Merge branch 'add-intro-slides' into 'master'

add intro slides

See merge request !161

slides/index.md

@@ -2,6 +2,7 @@
 title: DuMuX Course Slides
 ---
 
+- [Introduction to DuMu^x^](./intro.html)
 - [Property System](./properties.html)
 - [Introduction to Multidomain](./multidomain.html)
 - [Discrete Fracture Modeling](./fractures.html)

slides/intro.md

+---
+title: Introduction to DuMu^x^
+subtitle: Overview and Available Models
+---
+
+# Table of Contents
+
+## Table of Contents
+
+1. [History and Structure](#history-and-structure)
+2. [Available Models](#available-models)
+3. [Spatial Discretization](#spatial-discretization)
+4. [Model Components](#model-components)
+5. [Simulation Flow](#simulation-flow)
+
+# History and Structure
+
+## The DuMu^x^ Development Team (IWS-LH2)
+
+<img src="img/lh2_2021.jpg" width="600"/>
+
+## DuMu^x^ is a DUNE module
+
+<img src="img/dumux_dune_module.png"/>
+
+## The DUNE Framework
+
+* **Developed** by scientists at around 10 European research institutions.
+* **Separation** of data structures and algorithms by abstract interfaces.
+* Efficient implementation using **generic** programming techniques.
+* **Reuse** of existing FE packages with a large body of functionality.
+* Current stable release: **2.9** (November 2022).
+
+## DUNE Core Modules
+
+* **dune-common:** basic classes
+* **dune-geometry:** geometric entities
+* **dune-grid:** abstract grid/mesh interface
+* **dune-istl:** iterative solver template library
+* **dune-localfunctions:** finite element shape functions
+
+## Overview
+
+<img src="img/dumux.png" width="400"/>
+
+* **DuMu^x^:** DUNE for Multi-{Phase, Component, Scale, Physics, $\text{...}$} flow and transport in porous media.
+* **Goal:** **sustainable** and **consistent framework** for the implementation and application of **model concepts** and **constitutive relations**.
+* Meanwhile **developed** by more than 30 PhD students and post docs, mostly at LH2.
+
+## Application
+
+* **Successfully applied** to
+    * gas (CO~2~, H~2~, CH~4~, ...) storage scenarios
+    * environmental remediation problems
+    * transport of therapeutic agents through biological tissue
+    * root-soil interaction
+    * subsurface-atmosphere coupling (Navier-Stokes / Darcy)
+    * pore-network modelling
+    * flow and transport in fractured porous media
+
+## Exemplary DuMu^x^ Modules
+
+* **dumux-lecture:** example applications for lectures offered by LH2 in Stuttgart
+* **dumux-pub:** accompany a publication with all code and data to reproduce the results
+* **dumux-appl:** current unpublished development and ongoing research
+
+## History
+
+* 01/2007: Development **starts**.
+* 07/2009: Release **1.0**.
+* 09/2010: **Split** into stable and development part.
+* 12/2010: Anonymous **read access** to the **SVN** trunk of the stable part.
+* 02/2011: Release **2.0,** ..., 10/2017: Release **2.12**.
+* 09/2015: Transition from Subversion to **Git**.
+* 12/2018: Release **3.0,** ..., 03/2023: Release **3.7**.
+
+## Downloads and Publications
+
+* More than 1000 "real" and unique release **downloads**.
+* More than 200 peer-reviewed **publications** and PhD theses.
+
+## Evolution of C++ Files
