[MPL/Exp] Add additive offset.

Documentation/ProjectFile/properties/property/Exponential/c_Exponential.md

 Definition of a exponential property:
-\f$y(x) = y_{\textrm{ref}} \exp(m (x - x_{\textrm{ref}}))\f$
+\f$y(x) = y_{\textrm{offset}} + y_{\textrm{ref}} \exp(m (x - x_{\textrm{ref}}))\f$
 where
  - \f$y_{\textrm{ref}}\f$ is a reference value, for instance reference viscosity
  - \f$m\f$ is a factor influencing the exponent of the exponential relationship

Documentation/ProjectFile/properties/property/Exponential/t_offset.md

+\copydoc MaterialPropertyLib::Exponential::offset_

MaterialLib/MPL/Properties/CreateExponential.cpp

@@ -44,6 +44,10 @@ std::unique_ptr<Exponential> createExponential(
         //! \ogs_file_param{properties__property__Exponential__exponent__factor}
         exponent_data_config.getConfigParameter<double>("factor");
 
+    auto const offset =
+        //! \ogs_file_param{properties__property__Exponential__offset}
+        config.getConfigParameter<double>("offset");
+
     MaterialPropertyLib::Variable exp_data_type =
         MaterialPropertyLib::convertStringToVariable(variable_name);
 
@@ -51,6 +55,6 @@ std::unique_ptr<Exponential> createExponential(
         exp_data_type, reference_condition, factor};
 
     return std::make_unique<MaterialPropertyLib::Exponential>(
-        std::move(property_name), reference_value, exp_data);
+        std::move(property_name), offset, reference_value, exp_data);
 }
 }  // namespace MaterialPropertyLib

MaterialLib/MPL/Properties/Exponential.cpp

@@ -16,9 +16,10 @@
 namespace MaterialPropertyLib
 {
 Exponential::Exponential(std::string name,
+                         double const offset,
                          PropertyDataType const& property_reference_value,
                          ExponentData const& v)
-    : exponent_data_(v)
+    : exponent_data_(v), offset_(offset)
 {
     name_ = std::move(name);
     auto const f = std::get<double>(exponent_data_.factor);
@@ -35,7 +36,7 @@ PropertyDataType Exponential::value(
     auto const v =
         std::get<double>(variable_array[static_cast<int>(exponent_data_.type)]);
 
-    return std::get<double>(value_) * std::exp(f * v);
+    return offset_ + std::get<double>(value_) * std::exp(f * v);
 }
 
 PropertyDataType Exponential::dValue(

MaterialLib/MPL/Properties/Exponential.h

@@ -22,7 +22,7 @@ struct ExponentData
 };
 
 /// The exponential property class. This property calculates the exponential
-/// relationship \f$ \alpha(\beta) =
+/// relationship \f$ \alpha(\beta) = \alpha_{\mathrm{offset}} +
 /// \alpha_{\mathrm{ref}} \cdot \exp (-s (\beta - \beta_{\mathrm{ref}})\f$.
 /// The current implementation accepts only the double datatype defined in
 /// PropertyDataType.
@@ -33,6 +33,7 @@ public:
     /// the PropertyDataType definition and sets the protected attribute value_
     /// of the base class Property to that value.
     Exponential(std::string name,
+                double const offset,
                 PropertyDataType const& property_reference_value,
                 ExponentData const& v);
     /// This method computes the value of a property \f$\alpha\f$ depending
@@ -57,5 +58,6 @@ public:
 
 private:
     ExponentData const exponent_data_;
+    double const offset_;  //< additive offset in units of the property.
 };
 }  // namespace MaterialPropertyLib