<OpenGeoSysProject>
  <meshes>
    <mesh>ManSol3_mesh_unit_square_QU_10x10.vtu</mesh>
    <mesh>ManSol3_mesh_unit_square_QU_10x10_0.vtu</mesh>
    <mesh>ManSol3_mesh_unit_square_QU_10x10_1.vtu</mesh>
    <mesh>ManSol3_mesh_unit_square_QU_10x10_2.vtu</mesh>
    <mesh>ManSol3_mesh_unit_square_QU_10x10_3.vtu</mesh>
  </meshes>
  <processes>
    <process>
      <name>HeatConduction</name>
      <type>HEAT_CONDUCTION</type>
      <integration_order>2</integration_order>
      <process_variables>
        <process_variable>temperature</process_variable>
      </process_variables>
      <secondary_variables>
        <secondary_variable name="heat_flux" />
      </secondary_variables>
    </process>
  </processes>
  <media>
    <medium id="4">
      <phases>
        <phase>
          <type>AqueousLiquid</type>
          <properties>
            <property>
              <name>thermal_conductivity</name>
              <type>Constant</type>
              <value>0.58</value>
            </property>
            <property>
              <name>specific_heat_capacity</name>
              <type>Constant</type>
              <value>4.190</value>
            </property>
            <property>
              <name>density</name>
              <type>Constant</type>
              <value>1.000</value>
            </property>
          </properties>
        </phase>
        <phase>
          <type>FrozenLiquid</type>
          <properties>
            <property>
              <name>thermal_conductivity</name>
              <type>Constant</type>
              <value>2.2</value>
            </property>
            <property>
              <name>specific_heat_capacity</name>
              <type>Constant</type>
              <value>2.090</value>
            </property>
            <property>
              <name>density</name>
              <type>Constant</type>
              <value>0.920</value>
            </property>
          </properties>
        </phase>
        <phase>
          <type>Solid</type>
          <properties>
            <property>
              <name>thermal_conductivity</name>
              <type>Constant</type>
              <value>1.1</value>
            </property>
            <property>
              <name>specific_heat_capacity</name>
              <type>Constant</type>
              <value>0.900</value>
            </property>
            <property>
              <name>density</name>
              <type>Constant</type>
              <value>2.000</value>
            </property>
          </properties>
        </phase>
      </phases>
      <properties>
        <property>
          <name>porosity</name>
          <type>Constant</type>
          <value>0.5</value>
        </property>
        <property>
          <name>volume_fraction</name>
          <type>TemperatureDependentFraction</type>
          <steepness>2</steepness>
          <characteristic_temperature>273.15</characteristic_temperature>
        </property>
        <property>
          <name>density</name>
          <type>VolumeFractionAverage</type>
        </property>
        <property>
          <name>thermal_conductivity</name>
          <type>VolumeFractionAverage</type>
        </property>
        <property>
          <name>specific_heat_capacity</name>
          <type>SpecificHeatCapacityWithLatentHeat</type>
          <specific_latent_heat>334.000</specific_latent_heat>
        </property>
      </properties>
    </medium>
  </media>
  <parameters>
    <parameter>
      <name>HeatSource</name>
      <type>Function</type>
      <expression>(0.5*2.000*0.900
             +0.5*exp(2*(17*y*(x*cos(0.5*pi*t)+(1-x)*sin(0.5*pi*t))-7))/(1+exp(2*(17*y*(x*cos(0.5*pi*t)+(1-x)*sin(0.5*pi*t))-7)))*1.000*4.190
             +0.5/(1+exp(2*(17*y*(x*cos(0.5*pi*t)+(1-x)*sin(0.5*pi*t))-7)))*0.920*2.090
             +3.34e2*0.920*0.5*2*exp(2*(17*y*(x*cos(0.5*pi*t)+(1-x)*sin(0.5*pi*t))-7))/(1+exp(2*(17*y*(x*cos(0.5*pi*t)+(1-x)*sin(0.5*pi*t))-7)))^2 )
             0.5*pi*17*y((1-x)*cos(0.5*pi*t)-x*sin(0.5*pi*t))

             +(2.2-0.58)*0.5*2*exp(2*(17*y*(x*cos(0.5*pi*t)+(1-x)*sin(0.5*pi*t))-7))/(1+exp(2*(17*y*(x*cos(0.5*pi*t)+(1-x)*sin(0.5*pi*t))-7)))^2
             17^2(y^2*(1-sin(pi*t))+x*(1-x)*sin(pi*t)+(x-0.5)*cos(pi*t)+x^2-x+0.5)</expression>
