Merge branch '153-add-upwinding-option-to-richards-fv-solver' into 'master'

Resolve "Add upwinding option to Richards FV solver"

Closes #153

See merge request !161

CHANGELOG.md

@@ -46,6 +46,7 @@
 * Define compile-time settings via CPP macros !144
 * [Google Test](https://github.com/google/googletest) unit test framework
     as Git Submodule !159
+* Upwinding options for Richards finite volume local operator !161
 
 ### Changed
 * `Simulation` is renamed `RichardsSimulation` and moved to 

CMakeLists.txt

@@ -14,12 +14,6 @@ endif()
 # add extra flags to debug compiler flags
 set(CMAKE_CXX_FLAGS_DEBUG "${CMAKE_CXX_FLAGS_DEBUG} -Wall")
 
-# option to change DG scheme via config file
-option(EXPERIMENTAL_DG_FEATURES
-  "Enable experimental DG settings through the config file"
-  OFF
-)
-
 # 
 if(NOT (dune-common_DIR OR dune-common_ROOT OR
       "${CMAKE_PREFIX_PATH}" MATCHES ".*dune-common.*"))

README.md

@@ -199,16 +199,6 @@ If you installed [Anaconda](https://conda.io/docs/user-guide/install/download.ht
     path chosen as installation prefix when configuring HDF5.
 
 
-### Experimental Features
-The local operator implementing Richards equation's discretization supports
-multiple scheme settings. Setting these via the config file is disabled by
-default. You can enable this feature by reconfiguring DORiE with the CMake flag
-`-DEXPERIMENTAL_DG_FEATURES=On`, and rebuilding it.
-
-The configuration settings in the section `[dg.experimental]` will then override
-the default settings.
-
-
 ### Recommended Third-Party Software
 
 The following software packages are cross-platform, so you should be able to find a release that fits your operating system:

doc/default_files/richards-parameters.xml

@@ -231,13 +231,6 @@ adding an empty line, make text **bold** or ``monospaced``.
   </category>
 
   <category name="numerics">
-    <parameter name="penaltyFactor">
-      <definition> Penalty factor to be used in the Discontinuous Galerkin scheme
-      </definition>
-      <values> float </values>
-      <suggestion> 10 </suggestion>
-    </parameter>
-
     <parameter name="FEorder">
       <definition> Polynomial order of the DG method used. Setting this value
         to 0 (zero) selects the finite volume (FV) solver (only compatible to
@@ -245,6 +238,52 @@ adding an empty line, make text **bold** or ``monospaced``.
       </definition>
       <suggestion> 1 </suggestion>
       <values> 0, 1, 2, 3 </values>
+      <comment> Select '0' for the finite volume (FV) solver </comment>
+    </parameter>
+
+    <parameter name="upwinding">
+      <definition> Upwinding method for skeleton terms. Upwinding typically
+        increases numeric stability while reducing accuracy.
+
+        **semiUpwind:** Apply upwinding to conductivity factor (only).
+
+        **fullUpwind:** Apply upwinding to conductivity.
+        **Not recommended for DG**.
+      </definition>
+      <values> none, semiUpwind, fullUpwind </values>
+      <suggestion> none </suggestion>
+      <comment> Choose upwinding type: 'none', 'semiUpwind', 'fullUpwind'
+      </comment>
+    </parameter>
+
+    <parameter name="DGMethod">
+      <definition> DG discretization method for skeleton terms.
+
+        **SIPG:** Symmetric Interior Penalty
+
+        **NIPG:** Non-Symmetric Interior Penalty
+
+        **OBB:** Oden, Babuska, Baumann: no penalty term
+
+        **IIP:** Incomplete Interior Penalty: no symmetry term
+      </definition>
+      <values> SIPG, NIPG, OBB, IIP </values>
+      <suggestion> SIPG </suggestion>
+    </parameter>
+
+    <parameter name="DGWeights">
+      <definition> Apply harmonic weighting to skeleton term contributions
+        in DG.
+      </definition>
+      <values> true, false </values>
+      <suggestion> true </suggestion>
+    </parameter>
+
+    <parameter name="penaltyFactor">
+      <definition> Penalty factor to be used in the Discontinuous Galerkin scheme
+      </definition>
+      <values> float </values>
+      <suggestion> 10 </suggestion>
     </parameter>
   </category>
 
