implement WENO limiter for DG method

benchmarks/advection/rotate_shape_dg_bp.prm

@@ -0,0 +1,21 @@
+# Like rotate_shape_supg but with discontinuous Galerkin method
+# and bound-preserving limiter
+
+set Dimension                              = 2
+
+include rotate_shape_supg.prm
+
+set Output directory                       = output-rotate-shape-dg-bp
+
+subsection Discretization
+  set Use discontinuous temperature discretization = true
+  set Use discontinuous composition discretization = true
+  subsection Stabilization parameters
+    set Limiter for discontinuous temperature solution = bound preserving
+    set Limiter for discontinuous composition solution = bound preserving
+    set Global temperature maximum = 1
+    set Global temperature minimum = 0
+    set Global composition maximum = 1
+    set Global composition minimum = 0
+  end
+end

benchmarks/advection/rotate_shape_dg_weno.prm

@@ -0,0 +1,26 @@
+# Like rotate_shape_supg but with discontinuous Galerkin method
+# and WENO limiter
+
+set Dimension                              = 2
+
+include rotate_shape_supg.prm
+
+set Output directory                       = output-rotate-shape-dg-weno
+
+subsection Discretization
+  set Use discontinuous temperature discretization = true
+  set Use discontinuous composition discretization = true
+  subsection Stabilization parameters
+    set Limiter for discontinuous temperature solution = WENO
+    set Limiter for discontinuous composition solution = WENO
+  end
+end
+
+subsection Postprocess
+  subsection Visualization
+    set List of output variables = kxrcf indicator
+    subsection KXRCF indicator
+      set Name of advection field = C_1
+    end
+  end
+end

benchmarks/viscoelastic_beam_modified/20km_opentopbot_weno.prm

@@ -0,0 +1,33 @@
+# This parameter file modifies the benchmark 20kmh_05drho.prm to use the WENO limiter
+# for viscoelastic stress components.
+
+include $ASPECT_SOURCE_DIR/benchmarks/viscoelastic_bending_beam/20km_opentopbot.prm
+
+set Output directory = 20kmh_05drho_weno
+
+
+subsection Discretization
+  subsection Stabilization parameters
+    # Use WENO limiter for viscoelastic stress components, while using the
+    # bound-preserving limiter for the chemical field
+    set Limiter for discontinuous composition solution = WENO, WENO, WENO, bound preserving
+    # In this benchmark, the spurious oscillations at the boundaries of the beam
+    # are extremely serious, so we set the linear weight of neighbor cells one
+    # magnitude greater than the default value to make the reconstructed solution
+    # smoother.
+    set WENO linear weight of neighbor cells = 0.01
+    # The global maximum and minimum values are only used by the chemical field.
+    set Global composition maximum = 1.0
+    set Global composition minimum = 0.0
+  end
+end
+
+# Visualize the KXRCF indicator for ve_stress_xy
+subsection Postprocess
+  subsection Visualization
+    set List of output variables = material properties, strain rate, kxrcf indicator
+    subsection KXRCF indicator
+      set Name of advection field = ve_stress_xy
+    end
+  end
+end

benchmarks/viscoelastic_bending_beam/viscoelastic_bending_beam_weno.prm

@@ -0,0 +1,32 @@
+# This parameter file modifies the benchmark viscoealastic_bending_beam.prm
+# to use the WENO limiter for viscoelastic stress components.
+
+include $ASPECT_SOURCE_DIR/benchmarks/viscoelastic_bending_beam/viscoelastic_bending_beam.prm
+
+set Output directory = output_viscoelastic_bending_beam_weno
+
+subsection Discretization
+  subsection Stabilization parameters
+    # Use WENO limiter for viscoelastic stress components, while using the
+    # bound-preserving limiter for the chemical field
+    set Limiter for discontinuous composition solution = WENO, WENO, WENO, bound preserving
+    # In this benchmark, the spurious oscillations at the boundaries of the beam
+    # are extremely serious, so we set the linear weight of neighbor cells one
+    # magnitude greater than the default value to make the reconstructed solution
+    # smoother.
+    set WENO linear weight of neighbor cells = 0.01
+    # The global maximum and minimum values are only used by the chemical field.
+    set Global composition maximum = 1.0
+    set Global composition minimum = 0.0
+  end
+end
+
+# Visualize the KXRCF indicator for ve_stress_xy
+subsection Postprocess
+  subsection Visualization
+    set List of output variables = material properties, strain rate, kxrcf indicator
+    subsection KXRCF indicator
+      set Name of advection field = ve_stress_xy
+    end
+  end
+end

