Sep 23, 2014
Vít Orava, Charles University in Prague, Faculty of Mathematics and Physics, Prague, Czech Republic ZHAW Zürich University of Applied Sciences, Institute of Computational Physics, Winterthur, Switzerland Joint work with Ondrej Soucek and Peter Cendula We investigate modelling of fluidized bed reactor which, in presence of platinumbased (solid) catalytic particles, decomposes liquid formic acid and produces gaseous mixture of carbon dioxide and hydrogen. We treat the system as a mixture in a control volume where we distinguish partial densities and velocities sharing one thermal field. First of all, we consider four constituents, namely formic acid (FA), Platinum micro-pellets (Pt), carbon dioxide (CO2) and hydrogen (H2). Secondly, we reduce the four-constituents model to a binary mixture model of liquid phase (Pt + FA) and gaseous phase (CO2 + H2) which forms bubbles. Liquid phase is considered as non-Newtonian fluid satisfying compresible Navier- Stokes equation with temperature-dependent density and viscosity modelled by Boussinesq approximation and Williams-Landel-Ferry model. Physical interaction between the bubbles and liquid is modelled under equilibrium assumption by the pressure-drag balance. Chemical rates satisfy mass-action law and undergo Arrhenius kinetics. Simulations were performed in COMSOL Multiphysics.
MOdelling REvisited + MOdel REduction Modeling, analysis and computing in nonlinear PDEs. September 21-26, 2014, Chateau Liblice, Czech Republic. Recently developed implicit constitutive theory allows one to describe nonlinear response of complex materials in complicated processes and to model phenomena in both fluid and solid mechanics that have hitherto remained unexplained. The theory also provides a thermodynamically consistent framework for technologically important but so far only ad hoc engineering models without sound footing. The overall goal of the project is to develop accurate, efficient and robust numerical methods that allow one to perform large-scale simulations for the models arising from the new theoretical framework. A natural part of the goal is rigorous mathematical analysis of the models. The nonstandard structure of constitutive relations arising from the new framework requires the reconsideration of many existing approaches in the mathematical theory of partial differential equations and the development of new ones. In particular, basic notions such as the concept of the solution and its well-posedness need to be reconsidered. Further, the complexity of the constitutive relations calls for rigorous investigation on model reduction - the identification of simplified models that capture the chosen (practically relevant) information about the behaviour of the system and disregard irrelevant information. Reliable numerical simulations require the derivation of sharp a posteriori error estimates to control all possible sources of errors, including rarely studied but important algebraic errors. We believe that in solving difficult problems in mathematical modelling the individual aspects discussed above - physics, mathematical analysis and numerical analysis - are so closely interrelated that no breakthrough can be achieved without emphasising the holistic approach as the main principle. Our vision is to follow this principle: the entire process of modelling of complex materials will be revisited in an innovative manner.
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