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)

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:

1. Technomathematik (Master of Science)
   (Po-Vers. 2015w | NatFak | Technomathematik (Master of Science) | Gesamtkonto | Mathematische Wahlmodule | Forschungsmodule Studienrichtung Modellierung, Simulation und Optimierung)