222 research outputs found
G-CSC Report 2010
The present report gives a short summary of the research of the Goethe Center for Scientific Computing (G-CSC) of the Goethe University Frankfurt. G-CSC aims at developing and applying methods and tools for modelling and numerical simulation of problems from empirical science and technology. In particular, fast solvers for partial differential equations (i.e. pde) such as robust, parallel, and adaptive multigrid methods and numerical methods for stochastic differential equations are developed. These methods are highly adanvced and allow to solve complex problems..
The G-CSC is organised in departments and interdisciplinary research groups. Departments are localised directly at the G-CSC, while the task of interdisciplinary research groups is to bridge disciplines and to bring scientists form different departments together. Currently, G-CSC consists of the department Simulation and Modelling and the interdisciplinary research group Computational Finance
[Research activities in applied mathematics, fluid mechanics, and computer science]
This report summarizes research conducted at the Institute for Computer Applications in Science and Engineering in applied mathematics, fluid mechanics, and computer science during the period April 1, 1995 through September 30, 1995
Towards modelling physical and chemical effects during wettability alteration in carbonates at pore and continuum scales
Understanding what controls the enhanced oil recovery during waterflooding
of carbonate rocks is essential as the majority of the world’s
remaining hydrocarbon reserves are contained in carbonate rocks. To
further this understanding, in this thesis we develop a pore-scale simulator
that allows us to look at the fundamental physics of fluid flow and
reactive solute transport within the porous media. The simulator is based
on the combined finite element – finite volume method, it incorporates
efficient discretization schemes and can hence be applied to porous domains
with hundreds of pores. Our simulator includes the rule-based
method of accounting for the presence of the second immiscibly trapped
fluid phase. Provided that we know what chemical conditions initiate
enhanced oil recovery, our simulator allows us to analyse whether these
conditions occur, where they occur and how they are influenced by the
flow of the aqueous phase at the pore scale. To establish the nature of
chemical interactions between the injected brines and the carbonate rocks,
we analyze the available experimental data on the single-phase coreflooding
of carbonate rocks. We then build a continuum scale simulation that
incorporates various chemical reactions, such as ions adsorption and
mineral dissolution and precipitation. We match the output of the continuum
scale model with the experimental data to identify what chemical
interactions the ions dissolved in seawater are involved in
Efficient upwind algorithms for solution of the Euler and Navier-stokes equations
An efficient three-dimensionasl tructured solver for the Euler and
Navier-Stokese quations is developed based on a finite volume upwind algorithm
using Roe fluxes. Multigrid and optimal smoothing multi-stage time stepping accelerate convergence. The accuracy of the new solver is demonstrated for inviscid
flows in the range 0.675 :5M :5 25. A comparative grid convergence study for
transonic turbulent flow about a wing is conducted with the present solver and
a scalar dissipation central difference industrial design solver. The upwind solver
demonstrates faster grid convergence than the central scheme, producing more
consistent estimates of lift, drag and boundary layer parameters. In transonic
viscous computations, the upwind scheme with convergence acceleration is over
20 times more efficient than without it. The ability of the upwind solver to compute
viscous flows of comparable accuracy to scalar dissipation central schemes
on grids of one-quarter the density make it a more accurate, cost effective alternative.
In addition, an original convergencea cceleration method termed shock
acceleration is proposed. The method is designed to reduce the errors caused by
the shock wave singularity M -+ 1, based on a localized treatment of discontinuities.
Acceleration models are formulated for an inhomogeneous PDE in one
variable. Results for the Roe and Engquist-Osher schemes demonstrate an order
of magnitude improvement in the rate of convergence. One of the acceleration
models is extended to the quasi one-dimensiona Euler equations for duct flow.
Results for this case d monstrate a marked increase in convergence with negligible
loss in accuracy when the acceleration procedure is applied after the shock
has settled in its final cell. Typically, the method saves up to 60% in computational
expense. Significantly, the performance gain is entirely at the expense of
the error modes associated with discrete shock structure. In view of the success
achieved, further development of the method is proposed
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