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    <!DOCTYPE html>
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    <div class="reveal">
    <div class="slides">
    <section id="title-slide">
    <h1 class="title">Material system</h1>
    </section>
    <section>
    <section id="introduction-to-dumux--material-system"
    class="title-slide slide level1">
    <h1>Introduction to DuMuX- Material system</h1>
    </section>
    <section id="challenges-in-simulating-porous-media"
    class="slide level2">
    <h2>Challenges in simulating porous media:</h2>
    <ul>
    <li><p>Highly heterogeneous distribution of parameters and complex
    nonlinear material laws</p></li>
    <li><p>Strong interconnection of properties <strong>—&gt;</strong>
    difficult to achieve modularity</p></li>
    </ul>
    </section>
    <section id="modular-structure" class="slide level2">
    <h2>Modular structure:</h2>
    <ins>
    User-defined parameters and relationships:
    </ins>
    <ul>
    <li>Components</li>
    <li>Fluid system</li>
    <li>Solid system</li>
    <li>Binary coefficients</li>
    <li>Fluid-matrix interactions</li>
    <li>Chemistry</li>
    </ul>
    </section>
    <section id="dumux-specific-containers-and-solvers"
    class="slide level2">
    <h2><ins> Dumux-specific containers and solvers </ins></h2>
    <ul>
    <li>Fluid states</li>
    <li>Solid states</li>
    <li>Constraint solvers</li>
    </ul>
    </section></section>
    <section>
    <section id="material-system-component"
    class="title-slide slide level1">
    <h1>Material system: Component</h1>
    </section>
    <section id="component" class="slide level2">
    <h2>Component</h2>
    <p><img src="img/component.png" width="200"/></p>
    </section>
    <section id="what-it-does" class="slide level2">
    <h2><ins> What it does: </ins></h2>
    <ul>
    <li><strong>Thermodynamic relations</strong> (e.g. molar mass, vapor
    pressure, density) of a <strong>single chemical species</strong> or a
    fixed mixture of species</li>
    <li>Provide a convenient way to access these quantities</li>
    <li>Not supposed to be used by models directly</li>
    </ul>
    </section>
    <section id="example-implementations" class="slide level2">
    <h2><ins> Example implementations: </ins></h2>
    <ul>
    <li><p><em>H2O</em> : pure water, properties by IAPWS-97 or
    simplified</p></li>
    <li><p><em>Brine</em> : water with a given salt concentration</p></li>
    </ul>
    </section></section>
    <section>
    <section id="material-system-fluid-system"
    class="title-slide slide level1">
    <h1>Material system: Fluid system</h1>
    </section>
    <section id="fluid-system" class="slide level2">
    <h2>Fluid system</h2>
    <p><img src="img/fluidsystem.png" width="300"/></p>
    </section>
    <section id="what-it-does-1" class="slide level2">
    <h2><ins> What it does: </ins></h2>
    <p>Expresses the <strong>thermodynamic relations between fluid
    quantities</strong> (e.g. calculation of density or viscosity based on
    composition, fugacity coefficient based on temperature and
    pressure…)</p>
    </section>
    <section id="example-implementations-1" class="slide level2">
    <h2><ins> Example implementations: </ins></h2>
    <ul>
    <li><p><em>TwoPImmiscible</em> : two immiscible fluid phases</p></li>
    <li><p><em>H2OAir</em> : gas and liquid phase with components water and
    air</p></li>
    </ul>
    </section></section>
    <section>
    <section id="material-system-binary-coefficients"
    class="title-slide slide level1">
    <h1>Material system: Binary coefficients</h1>
    </section>
    <section id="binary-coefficients" class="slide level2">
    <h2>Binary coefficients</h2>
    <p><img src="img/binarycoefficients.png" width="350"/></p>
    </section>
    <section id="what-it-does-2" class="slide level2">
    <h2><ins> What it does: </ins></h2>
    <p><strong>Contains</strong> data and equations required for binary
    mixtures (e.g. binary diffusion coefficients, coefficients needed for
    constitutive relationships (like Henry coefficient))</p>
    </section>
    <section id="example-implementations-2" class="slide level2">
    <h2><ins> Example implementations: </ins></h2>
    <ul>
    <li><em>H2O_Air</em> : Henry coefficient, gas diffusion coefficient,
    liquid diffusion coefficent for water and air</li>
    </ul>
    </section></section>
    <section>
    <section id="material-system-solid-system"
    class="title-slide slide level1">
    <h1>Material system: Solid system</h1>
    </section>
    <section id="solid-system" class="slide level2">
    <h2>Solid system</h2>
    <p><img src="img/solidsystem.png" width="300"/></p>
    </section>
    <section id="what-it-does-3" class="slide level2">
    <h2><ins> What it does: </ins></h2>
    <p>Expresses the <strong>thermodynamic properties of the solid
    matrix</strong> (e.g. calculation of the solid density and solid heat
    capacity based on the composition…)</p>
