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Transport and Reaction in Porous Media: Simulation (RTpMNum)5 ECTS (englische Bezeichnung: Transport and Reaction in Porous Media: Simulation)
(Prüfungsordnungsmodul: Forschungsmodule Studienrichtung Modellierung, Simulation und Optimierung)
Modulverantwortliche/r: Serge Kräutle Lehrende:
Peter Knabner
Start semester: |
SS 2019 | Duration: |
1 semester | Cycle: |
jährlich (WS) |
Präsenzzeit: |
38 Std. | Eigenstudium: |
112 Std. | Language: |
Englisch |
Lectures:
Inhalt:
- Degenerate parabolic differential equations as multiphase flow models:
formulation, nonlinear solution methods, discretization methods
Models for transport and reactions in porous media, consisting of coupled PDEs and ODEs, if necessary coupled to algebraic equations (AEs) and inequalities for the description of local equilibria (differential-algebraic system)
Different formulations of the system (operator splitting, change of variables, combination of the equations, elimination of AEs), as a basis for different software packages for numerical simulations, connection to optimisation (Gibbs energy)
Treatment of numerical difficulties (Guarantee of nonnegativity of numerical solutions of the (nonlinear) problems, scaling problems, convection dominated problems
Lernziele und Kompetenzen:
Students
use methods for the numerical solving of a class of problems whose complexity goes significantly beyond standard problems (Poisson and heat equation): coupled nonlinear partial and ordinary differential equations (PDEs, ODEs) and algebraic equations (AEs),
put strategies for the treatment of possible difficulties during the numerical solving into practice.
Literatur:
Literature from various sources - in part scientific literature - is announced during the lectures
Verwendbarkeit des Moduls / Einpassung in den Musterstudienplan:
- Wirtschaftsmathematik (Master of Science)
(Po-Vers. 2015w | NatFak | Wirtschaftsmathematik (Master of Science) | Gesamtkonto | Mathematische Wahlmodule | Forschungsmodule Studienrichtung Modellierung, Simulation und Optimierung)
Dieses Modul ist daneben auch in den Studienfächern "Computational and Applied Mathematics (Master of Science)", "Mathematik (Master of Science)", "Technomathematik (Master of Science)" verwendbar. Details
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