13,576 research outputs found
Proceedings for the ICASE Workshop on Heterogeneous Boundary Conditions
Domain Decomposition is a complex problem with many interesting aspects. The choice of decomposition can be made based on many different criteria, and the choice of interface of internal boundary conditions are numerous. The various regions under study may have different dynamical balances, indicating that different physical processes are dominating the flow in these regions. This conference was called in recognition of the need to more clearly define the nature of these complex problems. This proceedings is a collection of the presentations and the discussion groups
An asymptotic induced numerical method for the convection-diffusion-reaction equation
A parallel algorithm for the efficient solution of a time dependent reaction convection diffusion equation with small parameter on the diffusion term is presented. The method is based on a domain decomposition that is dictated by singular perturbation analysis. The analysis is used to determine regions where certain reduced equations may be solved in place of the full equation. Parallelism is evident at two levels. Domain decomposition provides parallelism at the highest level, and within each domain there is ample opportunity to exploit parallelism. Run time results demonstrate the viability of the method
Numerical Methods for Solving Convection-Diffusion Problems
Convection-diffusion equations provide the basis for describing heat and mass
transfer phenomena as well as processes of continuum mechanics. To handle flows
in porous media, the fundamental issue is to model correctly the convective
transport of individual phases. Moreover, for compressible media, the pressure
equation itself is just a time-dependent convection-diffusion equation.
For different problems, a convection-diffusion equation may be be written in
various forms. The most popular formulation of convective transport employs the
divergent (conservative) form. In some cases, the nondivergent (characteristic)
form seems to be preferable. The so-called skew-symmetric form of convective
transport operators that is the half-sum of the operators in the divergent and
nondivergent forms is of great interest in some applications.
Here we discuss the basic classes of discretization in space: finite
difference schemes on rectangular grids, approximations on general polyhedra
(the finite volume method), and finite element procedures. The key properties
of discrete operators are studied for convective and diffusive transport. We
emphasize the problems of constructing approximations for convection and
diffusion operators that satisfy the maximum principle at the discrete level
--- they are called monotone approximations.
Two- and three-level schemes are investigated for transient problems.
Unconditionally stable explicit-implicit schemes are developed for
convection-diffusion problems. Stability conditions are obtained both in
finite-dimensional Hilbert spaces and in Banach spaces depending on the form in
which the convection-diffusion equation is written
Spectral methods for CFD
One of the objectives of these notes is to provide a basic introduction to spectral methods with a particular emphasis on applications to computational fluid dynamics. Another objective is to summarize some of the most important developments in spectral methods in the last two years. The fundamentals of spectral methods for simple problems will be covered in depth, and the essential elements of several fluid dynamical applications will be sketched
Monolithic simulation of convection-coupled phase-change - verification and reproducibility
Phase interfaces in melting and solidification processes are strongly
affected by the presence of convection in the liquid. One way of modeling their
transient evolution is to couple an incompressible flow model to an energy
balance in enthalpy formulation. Two strong nonlinearities arise, which account
for the viscosity variation between phases and the latent heat of fusion at the
phase interface.
The resulting coupled system of PDE's can be solved by a single-domain
semi-phase-field, variable viscosity, finite element method with monolithic
system coupling and global Newton linearization. A robust computational model
for realistic phase-change regimes furthermore requires a flexible
implementation based on sophisticated mesh adaptivity. In this article, we
present first steps towards implementing such a computational model into a
simulation tool which we call Phaseflow.
Phaseflow utilizes the finite element software FEniCS, which includes a
dual-weighted residual method for goal-oriented adaptive mesh refinement.
Phaseflow is an open-source, dimension-independent implementation that, upon an
appropriate parameter choice, reduces to classical benchmark situations
including the lid-driven cavity and the Stefan problem. We present and discuss
numerical results for these, an octadecane PCM convection-coupled melting
benchmark, and a preliminary 3D convection-coupled melting example,
demonstrating the flexible implementation. Though being preliminary, the latter
is, to our knowledge, the first published 3D result for this method. In our
work, we especially emphasize reproducibility and provide an easy-to-use
portable software container using Docker.Comment: 20 pages, 8 figure
A wildland fire model with data assimilation
A wildfire model is formulated based on balance equations for energy and
fuel, where the fuel loss due to combustion corresponds to the fuel reaction
rate. The resulting coupled partial differential equations have coefficients
that can be approximated from prior measurements of wildfires. An ensemble
Kalman filter technique with regularization is then used to assimilate
temperatures measured at selected points into running wildfire simulations. The
assimilation technique is able to modify the simulations to track the
measurements correctly even if the simulations were started with an erroneous
ignition location that is quite far away from the correct one.Comment: 35 pages, 12 figures; minor revision January 2008. Original version
available from http://www-math.cudenver.edu/ccm/report
Primjena automatskog rafiniranja računalne mreže u Numeričkoj mehanici fluida na problemima turbulentnog toka i izmjene topline
Most processes occurring in devices in air-conditioning systems require fluid flow and heat exchange, and the functioning of these devices is crucially dependent on their understanding. Computational Fluid Dynamics is a modern tool which enables development engineers to simulate the physics of processes on a computer. Such simulations may contain errors because the original problem has been replaced by a simplified discrete problem, solved on a mesh of non-overlapping control volumes and assuming certain solution behaviour in every control volume of the modelled domain. This paper presents the advantages of adaptive-mesh refinement which helps engineers get accurate solutions without their intervention by modifying the mesh where higher accuracy is needed. The potential of the method is shown on some examples often found in engineering practice.Strujanje fluida i izmjena topline su važni procesi u klimatizacijskim uređajima, stoga je njihovo funkcioniranje vrlo vezano uz razumijevanje procesa strujanja i izmjene topline. Numerička mehanika fluida (CFD) je moderni alat koji inženjerima omogućuje simuliranje fizike procesa na računalu. No, takve simulacije mogu sadržavati grješke zato jer se sustav parcijalnih diferencijalnih jednadžbi zamjenjuje s pojednostavljenim diskretnim problemom, koji se rješava na mreži ne-preklapajućih kontrolnih volumena, uz pretpostavku ponašanja rješenja u kontrolnom volumenu domene. U ovom članku iznesene su prednosti lokalnog rafiniranja računalne mreže koji omogućava inženjerima dobivanje točnih rješenja matematičkog modela automatski i bez njihove intervencije kroz automatsku modifikaciju računalne mreže na mjestima gdje je potrebna veća točnost. Mogućnosti metode su prikazane na primjerima prisutnima u inženjerskoj praksi
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