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EN
The hydrogen gas permeation through polymer materials is due to two different mechanisms : molecular and atomic diffusion. Indeed, this overall gas diffusion is strongly affected by the microstructural composition of the material, the production process, and also the experimental conditions. Consequently, the hydrogen permeation parameters, when available in the literature, are changing and unreliable. The need of an accurate knowledge of these parameters for a specific polymer, after complete process, leads us to design an experimental apparatus based on the manometric method and its corresponding numerical model. From initial approximate values roughly deduced from a first experiment, the numerical model implemented in Matlab language, allows a refining of the parameters, by fitting the simulated values to the experimental ones on successive experiments. These experiments are carried out on a sample with increasing upstream pressures from 25 bar up to 150 bar. Because of the high pressure values, the beginning of permeation experiments are affected by the gas flow disturbance due to the sharp pressure rising. Considering this delay time induced by the pressure increase, the permeation parameters are evaluated more accurately. In fact, with a single experiment the phenomenon cannot be readily separated from the so-called time-lag parameter occurring in gas diffusion through a material.
EN
A problem concerning finite-dimensional approximation for some group of continuous bioreactors with axial dispersion was discussed. An oxidation ditch with partial recirculation of biomass was assumed as a case study. The presented methods were used to obtain steady states and steady-state branches as well as to analyse their linear stability. Three finite-dimensional approximation methods were tested and compared, i.e.: equivalent tanks-in-series approximation, finite difference algorithm and orthogonal collocation. As a numerical example, the aerobic biodegradation of a carbonaceous substrate was analysed with a dual-substrate growth kinetics, namely the Haldane kinetics for the carbonaceous substrate and Monod kinetics for oxygen.
PL
Przedstawiono zagadnienie aproksymacji skończenie wymiarowej pewnej grupy obiektów biochemicznych z dyspersją wzdłużną. Jako przykład wybrano kanał napowietrzający z recyrkulacją biomasy. Omówione metody aproksymacyjne zastosowano do wyznaczania stanów ustalonych oraz gałęzi stanów stacjonarnych, a także do analizy stabilności lokalnej tych stanów. Przetestowano i porównano metodę kaskady zastępczej, metodę różnic skończonych i metodę kolokacji ortogonalnej. Analizowano aerobową biodegradację związku organicznego wykazującego inhibitujący wpływ na wzrost biomasy. Do opisu szybkości wzrostu biomasy oraz zużywania reagenta węglowego i tlenu użyto kinetyki dwusubstratowej Haldane-Monoda.
EN
This article presents the implementation of two well known absorbing boundary conditions in a fourth-order accurate staggered grid SH-wave finite difference (FD) algorithm with variable grid size, in a very simplified manner. Based on simulated results, it was confirmed that the Clayton and Engquist absorbing boundary condition causes edge-reflections in case of larger angle of incidence of body waves on the model edges. The results of various numerical experiments revealed that the Israeli and Orszag sponge boundary condition is efficient enough to avoid edge-reflections for any angle of incidence of the body. We recommend the use of both the Clayton and Engquist and Israeli and Orszag absorbing boundary conditions simultaneously to avoid any edge-reflections
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