+
+<img src="img/files_vs_releases.png" width="750"/>
+
+## Evolution of Code Lines
+
+<img src="img/lines_vs_releases.png" width="750"/>
+
+## Mathematical Models
+
+* **Porous medium flow (Darcy)**: Single and multi-phase models for flow and transport in porous materials.
+* **Free flow (Navier-Stokes)**: Single-phase models based on the Navier-Stokes equation.
+* **Shallow water flow**: Two-dimensional shallow water flow (depth-averaged).
+* **Geomechanics**: Models taking into account solid deformation.
+* **Pore network**: Single and multi-phase models for flow and transport in pore networks.
+
+## Mailing Lists and GitLab
+
+* **Mailing lists** of DUNE (<dune@dune-project.org>) and DuMu^x^ (<dumux@listserv.uni-stuttgart.de>)
+* Get **GitLab** accounts (non-anonymous) for better access
+    * DUNE GitLab (<https://gitlab.dune-project.org/core>)
+    * DuMu^x^ GitLab (<https://git.iws.uni-stuttgart.de/dumux-repositories/dumux>)
+* GitLab **Issue Tracker** (<https://git.iws.uni-stuttgart.de/dumux-repositories/dumux/issues>)
+
+## Documentation
+
+* **Doxygen** code **documentation** of
+    * DUNE (<https://dune-project.org/doxygen/>)
+    * DuMu^x^ (<https://dumux.org/docs/>)
+* DuMu^x^ **Handbook** (<https://dumux.org/docs/>)
+* Further information &rarr; <https://dumux.org/>
+
+# Available Models
+
+## Available Models
+
+<img src="img/models.png" width="650"/>
+
+## Darcy's law
+
+* Describes the advective flux in porous media on the macro-scale
+
+* One-phase flow
+
+    $v = - \frac{\mathbf{K}}{\mu} \left(\textbf{grad}\, p - \varrho \mathbf{g} \right)$
+
+* Multi-phase flow (phase $\alpha$)
+
+    $v_\alpha = - \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\textbf{grad}\, p_\alpha - \varrho_\alpha \mathbf{g} \right)$
+
+## 1p -- single-phase
+
+* Uses standard Darcy approach for the conservation of momentum
+* Mass continuity equation
+
+    $\phi \frac{\partial \varrho}{\partial t} + \text{div} \left\lbrace - \varrho \frac{\textbf{K}}{\mu} \left(\textbf{grad}\, p - \varrho \textbf{g} \right) \right\rbrace = q$
+
+* Primary variable: $p$
+
+## 1pnc -- single-phase, multi-component
+
+* Uses standard Darcy approach for the conservation of momentum
+* Transport of component $\kappa \in \{w, a, ...\}$
+
+    $\phi \frac{\partial \varrho X^\kappa}{\partial t} - \text{div} \left\lbrace \varrho X^\kappa \frac{\textbf {K}}{\mu} \left(\textbf{grad}\, p - \varrho \textbf{g} \right) + \varrho D^\kappa_\text{pm} \textbf{grad} X^\kappa \right\rbrace = q$
+
+* Primary variables: $p$ and $x^\kappa$
+
+## 1pncmin -- with mineralization
+
+* Transport equation for each component $\kappa \in \{w, a, ...\}$
+
+    $\frac{\partial \left( \varrho_f X^\kappa \phi \right)}{\partial t}$
+    $- \text{div} \left\lbrace \varrho_f X^\kappa \frac{k_{r}}{\mu} \mathbf{K} \left(\textbf{grad}\, p - \varrho_f \mathbf{g} \right) \right\rbrace$
+    $- \text{div} \left\lbrace \mathbf{D_{pm}^\kappa} \varrho_f \textbf{grad}\, X^\kappa \right\rbrace = q_\kappa$
+
+* Mass balance solid or mineral phases
+
+    $\frac{\partial \left(\varrho_\lambda \phi_\lambda \right)}{\partial t} = q_\lambda$
+
+* Primary variables: $p$, $x^k$ and $\phi_\lambda$
+
