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Reorganize the implementation of the mass conserving temperature prof… #588

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Feb 16, 2024
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Reorganize the implementation of the mass conserving temperature prof… #588

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13 changes: 13 additions & 0 deletions include/world_builder/features/subducting_plate_models/temperature/mass_conserving.h
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Original file line number Diff line number Diff line change
Expand Up @@ -91,6 +91,18 @@ namespace WorldBuilder
const WorldBuilder::Utilities::PointDistanceFromCurvedPlanes &distance_from_planes,
const AdditionalParameters &additional_parameters) const override final;

/**
* Returns a temperature based on the given heat content, temperatures, effective plate age,
* and adjusted distance to the coldest point in the slab. The temperature is formulated by
* the analytical solutions.
*/
double get_temperature_analytic(const double top_heat_content,
const double min_temperature,
const double background_temperature,
const double temperature_,
const double effective_plate_age,
const double adjusted_distance) const;


private:
// temperature submodule parameters
Expand All @@ -116,6 +128,7 @@ namespace WorldBuilder
plate_model
};
ReferenceModelName reference_model_name;
const int plate_model_summation_number = 100; // for the plate model
};
} // namespace Temperature
} // namespace SubductingPlateModels
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123 changes: 69 additions & 54 deletions source/world_builder/features/subducting_plate_models/temperature/mass_conserving.cc
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Expand Up @@ -235,8 +235,6 @@ namespace WorldBuilder
{

const double distance_from_plane = distance_from_planes.distance_from_plane;
const int plate_model_summation_number = 100; // for the plate model


if (distance_from_plane <= max_depth && distance_from_plane >= min_depth)
{
Expand Down Expand Up @@ -523,58 +521,8 @@ namespace WorldBuilder
top_heat_content = top_heat_content * std::erfc(taper_con*theta);
}

// Assign the temperature depending on whether distance is negative (above) or positive (below) the slab
if (adjusted_distance < 0)
{
// use 1D infinite space solution for top (side 2) of slab the slab
// 2 times the "top_heat_content" because all this heat needs to be on one side of the Gaussian
const double time_top_slab = (1/(Consts::PI*thermal_diffusivity)) *
pow(((2 * top_heat_content) / (2 * density * specific_heat * (min_temperature - temperature_ + 1e-16))),2) + 1e-16;

// for overriding plate region where plate temperature is less the minimum slab temperature
// need to set temperature = temperature_ otherwise end up with temperature less than surface temperature ;
if (temperature_ < min_temperature)
{
temperature = temperature_;
}
else
{
temperature = temperature_ + (2 * top_heat_content /
(2*density*specific_heat * std::sqrt(Consts::PI * thermal_diffusivity * time_top_slab)))*
std::exp(-(adjusted_distance*adjusted_distance)/(4*thermal_diffusivity*time_top_slab));
}
}
else
{
// use half-space cooling or plate model for the bottom (side 1) of the slab
if (reference_model_name == plate_model)
{
if (adjusted_distance < max_depth)
{
const double plate_velocity_UI = plate_velocity / seconds_in_year;
temperature = background_temperature + (min_temperature - background_temperature) * (1 - adjusted_distance / max_depth);
for (int i = 1; i< std::floor(plate_model_summation_number/2.0); ++i)
{
temperature = temperature - (min_temperature - background_temperature) *
((2 / (double(i) * Consts::PI)) * std::sin((double(i) * Consts::PI * adjusted_distance) / max_depth) *
std::exp((((plate_velocity_UI * max_depth)/(2 * thermal_diffusivity)) -
std::sqrt(((plate_velocity_UI*plate_velocity_UI*max_depth*max_depth) /
(4*thermal_diffusivity*thermal_diffusivity)) + double(i) * double(i) * Consts::PI * Consts::PI)) *
((plate_velocity_UI * effective_plate_age) / max_depth)));
}
}
else
{
temperature = background_temperature;
}
}
else
{
temperature = background_temperature + (min_temperature - background_temperature) *
std::erfc(adjusted_distance / (2 * std::sqrt(thermal_diffusivity * effective_plate_age)));

}
}
// Call the analytic solution to compute the temperature
temperature = get_temperature_analytic(top_heat_content, min_temperature, background_temperature, temperature_, effective_plate_age, adjusted_distance);
}
else
{
Expand All @@ -591,6 +539,73 @@ namespace WorldBuilder
return temperature_;
}

double
MassConserving::get_temperature_analytic(const double top_heat_content,
const double min_temperature,
const double background_temperature,
const double temperature_,
const double effective_plate_age,
const double adjusted_distance) const
{
const double seconds_in_year = 60.0 * 60.0 * 24.0 * 365.25; // sec/y

double temperature = 0.0;

// Assign the temperature depending on whether distance is negative (above) or positive (below) the slab
if (adjusted_distance < 0)
{
// use 1D infinite space solution for top (side 2) of slab the slab
// 2 times the "top_heat_content" because all this heat needs to be on one side of the Gaussian
const double time_top_slab = (1/(Consts::PI*thermal_diffusivity)) *
pow(((2 * top_heat_content) / (2 * density * specific_heat * (min_temperature - temperature_ + 1e-16))),2) + 1e-16;

// for overriding plate region where plate temperature is less the minimum slab temperature
// need to set temperature = temperature_ otherwise end up with temperature less than surface temperature ;
if (temperature_ < min_temperature)
{
temperature = temperature_;
}
else
{
temperature = temperature_ + (2 * top_heat_content /
(2*density*specific_heat * std::sqrt(Consts::PI * thermal_diffusivity * time_top_slab)))*
std::exp(-(adjusted_distance*adjusted_distance)/(4*thermal_diffusivity*time_top_slab));
}
}
else
{
// use half-space cooling or plate model for the bottom (side 1) of the slab
if (reference_model_name == plate_model)
{
if (adjusted_distance < max_depth)
{
const double plate_velocity_UI = plate_velocity / seconds_in_year;
temperature = background_temperature + (min_temperature - background_temperature) * (1 - adjusted_distance / max_depth);
for (int i = 1; i< std::floor(plate_model_summation_number/2.0); ++i)
{
temperature = temperature - (min_temperature - background_temperature) *
((2 / (double(i) * Consts::PI)) * std::sin((double(i) * Consts::PI * adjusted_distance) / max_depth) *
std::exp((((plate_velocity_UI * max_depth)/(2 * thermal_diffusivity)) -
std::sqrt(((plate_velocity_UI*plate_velocity_UI*max_depth*max_depth) /
(4*thermal_diffusivity*thermal_diffusivity)) + double(i) * double(i) * Consts::PI * Consts::PI)) *
((plate_velocity_UI * effective_plate_age) / max_depth)));
}
}
else
{
temperature = background_temperature;
}
}
else
{
temperature = background_temperature + (min_temperature - background_temperature) *
std::erfc(adjusted_distance / (2 * std::sqrt(thermal_diffusivity * effective_plate_age)));

}
}
return temperature;
}

WB_REGISTER_FEATURE_SUBDUCTING_PLATE_TEMPERATURE_MODEL(MassConserving, mass conserving)
} // namespace Temperature
} // namespace SubductingPlateModels
Expand Down
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