4,124 research outputs found
Solving the Poisson equation on small aspect ratio domains using unstructured meshes
We discuss the ill conditioning of the matrix for the discretised Poisson
equation in the small aspect ratio limit, and motivate this problem in the
context of nonhydrostatic ocean modelling. Efficient iterative solvers for the
Poisson equation in small aspect ratio domains are crucial for the successful
development of nonhydrostatic ocean models on unstructured meshes. We introduce
a new multigrid preconditioner for the Poisson problem which can be used with
finite element discretisations on general unstructured meshes; this
preconditioner is motivated by the fact that the Poisson problem has a
condition number which is independent of aspect ratio when Dirichlet boundary
conditions are imposed on the top surface of the domain. This leads to the
first level in an algebraic multigrid solver (which can be extended by further
conventional algebraic multigrid stages), and an additive smoother. We
illustrate the method with numerical tests on unstructured meshes, which show
that the preconditioner makes a dramatic improvement on a more standard
multigrid preconditioner approach, and also show that the additive smoother
produces better results than standard SOR smoothing. This new solver method
makes it feasible to run nonhydrostatic unstructured mesh ocean models in small
aspect ratio domains.Comment: submitted to Ocean Modellin
A mixed discontinuous/continuous finite element pair for shallow-water ocean modelling
We introduce a mixed discontinuous/continuous finite element pair for ocean
modelling, with continuous quadratic pressure/layer depth and discontinuous
velocity. We investigate the finite element pair applied to the linear
shallow-water equations on an f-plane. The element pair has the property that
all geostrophically balanced states which strongly satisfy the boundary
conditions have discrete divergence equal to exactly zero and hence are exactly
steady states of the discretised equations. This means that the finite element
pair has excellent geostrophic balance properties. We illustrate these
properties using numerical tests and provide convergence calculations which
show that the discretisation has quadratic errors, indicating that the element
pair is stable
Turbulent Flows and Pollution Dispersion around Tall Buildings Using Adaptive Large Eddy Simulation (LES)
The motivation for this work stems from the increased number of high-rise buildings/skyscrapers all over the world, and in London, UK, and hence the necessity to see their effect on the local environment. We concentrate on the mean velocities, Reynolds stresses, turbulent kinetic energies (TKEs) and tracer concentrations. We look at their variations with height at two main locations within the building area, and downstream the buildings. The pollution source is placed at the top of the central building, representing an emission from a Combined Heat and Power (CHP) plant. We see how a tall building may have a positive effect at the lower levels, but a negative one at the higher levels in terms of pollution levels. Mean velocities at the higher levels (over 60 m in real life) are reduced at both locations (within the building area and downstream it), whilst Reynolds stresses and TKEs increase. However, despite the observed enhanced turbulence at the higher levels, mean concentrations increase, indicating that the mean flow has a greater influence on the dispersion. At the lower levels (Z < 60 m), the presence of a tall building enhanced dispersion (hence lower concentrations) for many of the configurations
A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling
Dr D. Pavlidis would like to acknowledge the support from the following research grants: Innovate UK âOctopusâ, EPSRC âReactor Core-Structure Re-location Modelling for Severe Nuclear Accidentsâ) and Horizon 2020 âIn-Vessel Melt Retentionâ. Funding for Dr P. Salinas from ExxonMobil is gratefully acknowledged. Dr Z. Xie is supported by EPSRC âMulti-Scale Exploration of Multi-phase Physics in Flowsâ. Part funding for Prof Jackson under the TOTAL Chairs programme at Imperial College is also acknowledged. The authors would also like to acknowledge Mr Y. Debbabi for supplying analytic solutions.Peer reviewedPublisher PD
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