@@ -328,41 +367,4 @@ adding an empty line, make text **bold** or ``monospaced``.
     </parameter>
   </category>
 
-   <category name="numerics.experimental">
-    <parameter name="method">
-      <definition> DG discretization method for skeleton terms.
-
-        **SIPG:** Symmetric Interior Penalty
-
-        **NIPG:** Non-Symmetric Interior Penalty
-
-        **OOB:** Oden, Babuska, Baumann: no penalty term
-
-        **IIP:** Incomplete Interior Penalty: no symmetry term
-      </definition>
-      <values> SIPG, NIPG, OOB, IIP </values>
-      <suggestion> SIPG </suggestion>
-      <comment> Experimental settings are enabled by the appropriate CMake flag.
-      </comment>
-    </parameter>
-
-    <parameter name="upwinding">
-      <definition> Upwinding method for skeleton terms.
-
-        **semiUpwind:** Apply upwinding to conductivity factor (only).
-
-        **fullUpwind:** Apply upwinding on numeric flux and conductivity.
-      </definition>
-      <values> none, semiUpwind, fullUpwind </values>
-      <suggestion> none </suggestion>
-    </parameter>
-
-    <parameter name="weights">
-      <definition> Apply harmonic weighting to skeleton term contributions.
-      </definition>
-      <values> true, false </values>
-      <suggestion> true </suggestion>
-    </parameter>
-  </category>
-
 </dorie>

dune/dorie/CMakeLists.txt

@@ -22,8 +22,3 @@ endforeach()
 
 # Global target
 add_custom_target("dorie" DEPENDS richards transport)
-
-# enable setting operator scheme from config file
-if(EXPERIMENTAL_DG_FEATURES)
-    target_compile_definitions("dorie" PUBLIC -DEXPERIMENTAL_DG_FEATURES)
-endif()

dune/dorie/model/richards/adaptivity/operator_error_indicator.hh

@@ -15,7 +15,8 @@
 #include <dune/pdelab/localoperator/defaultimp.hh>
 #include <dune/pdelab/finiteelement/localbasiscache.hh>
 
-#include <dune/dorie/model/richards/local_operator_DG.hh>
+#include <dune/dorie/common/typedefs.hh>
+#include <dune/dorie/model/richards/local_operator_cfg.hh>
 
 namespace Dune {
   namespace Dorie {
@@ -63,14 +64,14 @@ namespace Dune {
 
       FluxErrorEstimator (const Dune::ParameterTree& config,
         const Parameter& param_, const Boundary& boundary_,
-        RichardsDGMethod::Type method_ = RichardsDGMethod::SIPG,
+        RichardsDGMethod method_ = RichardsDGMethod::SIPG,
         int intorderadd_ = 2, int quadrature_factor_ = 2)
       : param(param_), boundary(boundary_),
         intorderadd(intorderadd_), quadrature_factor(quadrature_factor_),
         penalty_factor(config.get<RF>("numerics.penaltyFactor")),
         time(0.0)
       {
-        if (method_ == RichardsDGMethod::OOB)
+        if (method_ == RichardsDGMethod::OBB)
           penalty_factor = 0.0;
       }
 
@@ -310,4 +311,4 @@ namespace Dune {
   } // namespace Dorie
 } // namespace Dune
 
-#endif // DUNE_DORIE_ERROR_INDICATOR_HH
\ No newline at end of file
+#endif // DUNE_DORIE_ERROR_INDICATOR_HH

dune/dorie/model/richards/local_operator_DG.hh

@@ -2,10 +2,8 @@
 #ifndef DUNE_DORIE_RICHARDS_OPERATOR_HH
 #define DUNE_DORIE_RICHARDS_OPERATOR_HH
 
-#include <string>
-#include <tuple>
-#include <map>
 #include <vector>
+#include <memory>
 
 #include <dune/common/parametertree.hh>
 #include <dune/common/exceptions.hh>
@@ -22,40 +20,12 @@
 #include <dune/pdelab/finiteelement/localbasiscache.hh>
 
