280 research outputs found
A robust method for calculating interface curvature and normal vectors using an extracted local level set
The level-set method is a popular interface tracking method in two-phase flow
simulations. An often-cited reason for using it is that the method naturally
handles topological changes in the interface, e.g. merging drops, due to the
implicit formulation. It is also said that the interface curvature and normal
vectors are easily calculated. This last point is not, however, the case in the
moments during a topological change, as several authors have already pointed
out. Various methods have been employed to circumvent the problem. In this
paper, we present a new such method which retains the implicit level-set
representation of the surface and handles general interface configurations. It
is demonstrated that the method extends easily to 3D. The method is validated
on static interface configurations, and then applied to two-phase flow
simulations where the method outperforms the standard method and the results
agree well with experiments.Comment: 31 pages, 18 figure
Multi-objective topology optimization of heat transfer surface using level-set method and adaptive mesh refinement in OpenFOAM
The present study proposes a new efficient and robust algorithm for
multi-objectives topology optimization of heat transfer surfaces to achieve
heat transfer enhancement with a less pressure drop penalty based on a
continuous adjoint approach. It is achieved with a customized OpenFOAM solver,
which is based on a volume penalization method for solving a steady and laminar
flow around iso-thermal solid objects with arbitrary geometries. The
fluid-solid interface is captured by a level-set function combined with a newly
proposed robust reinitialization scheme ensuring that the interface diffusion
is always kept within a single local grid spacing. Adaptive mesh refinement is
applied in near-wall regions automatically detected by the level-set function
to keep high resolution locally, thereby reduces the overall computational cost
for the forward and adjoint analyses. The developed solver is first validated
in a drag reduction problem of a flow around a two-dimensional cylinder at the
Reynolds numbers of 10 and 40 by comparing reference data. Then, the proposed
scheme is extended to heat transfer problems in a two-dimensional flow at the
Prandtl number of 0.7 and 6.9. Finally, three-dimensional topology optimization
for multi-objective problems is considered for cost functionals with different
weights for the total drag and heat transfer. Among various solutions obtained
on the Pareto front, 4.0% of heat transfer enhancement with 12.6% drag
reduction is achieved at the Reynolds number of 10 and the Prandtl number of
6.9. Moreover, the optimization of a staggered pin-fin array demonstrates that
the optimal shapes and arrangement of the fins strongly depend on the number of
rows from the inlet. Specifically, the pin-fins in the first and third rows
extended in the upstream direction further enhance heat transfer, while the
fins in the second row vanish to reduce pressure loss.Comment: Submitted to International Journal of Heat and Mass Transfer on Aug.
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Simulating water-entry/exit problems using Eulerian-Lagrangian and fully-Eulerian fictitious domain methods within the open-source IBAMR library
In this paper we employ two implementations of the fictitious domain (FD)
method to simulate water-entry and water-exit problems and demonstrate their
ability to simulate practical marine engineering problems. In FD methods, the
fluid momentum equation is extended within the solid domain using an additional
body force that constrains the structure velocity to be that of a rigid body.
Using this formulation, a single set of equations is solved over the entire
computational domain. The constraint force is calculated in two distinct ways:
one using an Eulerian-Lagrangian framework of the immersed boundary (IB) method
and another using a fully-Eulerian approach of the Brinkman penalization (BP)
method. Both FSI strategies use the same multiphase flow algorithm that solves
the discrete incompressible Navier-Stokes system in conservative form. A
consistent transport scheme is employed to advect mass and momentum in the
domain, which ensures numerical stability of high density ratio multiphase
flows involved in practical marine engineering applications. Example cases of a
free falling wedge (straight and inclined) and cylinder are simulated, and the
numerical results are compared against benchmark cases in literature.Comment: The current paper builds on arXiv:1901.07892 and re-explains some
parts of it for the reader's convenienc
A gradient-augmented level set method with an optimally local, coherent advection scheme
The level set approach represents surfaces implicitly, and advects them by
evolving a level set function, which is numerically defined on an Eulerian
grid. Here we present an approach that augments the level set function values
by gradient information, and evolves both quantities in a fully coupled
fashion. This maintains the coherence between function values and derivatives,
while exploiting the extra information carried by the derivatives. The method
is of comparable quality to WENO schemes, but with optimally local stencils
(performing updates in time by using information from only a single adjacent
grid cell). In addition, structures smaller than the grid size can be located
and tracked, and the extra derivative information can be employed to obtain
simple and accurate approximations to the curvature. We analyze the accuracy
and the stability of the new scheme, and perform benchmark tests.Comment: 28 pages, 14 figure
Adaptive mesh refinement in locally conservative level set methods for multiphase fluid displacements in porous media
