22,561 research outputs found
New numerical approaches for modeling thermochemical convection in a compositionally stratified fluid
Seismic imaging of the mantle has revealed large and small scale
heterogeneities in the lower mantle; specifically structures known as large low
shear velocity provinces (LLSVP) below Africa and the South Pacific. Most
interpretations propose that the heterogeneities are compositional in nature,
differing in composition from the overlying mantle, an interpretation that
would be consistent with chemical geodynamic models. Numerical modeling of
persistent compositional interfaces presents challenges, even to
state-of-the-art numerical methodology. For example, some numerical algorithms
for advecting the compositional interface cannot maintain a sharp compositional
boundary as the fluid migrates and distorts with time dependent fingering due
to the numerical diffusion that has been added in order to maintain the upper
and lower bounds on the composition variable and the stability of the advection
method. In this work we present two new algorithms for maintaining a sharper
computational boundary than the advection methods that are currently openly
available to the computational mantle convection community; namely, a
Discontinuous Galerkin method with a Bound Preserving limiter and a
Volume-of-Fluid interface tracking algorithm. We compare these two new methods
with two approaches commonly used for modeling the advection of two distinct,
thermally driven, compositional fields in mantle convection problems; namely,
an approach based on a high-order accurate finite element method advection
algorithm that employs an artificial viscosity technique to maintain the upper
and lower bounds on the composition variable as well as the stability of the
advection algorithm and the advection of particles that carry a scalar quantity
representing the location of each compositional field. All four of these
algorithms are implemented in the open source FEM code ASPECT
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 simulation of electrophoresis separation processes
A new Petrov-Galerkin finite element formulation has been proposed for transient convection-diffusion problems. Most Petrov-Galerkin formulations take into account the spatial discretization, and the weighting functions so developed give satisfactory solutions for steady state problems. Though these schemes can be used for transient problems, there is scope for improvement. The schemes proposed here, which consider temporal as well as spatial discretization, provide improved solutions. Electrophoresis, which involves the motion of charged entities under the influence of an applied electric field, is governed by equations similiar to those encountered in fluid flow problems, i.e., transient convection-diffusion equations. Test problems are solved in electrophoresis and fluid flow. The results obtained are satisfactory. It is also expected that these schemes, suitably adapted, will improve the numerical solutions of the compressible Euler and the Navier-Stokes equations
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
On the role of confinement on solidification in pure materials and binary alloys
We use a phase-field model to study the effect of confinement on dendritic
growth, in a pure material solidifying in an undercooled melt, and in the
directional solidification of a dilute binary alloy. Specifically, we observe
the effect of varying the vertical domain extent () on tip selection,
by quantifying the dendrite tip velocity and curvature as a function of
, and other process parameters. As decreases, we find that the
operating state of the dendrite tips becomes significantly affected by the
presence of finite boundaries. For particular boundary conditions, we observe a
switching of the growth state from 3-D to 2-D at very small , in both
the pure material and alloy. We demonstrate that results from the alloy model
compare favorably with those from an experimental study investigating this
effect.Comment: 13 pages, 9 figures, 3 table
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