+## 2p -- two-phase
+
+* Uses standard multi-phase Darcy approach for the conservation of momentum
+* Conservation of the phase mass of phase $\alpha \in \{w, n\}$
+
+    $\phi \frac{\partial \varrho_\alpha S_\alpha}{\partial t} - \text{div} \left\{\varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\textbf{grad}\, p_\alpha - \varrho_\alpha \mathbf{g} \right) \right\} = q_\alpha$
+
+* Constitutive relation $p_c = p_n - p_w$
+* $S_w + S_n = 1$
+* Primary variables: $p_w$ and $S_n$ or $p_n$ and $S_w$
+
+## 2pnc
+
+* Transport equation for each component $\kappa \in \{w, n, ...\}$ in phase $\alpha \in \{w, n\}$
+
+    $\frac{\partial \sum_\alpha \varrho_\alpha X_\alpha^\kappa \phi S_\alpha}{\partial t} - \sum_\alpha \text{div} \left\lbrace \varrho_\alpha X_\alpha^\kappa \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left( \textbf{grad}\, p_\alpha - \varrho_\alpha \mathbf{g} \right) \right\rbrace$
+    $- \sum_\alpha \text{div} \left\lbrace \mathbf{D_{\alpha, pm}^\kappa} \varrho_\alpha \textbf{grad}\, X^\kappa_\alpha \right\rbrace = \sum_\alpha q_\alpha^\kappa$
+
+* Constitutive relation $p_c = p_n - p_w$
+* $S_w + S_n = 1$ and $X^\kappa_w + X^\kappa_n = 1$
+* Primary variables: depend on the phase state
+
+## 2pncmin
+
+* Transport equation for each component $\kappa \in \{w, n, ...\}$ in phase $\alpha \in \{w, n\}$
+
+    $\frac{\partial \sum_\alpha \varrho_\alpha X_\alpha^\kappa \phi S_\alpha}{\partial t} - \sum_\alpha \text{div} \left\lbrace \varrho_\alpha X_\alpha^\kappa \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left( \textbf{grad}\, p_\alpha - \varrho_\alpha \mathbf{g} \right) \right\rbrace$
+    $- \sum_\alpha \text{div} \left\lbrace \mathbf{D_{\alpha, pm}^\kappa} \varrho_\alpha \textbf{grad}\, X^\kappa_\alpha \right\rbrace = \sum_\alpha q_\alpha^\kappa$
+
+* Mass balance solid or mineral phases
+
+    $\frac{\partial \left(\varrho_\lambda \phi_\lambda \right)}{\partial t} = q_\lambda$
+
+* $p_c = p_n - p_w$, $S_w + S_n = 1$ and $X^\kappa_w + X^\kappa_n = 1$
+* Primary variables: depend on the phase state
+
+## 3p -- three-phase
+
+* Uses standard multi-phase Darcy approach for the conservation of momentum
+* Conservation of the phase mass of phase $\alpha \in \{w, g, n\}$
+
+    $\phi \frac{\partial \varrho_\alpha S_\alpha}{\partial t} - \text{div} \left\lbrace \varrho_\alpha \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\textbf{grad}\, p_\alpha - \varrho_\alpha \mathbf{g} \right) \right\rbrace = q_\alpha$
+
+* $S_w + S_n + S_g = 1$
+* Primary variables: $p_g$, $S_w$ and $S_n$
+
+## 3p3c
+
+* Transport equation for each component $\kappa \in \{w, a, c\}$ in phase $\alpha \in \{w, g, n\}$
+
+    $\phi \frac{\partial \left(\sum_\alpha \varrho_{\alpha,mol} x_\alpha^\kappa S_\alpha \right)}{\partial t}$
+    $- \sum_\alpha \text{div} \left\lbrace \frac{k_{r\alpha}}{\mu_\alpha} \varrho_{\alpha,mol} x_\alpha^\kappa \mathbf{K} \left(\textbf{grad}\, p_\alpha - \varrho_{\alpha,mass} \mathbf{g} \right) \right\rbrace$
+    $- \sum_\alpha \text{div} \left\lbrace D_\text{pm}^\kappa \frac{1}{M_\kappa} \varrho_\alpha \textbf{grad} X^\kappa_{\alpha} \right\rbrace = q^\kappa$
+
+* $S_w + S_n + S_g = 1$ and $x^w_\alpha + x^a_\alpha + x^c_\alpha = 1$