contrib/utilities/update_scripts/prm_files/reformat_limiter_settings.py

@@ -0,0 +1,75 @@
+#!/usr/bin/env python3
+# -*- coding: utf-8 -*-
+
+""" This script changes 'Use limiter for discontinuous temperature/composition solution'
+to 'limiter for discontinuous temperature/composition solution' in order to allow users
+to specify different limiters for different fields
+"""
+
+
+import sys
+import os
+import re
+import argparse
+
+__author__ = 'The authors of the ASPECT code'
+__copyright__ = 'Copyright 2024, ASPECT'
+__license__ = 'GNU GPL 2 or later'
+
+# Add the ASPECT root directory to the path so we can import from the aspect_data module
+sys.path.append(os.path.join(os.path.dirname(__file__), '..', '..', '..'))
+import python.scripts.aspect_input as aspect
+
+
+
+def reformat_limiter_settings(parameters):
+    """change 'Use limiter for discontinuous temperature/composition solution' 
+    to 'limiter for discontinuous temperature/composition solution' in order to allow users
+    to specify different limiters for different fields
+    """
+
+    old_entries = ["Use limiter for discontinuous temperature solution",
+                   "Use limiter for discontinuous composition solution"]
+    new_entries = ["Limiter for discontinuous temperature solution",
+                   "Limiter for discontinuous composition solution"]
+
+    # go to the subsection
+    if "Discretization" in parameters:
+        if "Stabilization parameters" in parameters["Discretization"]["value"]:
+            subsection = parameters["Discretization"]["value"]["Stabilization parameters"]["value"]
+
+            for i in range(0,2):
+                if old_entries[i] in subsection:
+
+                    # Delete the old entry
+                    use_limiter = subsection[old_entries[i]]["value"]
+                    del subsection[old_entries[i]]
+
+                    # If limiter is used, then set the value of the new entry to "bound preserving"
+                    if use_limiter == "true":
+                        subsection[new_entries[i]] = {"comment"         : "", 
+                                                      "value"           : "bound preserving",  
+                                                      "type"            : "parameter", 
+                                                      "alignment spaces": 1}
+
+    return parameters
+
+
+
+def main(input_file, output_file):
+    """Echo the input arguments to standard output"""
+    parameters = aspect.read_parameter_file(input_file)
+    parameters = reformat_limiter_settings(parameters)
+    aspect.write_parameter_file(parameters, output_file)
+
+
+
+if __name__ == '__main__':
+    parser = argparse.ArgumentParser(
+                    prog='ASPECT .prm file reformatter',
+                    description='Reformats ASPECT .prm files to follow our general formatting guidelines. See the documentation of this script for details.')
+    parser.add_argument('input_file', type=str, help='The .prm file to reformat')
+    parser.add_argument('output_file', type=str, help='The .prm file to write the reformatted file to')
+    args = parser.parse_args()
+
+    sys.exit(main(args.input_file, args.output_file))

doc/manual/citing_aspect.bib

@@ -2068,4 +2068,32 @@ @article{SAKI2024107212
 keywords = {Mantle transition zone discontinuities, PP and SS precursors, Caribbean subduction, Plume-slab interaction}
 }
 
+@article{zhong2013,
+title = {A simple weighted essentially nonoscillatory limiter for {Runge}–{Kutta} discontinuous {Galerkin} methods},
+volume = {232},
+issn = {0021-9991},
+doi = {10.1016/j.jcp.2012.08.028},
+language = {en},
+number = {1},
+journal = {Journal of Computational Physics},
+author = {Zhong, Xinghui and Shu, Chi-Wang},
+month = jan,
+year = {2013},
+keywords = {Discontinuous Galerkin method, WENO limiter},
+pages = {397--415}
+}
 
+@article{krivodonova2004,
+series = {Workshop on {Innovative} {Time} {Integrators} for {PDEs}},
+title = {Shock detection and limiting with discontinuous {Galerkin} methods for hyperbolic conservation laws},
+volume = {48},
+issn = {0168-9274},
+doi = {10.1016/j.apnum.2003.11.002},
+language = {en},
+number = {3},
+journal = {Applied Numerical Mathematics},
+author = {Krivodonova, L. and Xin, J. and Remacle, J. -F. and Chevaugeon, N. and Flaherty, J. E.},
+month = mar,
+year = {2004},
+pages = {323--338}
+}

include/aspect/parameters.h

@@ -313,6 +313,41 @@ namespace aspect
       }
     };
 