 #include <dune/dorie/common/typedefs.hh>
+#include <dune/dorie/model/richards/local_operator_cfg.hh>
 
 namespace Dune {
 namespace Dorie {
 namespace Operator {
 
-//! Interior penalty type
-struct RichardsDGMethod
-{
-  enum Type { NIPG, //!< Non-symmetric interior penalty
-              SIPG, //!< Symmetric interior penalty (default)
-              OOB, //!< Oden, Babuska, Baumann (no penalty term)
-              IIP //!< Incomplete interior penalty (no symmetry)
-            };
-};
-
-//! Upwinding type
-struct RichardsDGUpwinding
-{
-  enum Type {
-    fullUpwind, //!< Upwind flux and conductiviy
-    semiUpwind, //!< Only upwind conductivity factor
-    none //!< No upwinding
-  };
-};
-
-//! Gradient weighting
-struct RichardsDGWeights
-{
-  enum Type {
-    weightsOn, //!< harmonic weighting of flux contributions
-    weightsOff //!< no weighting of flux contributions
-  };
-};
-
 //! Operator internal BC handling
 struct BCType
 {
@@ -65,62 +35,6 @@ struct BCType
             };
 };
 
-/// Read experimental operator settings from a parameter file
-/* \return Tuple of RichardsDGMethod, RichardsDGUpwinding, and
- *    RichardsDGWeights to be inserted into the local operator constructor.
- */
-inline auto read_experimental_operator_settings(
-  const Dune::ParameterTree &inifile)
-    -> std::tuple<Operator::RichardsDGMethod::Type,
-                  Operator::RichardsDGUpwinding::Type,
-                  Operator::RichardsDGWeights::Type>
-{
-  const auto log = Dorie::get_logger(log_richards);
-  log->debug("Reading experimental DG operator settings:");
-
-  RichardsDGMethod::Type method;
-  RichardsDGUpwinding::Type upwinding;
-  RichardsDGWeights::Type weights;
-
-  const auto method_str = inifile.get<std::string>("dg.experimental.method");
-  log->debug("  DG method: {}", method_str);
-  if (method_str == "SIPG")
-    method = RichardsDGMethod::SIPG;
-  else if (method_str == "NIPG")
-    method = RichardsDGMethod::NIPG;
-  else if (method_str == "OOB")
-    method = RichardsDGMethod::OOB;
-  else if (method_str == "IIP")
-    method = RichardsDGMethod::IIP;
-  else {
-    log->error("Unknown DG method: {}", method_str);
-    DUNE_THROW(Dune::IOError, "Unknown DG method");
-  }
-
-  const auto upwinding_str
-    = inifile.get<std::string>("dg.experimental.upwinding");
-  log->debug("  Upwinding scheme: {}", upwinding_str);
-  if (upwinding_str == "none")
-    upwinding = RichardsDGUpwinding::none;
-  else if (upwinding_str == "semiUpwind")
-    upwinding = RichardsDGUpwinding::semiUpwind;
-  else if (upwinding_str == "fullUpwind")
-    upwinding = RichardsDGUpwinding::fullUpwind;
-  else {
-    log->error("Unknown upwinding scheme: {}", upwinding_str);
-    DUNE_THROW(Dune::IOError, "Unknown upwinding scheme");
-  }
-
-  const auto weights_str = inifile.get<bool>("dg.experimental.weights");
-  log->debug("  Harmonic weights at interfaces: {}", weights_str);
-  if (weights_str)
-    weights = RichardsDGWeights::weightsOn;
-  else
-    weights = RichardsDGWeights::weightsOff;
-
-  return std::make_tuple(method, upwinding, weights);
-}
-
 /// A local operator for solving the Richards equation using upwinding.
 /** Written by Ole Klein, IWR, Heidelberg and modified by the
  *  DORiE developers, IUP, Heidelberg \n
@@ -167,9 +81,9 @@ protected:
   std::shared_ptr<const Parameter> param; //!< class providing equation parameters
   std::shared_ptr<const Boundary> boundary; //!< class providing boundary conditions
   std::shared_ptr<const SourceTerm> sourceTerm; //!< class providing source term information
-  const RichardsDGMethod::Type method; //!< Interior penalty type
-  const RichardsDGUpwinding::Type upwinding; //!< DG method weights switch
-  const RichardsDGWeights::Type weights; //!< Gradient weighting
+  const RichardsDGMethod method; //!< Interior penalty type
+  const RichardsUpwinding upwinding; //!< DG method weights switch
+  const RichardsDGWeights weights; //!< Gradient weighting
 
