches. In this work, we introduce a novel overlapping domain method based
on a partition of unity approach. Unified function spaces are defined as a
weighted sum of fields given on two overlapping meshes. The method is shown to
achieve optimal convergence rates and to be stable for steady-state Stokes,
Navier-Stokes, and ALE Navier-Stokes problems. Finally, we present results for
FSI in the case of a 2D mock aortic valve simulation. These initial results
point to the potential applicability of the method to a wide range of FSI
applications, enabling boundary layer refinement and large deformations without
the need for re-meshing or user-defined stabilization.Comment: 34 pages, 15 figur
Existence of optimal boundary control for the Navier-Stokes equations with mixed boundary conditions
Variational approaches have been used successfully as a strategy to take
advantage from real data measurements. In several applications, this approach
gives a means to increase the accuracy of numerical simulations. In the
particular case of fluid dynamics, it leads to optimal control problems with
non standard cost functionals which, when constraint to the Navier-Stokes
equations, require a non-standard theoretical frame to ensure the existence of
solution. In this work, we prove the existence of solution for a class of such
type of optimal control problems. Before doing that, we ensure the existence
and uniqueness of solution for the 3D stationary Navier-Stokes equations, with
mixed-boundary conditions, a particular type of boundary conditions very common
in applications to biomedical problems
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