    <ins>
    Note to solid system
    </ins>
    <p><em>Specifying a solid system is only necessary if you work with a
    non-isothermal or mineralization model. If no solid system is specified
    in the problem file, the default is the inert solid phase with the
    constant component. For the constant component you can set properties in
    the input file.</em></p>
    </section>
    <section id="implementations" class="slide level2">
    <h2><ins> Implementations: </ins></h2>
    <ul>
    <li><em>OneCSolid</em> : inert solid matrix of one solid component
    (e.g. granite)</li>
    <li><em>CompositionalSolidPhase</em> : composed solid matrix of inert or
    reactive components (e.g. NaCl and granite)</li>
    </ul>
    </section></section>
    <section>
    <section id="material-system-fluid-matrix-interactions"
    class="title-slide slide level1">
    <h1>Material system: Fluid-matrix interactions</h1>
    </section>
    <section id="fluid-materix-interactions" class="slide level2">
    <h2>Fluid-materix interactions</h2>
    <p><img src="img/fluidmatrixinteractions.png" width="250"/></p>
    </section>
    <section id="what-it-does-4" class="slide level2">
    <h2><ins> What it does: </ins></h2>
    <ul>
    <li>Description of the <strong>interaction of the fluid phases with the
    porous medium</strong> (e.g. capillary pressure-saturation and relative
    permeability relationships)</li>
    <li>Through modular adapters, regularization schemes can be imposed for
    extreme values</li>
    </ul>
    </section>
    <section id="example-implementations-3" class="slide level2">
    <h2><ins> Example implementations: </ins></h2>
    <ul>
    <li>Available parametrizations for the capillary pressure-saturation
    relationship are:
    <ul>
    <li><em>Van Genuchten</em></li>
    <li><em>Brooks Corey</em></li>
    </ul></li>
    </ul>
    </section>
    <section id="van-genuchten" class="slide level2">
    <h2>Van-Genuchten</h2>
    <p><span class="math inline">\(\begin{equation} p_c =
    \frac{1}{\alpha}\left(S_e^{-1/m} -1\right)^{1/n}
    \end{equation}\)</span></p>
    <p><img src="img/pc-Sw_VanGenuchten.png" width="500"/></p>
    <p><strong>—&gt;</strong> Necessary are here the empirical parameters
    <span class="math inline">\(\alpha\)</span> and <span
    class="math inline">\(n\)</span>.</p>
    </section>
    <section id="brooks-corey" class="slide level2">
    <h2>Brooks-Corey</h2>
    <p><span class="math inline">\(\begin{equation} p_c = p_d
    S_e^{-1/\lambda} \end{equation}\)</span></p>
    <p><img src="img/pc-Sw_BrooksCorey.png" width="500"/></p>
    <p><strong>—&gt;</strong> Necessary parameters are here the entry
    pressure <span class="math inline">\(p_d\)</span> and the shape factor
    <span class="math inline">\(\lambda\)</span>.</p>
    </section></section>
    <section>
    <section id="material-system-chemistry"
    class="title-slide slide level1">
    <h1>Material system: Chemistry</h1>
    </section>
    <section id="chemistry" class="slide level2">
    <h2>Chemistry</h2>
    <p><img src="img/chemistry.png" width="200"/></p>
    </section>
    <section id="what-it-does-5" class="slide level2">
    <h2><ins> What it does: </ins></h2>
    <p>Reactions between different components. There are extra models or
    they are realized with the introduction of a source term.</p>
    <p><strong>Note:</strong> <em>This contains some specific example
    implementations. One can implement specific things according to their
    need.</em></p>
    </section>
    <section id="example-implementations-4" class="slide level2">
    <h2><ins> Example implementations: </ins></h2>
    <p>Expresses the <strong>electrochemical models for a fuel cell
    application</strong>:</p>
    <ul>
    <li><em>Electrochemistry</em> : for isothermal system</li>
    <li><em>Electrochemistryni</em> : for non-isothermal system</li>
    </ul>
    </section></section>
    <section>
    <section id="material-system-fluid-state"
    class="title-slide slide level1">
    <h1>Material system: Fluid state</h1>
    </section>
    <section id="fluid-state" class="slide level2">
    <h2>Fluid state</h2>
    <p><img src="img/fluidstate.png" width="800"/></p>
    </section>
    <section id="what-it-does-6" class="slide level2">
    <h2><ins> What it does: </ins></h2>
    <ul>
    <li><strong>Stores</strong> the complete thermodynamic configuration of
    a system at a given spatial and temporal position (e.g. saturation, mole
    fraction, enthalpy)</li>
    <li><strong>Provides access</strong> methods to all thermodynamic
    quantities (e.g. saturation, mole fraction, enthalpy)</li>
    </ul>
    </section>
    <section id="example-implementations-5" class="slide level2">
    <h2><ins> Example implementations: </ins></h2>
    <ul>
    <li><em>ImmiscibleFluidState</em> : assumes immiscibility of the fluid
    phases. Phase compositions and fugacity coefficients do not need to be
    stored explicitly.</li>