   const int intorderadd; //!< integration order addend
   const int quadrature_factor; //!< factor to FEM integration order
@@ -198,9 +112,9 @@ public:
    *  \param param_ Object providing equation parameters
    *  \param boundary_ Object prividing boundary conditions
    *  \param sourceTerm_ Object providing source term information
-   *  \param method_ DG method type \see RichardsDGMethod::Type
-   *  \param upwinding_ Upwinding type \see RichardsDGUpwinding::Type
-   *  \param weights_ DG weigths switch \see RichardsDGWeights::Type
+   *  \param method_ DG method type \see RichardsDGMethod
+   *  \param upwinding_ Upwinding type \see RichardsUpwinding
+   *  \param weights_ DG weigths switch \see RichardsDGWeights
    *  \param intorderadd_ Addend to integration order
    *  \param quadrature_factor_ Factor to FEM integration order
    */
@@ -209,9 +123,9 @@ public:
     std::shared_ptr<const Parameter> param_,
     std::shared_ptr<const Boundary> boundary_,
     std::shared_ptr<const SourceTerm> sourceTerm_,
-    const RichardsDGMethod::Type method_ = RichardsDGMethod::SIPG,
-    const RichardsDGUpwinding::Type upwinding_ = RichardsDGUpwinding::none,
-    const RichardsDGWeights::Type weights_ = RichardsDGWeights::weightsOn,
+    const RichardsDGMethod method_ = RichardsDGMethod::SIPG,
+    const RichardsUpwinding upwinding_ = RichardsUpwinding::none,
+    const RichardsDGWeights weights_ = RichardsDGWeights::weightsOn,
     int intorderadd_ = 2,
     int quadrature_factor_ = 2
   ) :
@@ -231,12 +145,12 @@ public:
     cache(20)
   {
     theta = 0.; // IIP
-    if (method == RichardsDGMethod::NIPG || method == RichardsDGMethod::OOB)
+    if (method == RichardsDGMethod::NIPG || method == RichardsDGMethod::OBB)
       theta = 1.;
     else if (method == RichardsDGMethod::SIPG)
       theta = -1.;
 
-    if (method == RichardsDGMethod::OOB)
+    if (method == RichardsDGMethod::OBB)
       penalty_factor = 0.;
   }
 
@@ -527,13 +441,13 @@ public:
         RF omega_s = 0.5, omega_n = 0.5;
         if (weights == RichardsDGWeights::weightsOn)
         {
-          if (upwinding == RichardsDGUpwinding::none)
+          if (upwinding == RichardsUpwinding::none)
           {
             omega_s = cond_n / ((cond_s) + (cond_n));
             omega_n = cond_s / ((cond_s) + (cond_n));
           }
-          else if (upwinding == RichardsDGUpwinding::semiUpwind
-            || upwinding == RichardsDGUpwinding::fullUpwind)
+          else if (upwinding == RichardsUpwinding::semiUpwind
+            || upwinding == RichardsUpwinding::fullUpwind)
           {
             omega_s = satCond_n / (satCond_s + satCond_n);
             omega_n = satCond_s / (satCond_s + satCond_n);
@@ -560,7 +474,7 @@ public:
         numFlux_s *= satCond_s;
         numFlux_n *= satCond_n;
 
-        if (upwinding == RichardsDGUpwinding::none)
+        if (upwinding == RichardsUpwinding::none)
         {
           numFlux_s *= relCond_s;
           numFlux_n *= relCond_n;
@@ -569,8 +483,8 @@ public:
 
         // Upwind in relative conductivity
         RF relCond_upwind=0.0, satCond_upwind=0.0;
-        if (upwinding == RichardsDGUpwinding::semiUpwind
-          || upwinding == RichardsDGUpwinding::fullUpwind)
+        if (upwinding == RichardsUpwinding::semiUpwind
+          || upwinding == RichardsUpwinding::fullUpwind)
         {
           RF cond_upwind;
           if (numFlux > 0)
@@ -593,21 +507,21 @@ public:
           // diffusion term
           // consistency term
           // + penalty term
-          if (upwinding == RichardsDGUpwinding::none)
+          if (upwinding == RichardsUpwinding::none)
           {
             for (unsigned int i = 0; i < lfsv_s.size(); i++)
               r_s.accumulate(lfsv_s, i,   numFlux * phiv_s[i] * factor);
             for (unsigned int i = 0; i < lfsv_n.size(); i++)
               r_n.accumulate(lfsv_n, i, - numFlux * phiv_n[i] * factor);
           }
-          else if (upwinding == RichardsDGUpwinding::semiUpwind)
+          else if (upwinding == RichardsUpwinding::semiUpwind)
           {
             for (unsigned int i = 0; i<lfsv_s.size(); i++)
               r_s.accumulate(lfsv_s,i,   relCond_upwind * numFlux * phiv_s[i] * factor);
             for (unsigned int i = 0; i<lfsv_n.size(); i++)
               r_n.accumulate(lfsv_n,i, - relCond_upwind * numFlux * phiv_n[i] * factor);
           }
-          else if (upwinding == RichardsDGUpwinding::fullUpwind)
+          else if (upwinding == RichardsUpwinding::fullUpwind)
           {
             // Upwind numerical flux
             double numFlux_upwind = (numFlux > 0) ? numFlux_s : numFlux_n;
@@ -628,21 +542,21 @@ public:
           // discrete gradient sign: Negative for lifting
           double dg_sign = (lopcase == LOPCase::RTVolume) ? -1. : 1.;
 