    </parameter>
    <parameter>
      <name>T0</name>
      <type>Function</type>
      <expression>17*x*y+266.15</expression>
    </parameter>
    <parameter>
      <name>T1b</name>
      <type>Function</type>
      <expression>266.15</expression>
    </parameter>
    <parameter>
      <name>T1r</name>
      <type>Function</type>
      <expression>17*y*(x*cos(0.5*pi*t)+(1-x)*sin(0.5*pi*t))+266.15</expression>
    </parameter>
    <parameter>
      <name>T1t</name>
      <type>Function</type>
      <expression>17*y*(x*cos(0.5*pi*t)+(1-x)*sin(0.5*pi*t))+266.15</expression>
    </parameter>
    <parameter>
      <name>T1l</name>
      <type>Function</type>
      <expression>17*y*(x*cos(0.5*pi*t)+(1-x)*sin(0.5*pi*t))+266.15</expression>
    </parameter>
  </parameters>
  <process_variables>
    <process_variable>
      <name>temperature</name>
      <components>1</components>
      <order>1</order>
      <initial_condition>T0</initial_condition>
      <boundary_conditions>
        <boundary_condition>
          <mesh>ManSol3_mesh_unit_square_QU_10x10_0</mesh>
          <type>Dirichlet</type>
          <parameter>T1b</parameter>
        </boundary_condition>
        <boundary_condition>
          <mesh>ManSol3_mesh_unit_square_QU_10x10_1</mesh>
          <type>Dirichlet</type>
          <parameter>T1r</parameter>
        </boundary_condition>
        <boundary_condition>
          <mesh>ManSol3_mesh_unit_square_QU_10x10_2</mesh>
          <type>Dirichlet</type>
          <parameter>T1t</parameter>
        </boundary_condition>
        <boundary_condition>
          <mesh>ManSol3_mesh_unit_square_QU_10x10_3</mesh>
          <type>Dirichlet</type>
          <parameter>T1l</parameter>
        </boundary_condition>
      </boundary_conditions>
      <source_terms>
        <source_term>
          <mesh>ManSol3_mesh_unit_square_QU_10x10</mesh>
          <type>Volumetric</type>
          <parameter>HeatSource</parameter>
        </source_term>
      </source_terms>
    </process_variable>
  </process_variables>
  <time_loop>
    <processes>
      <process ref="HeatConduction">
        <nonlinear_solver>basic_picard</nonlinear_solver>
        <convergence_criterion>
          <type>DeltaX</type>
          <norm_type>NORM2</norm_type>
          <abstol>2e-12</abstol>
        </convergence_criterion>
        <time_discretization>
          <type>BackwardEuler</type>
        </time_discretization>
        <time_stepping>
          <type>FixedTimeStepping</type>
          <t_initial>0.0</t_initial>
          <t_end>1.0</t_end>
          <timesteps>
            <pair>
              <repeat>200</repeat>
              <delta_t>0.005</delta_t>
            </pair>
          </timesteps>
        </time_stepping>
      </process>
    </processes>
    <output>
      <type>VTK</type>
      <prefix>ManSol_IceWaterMix_T-plot</prefix>
      <timesteps>
        <pair>
          <repeat>10000</repeat>
          <each_steps>10</each_steps>
        </pair>
      </timesteps>
      <variables>
        <variable>temperature</variable>
        <variable>heat_flux</variable>
      </variables>
      <suffix>ts{:timestep}_t_{:gtime}</suffix>
    </output>
  </time_loop>
  <nonlinear_solvers>
    <nonlinear_solver>
      <name>basic_picard</name>
      <type>Picard</type>
      <max_iter>200</max_iter>
      <linear_solver>general_linear_solver</linear_solver>
    </nonlinear_solver>
  </nonlinear_solvers>
  <linear_solvers>
    <linear_solver>
      <name>general_linear_solver</name>
      <eigen>
        <solver_type>SparseLU</solver_type>
        <scaling>true</scaling>
      </eigen>
    </linear_solver>
  </linear_solvers>
  <test_definition>
    <vtkdiff>
      <file>ManSol_IceWaterMix_T-plot_ts_50_t_0.25.vtu</file>
      <field>temperature</field>
      <absolute_tolerance>2e-6</absolute_tolerance>
      <relative_tolerance>0</relative_tolerance>
    </vtkdiff>
    <vtkdiff>
      <file>ManSol_IceWaterMix_T-plot_ts_100_t_0.5.vtu</file>
      <field>temperature</field>
      <absolute_tolerance>5e-6</absolute_tolerance>
      <relative_tolerance>0</relative_tolerance>
    </vtkdiff>
  </test_definition>
</OpenGeoSysProject>