172 research outputs found
A sequential regularization method for time-dependent incompressible Navier--Stokes equations
The objective of the paper is to present a method, called sequential regularization method (SRM), for the nonstationary incompressible Navier-Stokes equations from the viewpoint of regularization of differential-algebraic equations (DAEs) , and to provide a way to apply a DAE method to partial differential-algebraic equations (PDAEs). The SRM is a functional iterative procedure. It is proved that its convergence rate is O(ffl m ), where m is the number of the SRM iterations and ffl is the regularization parameter. The discretization and implementation issues of the method are considered. In particular, a simple explicit difference scheme is analyzed and its stability is proved under the usual step size condition of explicit schemes. It appears that the SRM formulation is new in the Navier-Stokes context. Unlike other regularizations or pseudo-compressibility methods in the Navier-Stokes context, the regularization parameter ffl in the SRM need not be very small, and the regularized..
The Dynamics of Liquid Drops and their Interaction with Solids of Varying Wettabilites
Microdrop impact and spreading phenomena are explored as an interface
formation process using a recently developed computational framework. The
accuracy of the results obtained from this framework for the simulation of high
deformation free-surface flows is confirmed by a comparison with previous
numerical studies for the large amplitude oscillations of free liquid drops.
Our code's ability to produce high resolution benchmark calculations for
dynamic wetting flows is then demonstrated by simulating microdrop impact and
spreading on surfaces of greatly differing wettability. The simulations allow
one to see features of the process which go beyond the resolution available to
experimental analysis. Strong interfacial effects which are observed at the
microfluidic scale are then harnessed by designing surfaces of varying
wettability that allow new methods of flow control to be developed
The Detection of Unsteady Flow Separation with Bioinspired Hair-Cell Sensors
Biologists hypothesize that thousands of micro-scale hairs found on bat wings function as a network of air-flow sensors as part of a biological feedback flow control loop. In this work, we investigate hair-cell sensors as a means of detecting flow features in an unsteady separating flow over a cylinder. Individual hair-cell sensors were modeled using an Euler-Bernoulli beam equation forced by the fluid flow. When multiple sensor simulations are combined into an array of hair-cells, the response is shown to detect the onset and span of flow reversal, the upstream movement of the point of zero wall shear-stress, and the formation and growth of eddies near the wall of a cylinder. A linear algebraic hair-cell model, written as a function of the flow velocity, is also derived and shown to capture the same features as the hair-cell array simulatio
Singular and regular solutions of a non-linear parabolic system
We study a dissipative nonlinear equation modelling certain features of the
Navier-Stokes equations. We prove that the evolution of radially symmetric
compactly supported initial data does not lead to singularities in dimensions
. For dimensions we present strong numerical evidence supporting
existence of blow-up solutions. Moreover, using the same techniques we
numerically confirm a conjecture of Lepin regarding existence of self-similar
singular solutions to a semi-linear heat equation.Comment: 16 page
Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations
The Navier--Stokes equations are commonly used to model and to simulate flow
phenomena. We introduce the basic equations and discuss the standard methods
for the spatial and temporal discretization. We analyse the semi-discrete
equations -- a semi-explicit nonlinear DAE -- in terms of the strangeness index
and quantify the numerical difficulties in the fully discrete schemes, that are
induced by the strangeness of the system. By analyzing the Kronecker index of
the difference-algebraic equations, that represent commonly and successfully
used time stepping schemes for the Navier--Stokes equations, we show that those
time-integration schemes factually remove the strangeness. The theoretical
considerations are backed and illustrated by numerical examples.Comment: 28 pages, 2 figure, code available under DOI: 10.5281/zenodo.998909,
https://doi.org/10.5281/zenodo.99890
Phase Field Model for Three-Dimensional Dendritic Growth with Fluid Flow
We study the effect of fluid flow on three-dimensional (3D) dendrite growth
using a phase-field model on an adaptive finite element grid. In order to
simulate 3D fluid flow, we use an averaging method for the flow problem coupled
to the phase-field method and the Semi-Implicit Approximated Projection Method
(SIAPM). We describe a parallel implementation for the algorithm, using Charm++
FEM framework, and demonstrate its efficiency. We introduce an improved method
for extracting dendrite tip position and tip radius, facilitating accurate
comparison to theory. We benchmark our results for two-dimensional (2D)
dendrite growth with solvability theory and previous results, finding them to
be in good agreement. The physics of dendritic growth with fluid flow in three
dimensions is very different from that in two dimensions, and we discuss the
origin of this behavior
Finite element simulation of three-dimensional free-surface flow problems
An adaptive finite element algorithm is described for the stable solution of three-dimensional free-surface-flow problems based primarily on the use of node movement. The algorithm also includes a discrete remeshing procedure which enhances its accuracy and robustness. The spatial discretisation allows an isoparametric piecewise-quadratic approximation of the domain geometry for accurate resolution of the curved free surface.
The technique is illustrated through an implementation for surface-tension-dominated viscous flows modelled in terms of the Stokes equations with suitable boundary conditions on the deforming free surface. Two three-dimensional test problems are used to demonstrate the performance of the method: a liquid bridge problem and the formation of a fluid droplet
GANDALF - Graphical Astrophysics code for N-body Dynamics And Lagrangian Fluids
GANDALF is a new hydrodynamics and N-body dynamics code designed for investigating planet formation, star formation and star cluster problems. GANDALF is written in C++, parallelised with both OpenMP and MPI and contains a python library for analysis and visualisation. The code has been written with a fully object-oriented approach to easily allow user-defined implementations of physics modules or other algorithms. The code currently contains implementations of Smoothed Particle Hydrodynamics, Meshless Finite-Volume and collisional N-body schemes, but can easily be adapted to include additional particle schemes. We present in this paper the details of its implementation, results from the test suite, serial and parallel performance results and discuss the planned future development. The code is freely available as an open source project on the code-hosting website github at https://github.com/gandalfcode/gandalf and is available under the GPLv2 license.This research was supported by the DFG cluster of excellence "Origin and Structure of the Universe", DFG Projects 841797-4, 841798-2 (DAH, GPR), the DISCSIM project, grant agreement 341137 funded by the European Research Council under ERC-2013-ADG (GPR, RAB). Some development of the code and simulations have been carried out on the computing facilities of the Computational centre for Particle and Astrophysics (C2PAP) and on the DiRAC Data Analytic system at the University of Cambridge, operated by the University of Cambridge High Performance Computing Service on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk); the equipment was funded by BIS National E-infrastructure capital grant (ST/K001590/1), STFC capital grants ST/H008861/1 and ST/H00887X/1, and STFC DiRAC Operations grant ST/K00333X/1
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