<OpenGeoSysProject>
  <meshes>
    <mesh axially_symmetric="true">sphere.vtu</mesh>
    <mesh axially_symmetric="true">sphere_top.vtu</mesh>
    <mesh axially_symmetric="true">sphere_in.vtu</mesh>
    <mesh axially_symmetric="true">sphere_bot.vtu</mesh>
    <mesh axially_symmetric="true">sphere_out.vtu</mesh>
  </meshes>
  <processes>
    <process>
      <name>HM</name>
      <type>HYDRO_MECHANICS</type>
      <integration_order>3</integration_order>
      <constitutive_relation>
        <type>LinearElasticIsotropic</type>
        <youngs_modulus>E</youngs_modulus>
        <poissons_ratio>nu</poissons_ratio>
      </constitutive_relation>
      <process_variables>
        <displacement>displacement</displacement>
        <pressure>pressure</pressure>
      </process_variables>
      <secondary_variables>
        <secondary_variable name="sigma" />
        <secondary_variable name="epsilon" />
        <secondary_variable name="velocity" />
      </secondary_variables>
      <specific_body_force>0 0</specific_body_force>
    </process>
  </processes>
  <time_loop>
    <processes>
      <process ref="HM">
        <nonlinear_solver>basic_newton</nonlinear_solver>
        <convergence_criterion>
          <type>DeltaX</type>
          <norm_type>NORM2</norm_type>
          <reltol>1e-15</reltol>
        </convergence_criterion>
        <time_discretization>
          <type>BackwardEuler</type>
        </time_discretization>
        <time_stepping>
          <type>FixedTimeStepping</type>
          <t_initial>0</t_initial>
          <t_end>1</t_end>
          <timesteps>
            <pair>
              <repeat>1</repeat>
              <delta_t>1</delta_t>
            </pair>
          </timesteps>
        </time_stepping>
      </process>
    </processes>
    <output>
      <type>VTK</type>
      <prefix>output</prefix>
      <timesteps>
        <pair>
          <repeat>1</repeat>
          <each_steps>1</each_steps>
        </pair>
      </timesteps>
      <variables>
        <variable>displacement</variable>
        <variable>pressure</variable>
        <variable>sigma</variable>
        <variable>epsilon</variable>
        <variable>velocity</variable>
        <variable>principal_stress_values</variable>
      </variables>
      <suffix>ts{:timestep}_t_{:time}</suffix>
    </output>
  </time_loop>
  <media>
    <medium>
      <phases>
        <phase>
          <type>Gas</type>
          <properties>
            <property>
              <name>viscosity</name>
              <type>Constant</type>
              <value>1e-3</value>
            </property>
            <property>
              <name>density</name>
              <type>Constant</type>
              <value>1</value>
            </property>
          </properties>
        </phase>
        <phase>
          <type>Solid</type>
          <properties>
            <property>
              <name>density</name>
              <type>Constant</type>
              <value>8.96e3</value>
            </property>
          </properties>
        </phase>
      </phases>
      <properties>
        <property>
          <name>porosity</name>
          <type>Constant</type>
          <value>0.0</value>
        </property>
        <property>
          <name>biot_coefficient</name>
          <type>Constant</type>
          <value>0</value>
        </property>
        <property>
          <name>reference_temperature</name>
          <type>Constant</type>
          <value>293.15</value>
        </property>
        <property>
          <name>permeability</name>
          <type>Constant</type>
          <value>1e-16</value>
        </property>
      </properties>
    </medium>
  </media>
  <parameters>
    <parameter>
      <name>E</name>
      <type>Constant</type>
      <value>128e9</value>
    </parameter>
    <parameter>
      <name>nu</name>
      <type>Constant</type>
      <value>0.3</value>
    </parameter>
    <parameter>
      <name>displacement0</name>
      <type>Constant</type>
      <values>0 0</values>
    </parameter>
    <parameter>
      <name>pressure0</name>
      <type>Constant</type>
      <values>0</values>
    </parameter>
    <parameter>
      <name>p_in</name>
      <type>Constant</type>
      <value>1e3</value>
    </parameter>
    <parameter>
      <name>p_out</name>
      <type>Constant</type>
      <value>1.01325e5</value>
    </parameter>
    <parameter>
      <name>p_in_x</name>
      <mesh>sphere_in</mesh>
      <type>Function</type>
      <expression>x*1e3/0.175</expression>
    </parameter>
    <parameter>
      <name>p_in_y</name>
      <mesh>sphere_in</mesh>
      <type>Function</type>
      <expression>y*1e3/0.175</expression>
    </parameter>
    <parameter>
      <name>p_out_x</name>
      <mesh>sphere_out</mesh>
      <type>Function</type>
      <expression>-x*1.01325e5/0.225</expression>
    </parameter>
    <parameter>
      <name>p_out_y</name>
      <mesh>sphere_out</mesh>
      <type>Function</type>
      <expression>-y*1.01325e5/0.225</expression>
    </parameter>
    <parameter>
      <name>zero</name>
      <type>Constant</type>
      <value>0</value>
    </parameter>
  </parameters>
  <process_variables>
    <process_variable>
      <name>displacement</name>
      <components>2</components>
      <order>2</order>
      <initial_condition>displacement0</initial_condition>
      <boundary_conditions>
        <boundary_condition>
          <mesh>sphere_top</mesh>
          <type>Dirichlet</type>
          <component>0</component>
          <parameter>zero</parameter>
        </boundary_condition>
        <boundary_condition>
          <mesh>sphere_bot</mesh>
          <type>Dirichlet</type>
          <component>1</component>
          <parameter>zero</parameter>
        </boundary_condition>
        <boundary_condition>
          <mesh>sphere_in</mesh>
          <type>NormalTraction</type>
          <parameter>p_in</parameter>
        </boundary_condition>
        <boundary_condition>
          <mesh>sphere_out</mesh>
          <type>NormalTraction</type>
          <parameter>p_out</parameter>
        </boundary_condition>
      </boundary_conditions>
    </process_variable>
    <process_variable>
      <name>pressure</name>
      <components>1</components>
      <order>2</order>
      <initial_condition>pressure0</initial_condition>
      <boundary_conditions />
    </process_variable>
  </process_variables>
  <nonlinear_solvers>
    <nonlinear_solver>
      <name>basic_newton</name>
      <type>Newton</type>
      <max_iter>50</max_iter>
      <linear_solver>general_linear_solver</linear_solver>
    </nonlinear_solver>
  </nonlinear_solvers>
  <linear_solvers>
    <linear_solver>
      <name>general_linear_solver</name>
      <lis>-i bicgstab -p ilu -tol 1e-16 -maxiter 10000</lis>
      <eigen>
        <solver_type>BiCGSTAB</solver_type>
        <precon_type>ILUT</precon_type>
        <max_iteration_step>10000</max_iteration_step>
        <error_tolerance>1e-16</error_tolerance>
      </eigen>
    </linear_solver>
  </linear_solvers>
  <test_definition>
    <vtkdiff>
      <regex>output_ts_.*_t_.*.vtu</regex>
      <field>displacement</field>
      <absolute_tolerance>0</absolute_tolerance>
      <relative_tolerance>1e-12</relative_tolerance>
    </vtkdiff>
    <vtkdiff>
      <regex>output_ts_.*_t_.*.vtu</regex>
      <field>principal_stress_values</field>
      <absolute_tolerance>0</absolute_tolerance>
      <relative_tolerance>1e-10</relative_tolerance>
    </vtkdiff>
  </test_definition>
</OpenGeoSysProject>