    <li><em>CompositionalFluidState</em> : assumes thermodynamic
    equilibrium, only a single temperature needs to be stored.</li>
    </ul>
    </section></section>
    <section>
    <section id="material-system-solid-state"
    class="title-slide slide level1">
    <h1>Material system: Solid state</h1>
    </section>
    <section id="solid-state" class="slide level2">
    <h2>Solid state</h2>
    <p><img src="img/solidstate.png" width="800"/></p>
    </section>
    <section id="what-it-does-7" class="slide level2">
    <h2><ins> What it does: </ins></h2>
    <ul>
    <li><strong>Stores</strong> the complete solid configuration of a system
    at a given spatial and temporal position (e.g. solid volume fractions,
    solid heat capacity)</li>
    <li><strong>Provides</strong> access methods to all solid quantities
    (e.g. porosity, density, temperature)</li>
    </ul>
    </section>
    <section id="example-implementations-6" class="slide level2">
    <h2><ins> Example implementations: </ins></h2>
    <ul>
    <li><p><em>InertSolidState</em> : assumes an inert solid phase. Solid
    volume fractions do not change. This is the
    <strong>default</strong>.</p></li>
    <li><p><em>CompositionalSolidState</em> : assumes a solid matrix
    composed out of two components. The volume fractions can change and
    properties such as heat capacity are adapted.</p></li>
    </ul>
    </section></section>
    <section>
    <section id="material-system-constraint-solver"
    class="title-slide slide level1">
    <h1>Material system: Constraint Solver</h1>
    </section>
    <section id="constraint-solver" class="slide level2">
    <h2>Constraint solver</h2>
    <p><img src="img/constraintsolver.png" width="1000"/></p>
    </section>
    <section id="what-it-does-8" class="slide level2">
    <h2><ins> What it does: </ins></h2>
    <p><strong>Connects</strong> the thermodynamic relations expressed by
    fluid systems with the thermodynamic quantities stored by fluid states
    (e.g. mole fraction, density)</p>
    </section>
    <section id="example-implementation" class="slide level2">
    <h2><ins> Example implementation: </ins></h2>
    <p><em>CompositionFromFugacities</em> : takes all component fugacities,
    the temperature and pressure of a phase as input and calculates the
    phase composition</p>
    </section></section>
    <section>
    <section id="example-from-component-to-fluid-system"
    class="title-slide slide level1">
    <h1>Example: From component to fluid system</h1>
    </section>
    <section id="component-fluid-system" class="slide level2">
    <h2>Component <strong>—&gt;</strong> fluid system</h2>
    <p><img src="img/component-fluidsystem.png" width="500"/></p>
    </section>
    <section id="example-2-phases-miscible" class="slide level2">
    <h2>Example: 2 phases, miscible</h2>
    <ul>
    <li>Components: <em>H2O</em>, <em>Air</em></li>
    <li>Fluid system: <em>TwoPTwoC</em></li>
    </ul>
    </section>
    <section id="include-headers-in-properties-file-components"
    class="slide level2">
    <h2>Include headers in properties file: components</h2>
    <div class="sourceCode" id="cb1"><pre
    class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="co">// The two-phase fluid system for compents water and air</span></span>
    <span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;dumux/material/fluidsystems/h2oair.hh&gt;</span></span>
    <span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="co">// The water component</span></span>
    <span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;dumux/material/components/h2o.hh&gt;</span></span>
    <span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="co">// The air component</span></span>
    <span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="pp">#include </span><span class="im">&lt;dumux/material/components/air.hh&gt;</span></span></code></pre></div>
    </section>
    <section id="specify-fluid-system-in-properties-file"
    class="slide level2">
    <h2>Specify fluid system in properties file:</h2>
    <div class="sourceCode" id="cb2"><pre
    class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span><span class="op">&lt;</span><span class="kw">class</span> TypeTag<span class="op">&gt;</span></span>
    <span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> FluidSystem<span class="op">&lt;</span>TypeTag<span class="op">,</span> TTag<span class="op">::</span>H2OAir<span class="op">&gt;</span></span>
    <span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a><span class="op">{</span></span>
    <span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="kw">private</span><span class="op">:</span></span>
    <span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a> <span class="kw">using</span> Scalar <span class="op">=</span> GetPropType<span class="op">&lt;</span>TypeTag<span class="op">,</span> Properties<span class="op">::</span>Scalar<span class="op">&gt;;</span></span>