-          if (upwinding == RichardsDGUpwinding::none)
+          if (upwinding == RichardsUpwinding::none)
           {
             for (unsigned int i = 0; i < lfsv_s.size(); i++)
               r_s.accumulate(lfsv_s, i, dg_sign * theta * omega_s * (gradphiv_s[i] * normal) * relCond_s * satCond_s * jump * factor);
             for (unsigned int i = 0; i < lfsv_n.size(); i++)
               r_n.accumulate(lfsv_n, i, dg_sign * theta * omega_n * (gradphiv_n[i] * normal) * relCond_n * satCond_n * jump * factor);
           }
-          else if (upwinding == RichardsDGUpwinding::semiUpwind)
+          else if (upwinding == RichardsUpwinding::semiUpwind)
           {
             for (unsigned int i = 0; i<lfsv_s.size(); i++)
               r_s.accumulate(lfsv_s,i, dg_sign * theta * omega_s * (gradphiv_s[i] * normal) * relCond_upwind * satCond_s * jump * factor);
             for (unsigned int i = 0; i<lfsv_n.size(); i++)
               r_n.accumulate(lfsv_n,i, dg_sign * theta * omega_n * (gradphiv_n[i] * normal) * relCond_upwind * satCond_n * jump * factor);
           }
-          else if (upwinding == RichardsDGUpwinding::fullUpwind)
+          else if (upwinding == RichardsUpwinding::fullUpwind)
           {
             for (unsigned int i = 0; i < lfsv_s.size(); i++)
               r_s.accumulate(lfsv_s, i, dg_sign * theta * (gradphiv_s[i] * normal) * relCond_upwind * satCond_upwind * jump * factor);
@@ -813,15 +727,15 @@ public:
 
           // compute conductivity factor
           RF relCond;
-          if (upwinding == RichardsDGUpwinding::semiUpwind
-            || upwinding == RichardsDGUpwinding::fullUpwind)
+          if (upwinding == RichardsUpwinding::semiUpwind
+            || upwinding == RichardsUpwinding::fullUpwind)
           {
             if (numFlux > 0)
               relCond = relCond_s;
             else
               relCond = relCond_n;
           }
-          else // (upwinding == RichardsDGUpwinding::none)
+          else // (upwinding == RichardsUpwinding::none)
           {
             // harmonic average of conductivity factors
             relCond = 2 * relCond_s * relCond_n / (relCond_s + relCond_n);

dune/dorie/model/richards/local_operator_FV.hh

@@ -10,6 +10,7 @@
 #include <dune/pdelab/localoperator/defaultimp.hh>
 
 #include <dune/dorie/common/typedefs.hh>
+#include <dune/dorie/model/richards/local_operator_cfg.hh>
 
 namespace Dune {
 namespace Dorie {
@@ -60,9 +61,11 @@ public:
    */
   RichardsFVSpatialOperator(
     const std::shared_ptr<const Parameter>& param,
-    const std::shared_ptr<const Boundary>& boundary
+    const std::shared_ptr<const Boundary>& boundary,
+    const RichardsUpwinding upwinding = RichardsUpwinding::none
   ) : _param(param)
     , _boundary(boundary)
+    , _upwinding(upwinding)
     , _time(0.)
   {}
 
@@ -126,10 +129,21 @@ public:
     const auto center_position_i_g = geo_i.center();
     const auto center_position_o_g = geo_o.center();
 