Multiphase flow in porous media often occurs with the formation and coalescence of fluid ganglia. Accurate predictions of such mechanisms in complex pore geometries require simulation models with local mass conservation and with the option to improve resolution in areas of interest. In this work, we incorporate patch-based, structured adaptive mesh refinement capabilities into a method for local volume conservation that describes the behaviour of disconnected fluid ganglia during level set simulations of capillary-controlled displacement in porous media. We validate the model against analytical solutions for three-phase fluid configurations in idealized pores containing gas, oil, and water, by modelling the intermediate-wet oil layers as separate domains with their volumes preserved. Both the pressures and volumes of disconnected ganglia converge to analytical values with increased refinement levels of the adaptive mesh. Favourable results from strong and weak scaling tests emphasize that the number of patches per processor and the total number of patches are important parameters for efficient parallel simulations with adaptive mesh refinement. Simulations of two-phase imbibition and three-phase gas invasion on segmented 3D images of water-wet sandstone show that adaptive mesh refinement has the highest impact on three-phase displacements, especially concerning the behaviour of the conserved, intermediate-wet phase.publishedVersio
A Deep Learning Approach for the Computation of Curvature in the Level-Set Method
We propose a deep learning strategy to estimate the mean curvature of
two-dimensional implicit interfaces in the level-set method. Our approach is
based on fitting feed-forward neural networks to synthetic data sets
constructed from circular interfaces immersed in uniform grids of various
resolutions. These multilayer perceptrons process the level-set values from
mesh points next to the free boundary and output the dimensionless curvature at
their closest locations on the interface. Accuracy analyses involving irregular
interfaces, both in uniform and adaptive grids, show that our models are
competitive with traditional numerical schemes in the and norms. In
particular, our neural networks approximate curvature with comparable precision
in coarse resolutions, when the interface features steep curvature regions, and
when the number of iterations to reinitialize the level-set function is small.
Although the conventional numerical approach is more robust than our framework,
our results have unveiled the potential of machine learning for dealing with
computational tasks where the level-set method is known to experience
difficulties. We also establish that an application-dependent map of local
resolutions to neural models can be devised to estimate mean curvature more
effectively than a universal neural network.Comment: Submitted to SIAM Journal on Scientific Computin
Level set methods for high-order unfitted discontinuous Galerkin schemes
This work presents three algorithms for the level set modeling of phase boundaries.
The application of these algorithms are high-order extended discontinuous Galerkin
methods for multiphase flow simulations.
The first algorithm is a reinitialization method, which is based on solving an elliptic
partial differential equation. The algorithm is high order accurate in global norms. This
reinitialization technique can be applied to arbitrary problems by using a first-order
solver as preconditioning.
The second algorithm is a high-order accurate solver for extending quantities from
the interface into the domain. This is especially helpful for using a so called extension
velocity for cases, in which the velocity of the interface is not given by a global field.
Like the reinitialization algorithm, the method relies on solving an elliptic partial
differential equation. Based on the underlying level-set, this problem might be ill-
posed. An extension by an artificial viscosity allows stable solutions even for these
cases.
The third algorithm is a coupling of these two algorithms to an upwind discretiza-
tion of the level set transport equation using an implicit time stepping scheme. For
sufficiently smooth problems, this coupling gives high order accuracy as well. Last,
this coupled scheme is applied to the simulation of a rising bubble using an unfitted
discontinuous Galerkin scheme, which shows good agreement with reference solutions
from literature
An Energy Formulation of Surface Tension or Willmore Force For Two-Phase Flow
The motion of a biological cell in liquid is a rich subject for modeling. In the early 1970’s, it was realized by Canham that biological vesicles with lipid bilayer membranes reach a steady state shape that minimizes bending. Helfrich soon after mathematically quantified the related bending energy and showed that the shapes from minimizing this bending energy match the types of shapes observed in nature. The resulting Canham-Helfrich energy, consisting of bending energy and a constant surface area and volume constraint, is a major component of any model of cellular motility.
To this end, we consider the cellular vesicle to be a closed interface between two fluids and we present a finite element model for a two-phase flow coupling the minimization of some given energy defined on the interface to the incompressible flow of the two fluids, which is then advected according to the resulting velocity field. We provide a general framework for incorporating the energies on the interface and then focus on three applications of energy on the interface: the first is surface tension minimizing the surface area energy, the second minimizes the bending energy without explicit surface area or volume constraints, the third minimizes the Canham-Helfrich energy including the constraints. We present a semi-implicit model for bending energy which uses an implicit levelset formulation for the interface and couples the forces from the interface to the two phase incompressible Navier-Stokes system through the use of an approximate Dirac delta function defined on a band around the interface. By using energies to describe the motion, our model is immediately provided with a sense of energy stability.
We provide various numerical simulations and validations of flow under these three energies in two and three dimensions. Our simulations confirm that enforcing the volume constraint in the incompressible flow is vital to achieve the desired steady state shapes
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