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1

Two implementations of the preconditioned conjugate gradient method on heterogeneous computing grids

Collignon T. P., Van Gijzen M. B.

International Journal of Applied Mathematics and Computer Science

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2010

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Vol. 20, no 1

109-121

EN

Efficient iterative solution of large linear systems on grid computers is a complex problem. The induced heterogeneity and volatile nature of the aggregated computational resources present numerous algorithmic challenges. This paper describes a case study regarding iterative solution of large sparse linear systems on grid computers within the software constraints of the grid middleware GridSolve and within the algorithmic constraints of preconditioned Conjugate Gradient (CG) type methods. We identify the various bottlenecks induced by the middleware and the iterative algorithm. We consider the standard CG algorithm of Hestenes and Stiefel, and as an alternative the Chronopoulos/Gear variant, a formulation that is potentially better suited for grid computing since it requires only one synchronisation point per iteration, instead of two for standard CG. In addition, we improve the computation-to-communication ratio by maximising the work in the preconditioner. In addition to these algorithmic improvements, we also try to minimise the communication overhead within the communication model currently used by the GridSolve middleware. We present numerical experiments on 3D bubbly flow problems using heterogeneous computing hardware that show lower computing times and better speed-up for the Chronopoulos/Gear variant of conjugate gradients. Finally, we suggest extensions to both the iterative algorithm and the middleware for improving granularity.

2

Hydrodynamic regimes of gas-liquid flow in a microreactor channel

Pohorecki R., Sobieszuk P., Kula K., Moniuk W., Zieliński M.

Prace Naukowe Instytutu Inżynierii Chemicznej Polskiej Akademii Nauk

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2006

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nr 7

53-58

EN

The hydrodynamic regimes of gas-liquid flow in a microreactor channel have been investigated, using water and 1-propanol (liquids with different contact angle and surface tension values) and nitrogen as an inert gas. The microreactor was Y shaped. Experiments were carried out to determine the character ofgas and liquid flow ("regime map"). Four main flow types were observed: bubbie, sług, slug/annular and annular.

PL

Zbadano reżimy hydrodynamiczne w mikroreaktorze gaz - ciecz. Użyto wody oraz 1-propanolu (cieczy o zróżnicowanych kątach zwilżania i napięcia powierzchniowego) i azotu jako gazu inertnego. Kanał mikroreaktora miał kształt litery Y. Eksperymenty były prowadzone w celu zdefiniowania charakteru przepływu gazu i cieczy ("mapa reżimów"). Zaobserwowano główne 4 typy przepływów: pęcherzykowy "bubble", rzutowy "slug", rzutowo - pierścieniowy "slug/annular" oraz pierścieniowy "annular".

3

Improved model of void fraction distribution in two-phase flow in the boundary layer

Mikielewicz D., Wajs J.

Archives of Thermodynamics

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2006

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Vol. 27, no. 3

95-116

EN

The aim of present work is investigation focused on experimental verification of forces acting on bubble flowing along the wall and subsequent implementation of the findings into the model of void fraction distribution, developed earlier by one of the co-authors [6]. In experimental investigations the bubble is represented by a solid sphere suspended on a thin string. Authors are convinced that the presented model of a bubble motion captures at least a qualitative behaviour of a bubble in the bubbly flow and will compliment the transverse force balance acting on the bubble. Such transverse balance of forces forms one of equations involved in the model of void fraction developed by Mikielewicz [6]. Presented results of experimental research show periodic character of sphere movement (simplified bubble model) along the wall of vertical channel, which is in line with findings of the experiments preformed on bubbles in vicinity of wall. Sphere trajectory visibly changes, which are caused by non-uniform velocity distribution of fluid around the sphere related to non-uniform pressure field around it, giving in such a way rise to the repelling force. The wall force was introduced to the model of void fraction distribution and improved results were obtained.

4

Simulation of condensation in a subcooled bubbly steam-water flow along a large vertical pipe

Lucas D., Prasser H.

Archives of Thermodynamics

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2005

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Vol. 26, no. 4

49-59

EN

Detailed experimental data obtained at the TOPFLOW facility for steam-water vertical pipe flow were used to test the complex interaction of local bubble distributions, bubble size distributions and local heat and mass transfer. Steam is injected into subcooled water and condenses during the upward flow. The model considers a large number of bubble classes (50). This allows the investigation of the influence of the bubble size distribution. The results of the simulations show a good agreement with experimental data. The condensation process is clearly slower, if large bubbles are injected (4 mm holes). Also the bubble break-up has a strong influence on the condensation process because of the change of the interfacial area. Some unsureness arises from the unknown interfacial area for large bubbles and possible uncertainties of the heat transfer coefficient.