+    // Distance between the two entity centers
+    const auto center_position_diff = center_position_i_g
+                                      - center_position_o_g;
+    const auto distance = center_position_diff.two_norm();
+
     // Inside/outside solute value
     const RangeU u_i = x_i(lfsu_i,0);
     const RangeU u_o = x_o(lfsu_o,0);
 
+    // Finite difference of u between the two entities
+    RangeU dudn = (u_o-u_i) / distance;
+
+    // Update gradient with gravity vector
+    dudn -= _param->gravity() * normal_f;
+
     // bind parameterization and retrieve functions
     _param->bind(entity_i);
     const auto saturation_f_i = _param->saturation_f();
@@ -143,28 +157,49 @@ public:
     const RangeU cond_i = conductivity_f_i(saturation_f_i(u_i));
     const RangeU cond_o = conductivity_f_o(saturation_f_o(u_o));
 
-    // Harmonic average for interface conductivity
-    const RangeU cond_f = 2.0/(   1.0/(cond_i + 1E-30) 
-                                + 1.0/(cond_o + 1E-30) );
-
-    // Distance between the two entity centers
-    const auto center_position_diff = center_position_i_g - center_position_o_g;
-    const auto distance = center_position_diff.two_norm();
-
-    // Finite difference of u between the two entities
-    RangeU dudn = (u_o-u_i)/distance;
-
-    // Update gradient with gravity vector
-    dudn -= _param->gravity()*normal_f;
+    // Interface conductivity factor (Upwinding applies)
+    RangeU cond_f(0.0);
+    if (_upwinding == RichardsUpwinding::none)
+    {
+      // Harmonic average for interface conductivity
+      cond_f = 2.0/(   1.0/(cond_i + 1E-30)
+                     + 1.0/(cond_o + 1E-30) );
+    }
+    else if (_upwinding == RichardsUpwinding::semiUpwind)
+    {
+      // Harmonic average of saturated conductivities
+      const RangeU cond_sat_i = conductivity_f_i(1.0);
+      const RangeU cond_sat_o = conductivity_f_o(1.0);
+
+      // Upwinding conductivity factor
+      RangeU cond_upwind_factor(0.0);
+      if (dudn < 0.0) {
+        // inward flux
+        cond_upwind_factor = cond_o / cond_sat_o;
+      }
+      else {
+        // outward flux
+        cond_upwind_factor = cond_i / cond_sat_i;
+      }
+
+      cond_f = 2.0 * cond_upwind_factor / (   1.0/(cond_sat_i + 1E-30)
+                                            + 1.0/(cond_sat_o + 1E-30) );
+    }
+    else // RichardsFVUpwinding::fullUpwind
+    {
+      // No average: Use upwind conductivity
+      if (dudn < 0.0) {
+        // inward flux
+        cond_f = cond_o;
+      }
+      else {
+        // outward flux
+        cond_f = cond_i;
+      }
+    }
 
     // Water flux in normal direction w.r.t the intersection
-    auto water_flux_n = - cond_f*dudn;
-
-    // // Upwinding
-    // if (water_flux_n > 0.)
-    //   water_flux_n = - cond_i*dudn;
-    // else
-    //   water_flux_n = - cond_o*dudn;
+    const auto water_flux_n = - cond_f * dudn;
 
     // Symmetric contribution to residual on inside element
     r_i.accumulate(lfsv_i, 0,  water_flux_n*volume_f );
@@ -290,6 +325,9 @@ private:
   const std::shared_ptr<const Parameter> _param;
   /// Class providing boundary conditions
   const std::shared_ptr<const Boundary> _boundary;
+  /// Upwinding setting
+  const RichardsUpwinding _upwinding;
+  /// Operator internal time
   double _time;
 };
 

dune/dorie/model/richards/local_operator_cfg.hh

+#ifndef DUNE_DORIE_RICHARDS_LOP_CFG_HH
+#define DUNE_DORIE_RICHARDS_LOP_CFG_HH
+
+#include <tuple>
+#include <string>
+
+#include <dune/common/exceptions.hh>
+#include <dune/common/parametertree.hh>
+
+#include <dune/dorie/common/logging.hh>
+
+namespace Dune {
+namespace Dorie {
+namespace Operator {
+
+/**
+ *  \addtogroup RichardsModel
+ *  \{
+ */
+
+//! Interior penalty type
+enum class RichardsDGMethod
+{
+    NIPG, //!< Non-symmetric interior penalty