Numerické metody pro nelineární proudění v porézním prostředí s puklinami
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Hlavním cílem této diplomové práce je formulace, aproximace a numerické řešení Darcyovy-Forchheimerovy rovnice. Pro numerické řešení byly vybrány tři linearizační metody; Picardova iterace, Newtonova metoda a metoda L-schéma. Všechny tři linearizační metody byly naimplementovány do softwaru Flow123d. Metody byly nejdříve otestovány na jednoduchém analytickém řešení a na problému dvou kolmých puklin. Nakonec byla vybrána jedna linearizační metoda a otestována na benchmarkovém problému.
The main goal of this Master Thesis is the formulation, approximation and numerical solution of the Darcy-Forchheimer equation for non-linear flow in fractured porous media. For the numerical solution, three linearization methods have been chosen; Picard iterations, Newton's method and L-scheme method. All three of them have been implemented into the software Flow123d. The methods have been compared and verified on a simple analytical solution, and on a problem of two perpendicular fractures. Finally, one linearization method was chosen and tested on a benchmark case.
The main goal of this Master Thesis is the formulation, approximation and numerical solution of the Darcy-Forchheimer equation for non-linear flow in fractured porous media. For the numerical solution, three linearization methods have been chosen; Picard iterations, Newton's method and L-scheme method. All three of them have been implemented into the software Flow123d. The methods have been compared and verified on a simple analytical solution, and on a problem of two perpendicular fractures. Finally, one linearization method was chosen and tested on a benchmark case.
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Darcyova-Forchheimerova rovnice, nelineární parciální diferenciální rovnice, smíšená hybridní formulace, metoda konečných prvků, iterační metody, Picardova iterace, Newtonova metoda, metoda L-schéma, Flow123d, benchmark, Darcy-Forchheimer equation, non-linear partial differential equation, mixed hybrid approximation, finite element method, iterative methods, Picard iterations, Newton's method, L-scheme method, Flow123d, benchmark