    <span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a><span class="kw">public</span><span class="op">:</span></span>
    <span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a> <span class="kw">using</span> type <span class="op">=</span> FluidSystems<span class="op">::</span>H2OAir<span class="op">&lt;</span>Scalar<span class="op">,</span></span>
    <span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a> Components<span class="op">::</span>TabulatedComponent</span>
    <span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a> <span class="op">&lt;</span>Components<span class="op">::</span>H2O<span class="op">&lt;</span>Scalar<span class="op">&gt;&gt;,</span></span>
    <span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a> FluidSystems<span class="op">::</span>H2OAirDefaultPolicy</span>
    <span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a> <span class="op">&lt;</span><span class="co">/*fastButSimplifiedRelations=*/</span><span class="kw">true</span><span class="op">&gt;,</span></span>
    <span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a> <span class="kw">true</span> <span class="co">/*useKelvinEquation*/</span><span class="op">&gt;;</span></span>
    <span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a><span class="op">};</span></span></code></pre></div>
    </section></section>
    <section>
    <section id="example-from-component-to-solid-system"
    class="title-slide slide level1">
    <h1>Example: From component to solid system</h1>
    </section>
    <section id="example-2-phases-miscible-1" class="slide level2">
    <h2>Example: 2 phases, miscible</h2>
    <ul>
    <li>Components: <em>CaO</em>, <em>CaO2H2</em> (slaked lime)</li>
    <li>Solid system: <em>OnePNCMin</em></li>
    </ul>
    </section>
    <section id="specify-solid-system-in-properties-file"
    class="slide level2">
    <h2>Specify solid system in properties file:</h2>
    <div class="sourceCode" id="cb3"><pre
    class="sourceCode cpp"><code class="sourceCode cpp"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a><span class="co">// The solid system</span></span>
    <span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a><span class="kw">template</span><span class="op">&lt;</span><span class="kw">class</span> TypeTag<span class="op">&gt;</span></span>
    <span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a><span class="kw">struct</span> SolidSystem<span class="op">&lt;</span>TypeTag<span class="op">,</span> TTag<span class="op">::</span>ThermoChem<span class="op">&gt;</span></span>
    <span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a><span class="op">{</span></span>
    <span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a> <span class="kw">using</span> Scalar <span class="op">=</span> GetPropType<span class="op">&lt;</span>TypeTag<span class="op">,</span> Properties<span class="op">::</span>Scalar<span class="op">&gt;;</span></span>
    <span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a> <span class="kw">using</span> ComponentOne <span class="op">=</span> Components<span class="op">::</span>ModifiedCaO<span class="op">&lt;</span>Scalar<span class="op">&gt;;</span></span>
    <span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a> <span class="kw">using</span> ComponentTwo <span class="op">=</span> Components<span class="op">::</span>CaO2H2<span class="op">&lt;</span>Scalar<span class="op">&gt;;</span></span>
    <span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a> <span class="kw">using</span> type <span class="op">=</span> SolidSystems<span class="op">::</span>CompositionalSolidPhase</span>
    <span id="cb3-9"><a href="#cb3-9" aria-hidden="true" tabindex="-1"></a> <span class="op">&lt;</span>Scalar<span class="op">,</span> ComponentOne<span class="op">,</span> ComponentTwo<span class="op">&gt;;</span></span>
    <span id="cb3-10"><a href="#cb3-10" aria-hidden="true" tabindex="-1"></a><span class="op">};</span></span></code></pre></div>
    </section></section>
    <section>
    <section id="exercise" class="title-slide slide level1">
    <h1>Exercise</h1>
    </section>
    <section id="tasks" class="slide level2">
    <h2><ins> Tasks: </ins></h2>
    <ol type="1">
    <li>Get familiar with the code</li>
    <li>2p model: Implement a new component (incompressible and
    compressible)</li>
    <li>2p2c model: Implement a new fluid system</li>
    <li>Change wettability of the porous medium</li>
    <li>Advanced: Use van Genuchten relationship with parameters: alpha =
    0.0037 and alphalense = 0.00045, n = 4.7 and nlense = 7.3</li>
    </ol>
    <p><strong>First step:</strong> Go to <a
    href="https://git.iws.uni-stuttgart.de/dumux-repositories/dumux-course/tree/master/exercises/exercise-fluidsystem"
    class="uri">https://git.iws.uni-stuttgart.de/dumux-repositories/dumux-course/tree/master/exercises/exercise-fluidsystem</a>
    and check out the README</p>
    </section></section>
    </div>
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