+* Primary variables: depend on the locally present fluid phases
+
+## Non-Isothermal
+
+* Local thermal equilibrium is assumed
+
+* One energy conservation equation for the porous solid matrix and the fluids
+
+    $\phi \frac{\partial \sum_\alpha \varrho_\alpha u_\alpha S_\alpha}{\partial t} + \left(1 - \phi \right) \frac{\partial \left(\varrho_s c_s T \right)}{\partial t}$
+    $- \sum_\alpha \text{div} \left\lbrace \varrho_\alpha h_\alpha \frac{k_{r\alpha}}{\mu_\alpha} \mathbf{K} \left(\textbf{grad}\, p_\alpha - \varrho_\alpha \mathbf{g} \right) \right\rbrace$
+    $- \text{div} \left(\lambda_{pm} \textbf{grad}\, T \right) = q^h$
+
+* $u_\alpha = h_\alpha - p_\alpha / \varrho_\alpha$
+
+## Reynolds-Averaged Navier-Stokes (RANS)
+
+* Momentum balance equation for a single-phase, isothermal RANS model
+
+    $\frac{\partial \left(\varrho \textbf{v} \right)}{\partial t} + \nabla \cdot \left(\varrho \textbf{v} \textbf{v}^{\text{T}} \right) = \nabla \cdot \left(\mu_\textrm{eff} \left(\nabla \textbf{v} + \nabla \textbf{v}^{\text{T}} \right) \right)$
+    $- \nabla p + \varrho \textbf{g} - \textbf{f}$
+
+* The effective viscosity is composed of the fluid and the eddy viscosity
+
+    $\mu_\textrm{eff} = \mu + \mu_\textrm{t}$
+
+# Spatial Discretization
+
+## Cell Centered Finite Volume Methods
+
+* Use elements of the grid as control volumes
+* Discrete **values** are determined at the element/control volume **center**
+* **Two-point flux approximation (TPFA)**
+    * Simple but robust
+* **Multi-point flux approximation (MPFA)**
+    * A consistent discrete gradient is constructed
+
+## Two-Point Flux Approximation (TPFA)
+
+<img src="img/tpfa.png" width="75%"/>
+
+## Multi-Point Flux Approximation (MPFA)
+
+<img src="img/mpfa.png" width="80%"/>
+
+## Box method
+
+* Model domain is discretized using a **FE** mesh
+* Secondary **FV** mesh is constructed &rarr; control volume/**box**
+* Control volumes are partitioned into sub-control volumes (scvs)
+* Faces of control volumes are partitioned into sub-control volume faces (scvfs)
+* Unites advantages of finite-volume and finite-element methods
+    * **Unstructured grids** (from FE method)
+    * **Mass conservative** (from FV method)
+
+## Box method
+
+<img src="img/box.png"/>
+
+## Staggered Grid
+
+* Uses a finite volume method with different control volumes for different equations
+* Fluxes are evaluated with a two-point flux approximation
+* **Robust** and **mass conservative**
+* Should be applied for **structured grids** only
+
+## Staggered Grid
+
+<img src="img/staggered_grid.png"/>
+
+# Model Components
+
+## Model Components
+
+* The following components have to be specified
+    * **Solver**: Type of solution stategy
+    * **Assembler**: Key properties
+        * Geometry, Variables, LocalResidual
+    * **LinearSolver**: How to solve algebraic equations
+    * **Problem**: Initial and boundary conditions
+    * **SolutionVector**: Container to store the solution
+    * **TimeLoop**: For time-dependent problems
+    * **IOFields** and **VtkOutputModule**: Output of the simulation
+
+# Simulation Flow
+
+## Simulation Flow
+
+<img src="img/simulation_flow.png"/>