+    /**
+     * A struct to provide the different choices of limiters for
+     * the discontinuous Galerkin method.
+     */
+    struct DGLimiterType
+    {
+      enum Kind
+      {
+        bound_preserving,
+        WENO,
+        none
+      };
+
+      static
+      Kind
+      parse(const std::string &input)
+      {
+        if (input == "bound preserving")
+          return bound_preserving;
+        else if (input == "WENO")
+          return WENO;
+        else if (input == "none")
+          return none;
+        else
+          AssertThrow(false, ExcNotImplemented());
+
+        return Kind();
+      }
+
+      static const std::string pattern()
+      {
+        return "bound preserving|WENO|none";
+      }
+    };
+
     /**
      * This enum represents the different choices for the linear solver
      * for the Stoke system. See @p stokes_solver_type.
@@ -656,12 +691,15 @@ namespace aspect
     std::vector<double>            stabilization_beta;
     double                         stabilization_gamma;
     double                         discontinuous_penalty;
-    bool                           use_limiter_for_discontinuous_temperature_solution;
-    std::vector<bool>              use_limiter_for_discontinuous_composition_solution;
+    typename DGLimiterType::Kind   limiter_for_discontinuous_temperature_solution;
+    std::vector<typename DGLimiterType::Kind> limiter_for_discontinuous_composition_solution;
     double                         global_temperature_max_preset;
     double                         global_temperature_min_preset;
     std::vector<double>            global_composition_max_preset;
     std::vector<double>            global_composition_min_preset;
+    double                         temperature_KXRCF_indicator_threshold;
+    std::vector<double>            composition_KXRCF_indicator_threshold;
+    double                         WENO_linear_weight;
 
     std::vector<std::string>       compositional_fields_with_disabled_boundary_entropy_viscosity;
     /**

include/aspect/postprocess/visualization/kxrcf_indicator.h

@@ -0,0 +1,80 @@
+/*
+  Copyright (C) 2011 - 2022 by the authors of the ASPECT code.
+
+  This file is part of ASPECT.
+
+  ASPECT is free software; you can redistribute it and/or modify
+  it under the terms of the GNU General Public License as published by
+  the Free Software Foundation; either version 2, or (at your option)
+  any later version.
+
+  ASPECT is distributed in the hope that it will be useful,
+  but WITHOUT ANY WARRANTY; without even the implied warranty of
+  MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+  GNU General Public License for more details.
+
+  You should have received a copy of the GNU General Public License
+  along with ASPECT; see the file LICENSE.  If not see
+  <http://www.gnu.org/licenses/>.
+*/
+
+
+#ifndef _aspect_postprocess_visualization_kxrcf_indicator_h
+#define _aspect_postprocess_visualization_kxrcf_indicator_h
+
+#include <aspect/postprocess/visualization.h>
+#include <aspect/simulator_access.h>
+
+
+namespace aspect
+{
+  namespace Postprocess
+  {
+    namespace VisualizationPostprocessors
+    {
+      /**
+       * A class derived that implements a function that provides the
+       * KXRCF indicator for a given advection field on each cell for
+       * graphical output.
+       */
+      template <int dim>
+      class KXRCFIndicator : public CellDataVectorCreator<dim>,
+        public SimulatorAccess<dim>
+      {
+        public:
+          /**
+           * Constructor.
+           */
+          KXRCFIndicator();
+
+          /**
+           * @copydoc CellDataVectorCreator<dim>::execute()
+           */
+          std::pair<std::string, std::unique_ptr<Vector<float>>>
+          execute () const override;
+
+          /**
+           * Declare the parameters this class takes through input files.
+           */
+          static
+          void
+          declare_parameters (ParameterHandler &prm);
+
+          /**
+           * Read the parameters this class declares from the parameter file.
+           */
+          void
+          parse_parameters (ParameterHandler &prm) override;
+
+        private:
+          /**
+           * A parameter that tells us for which advection field the
+           * KXRCF indicator should be visualized.
+           */
+          unsigned int field_index;
+      };
+    }
+  }
+}
+
+#endif

include/aspect/simulator.h

@@ -1373,10 +1373,29 @@ namespace aspect
        * the discontinuous Galerkin solution will stay in the prescribed bounds.
        *
        * This function is implemented in
-       * <code>source/simulator/helper_functions.cc</code>.
+       * <code>source/simulator/limiters.cc</code>.
+       */
+      void apply_BP_limiter_to_dg_solutions (const AdvectionField &advection_field);
+
+      /**
+       * Apply the WENO limiter to the discontinuous Galerkin solutions.
+       * The WENO scheme implemented in this function is proposed by Zhong and Shu, 2013.
+       *
+       * This function is implemented in
+       * <code>source/simulator/limiters.cc</code>.
        */
-      void apply_limiter_to_dg_solutions (const AdvectionField &advection_field);
+      void apply_WENO_limiter_to_dg_solutions (const AdvectionField &advection_field);
 
+      /**
+       * Compute the KXRCF indicator that detect shocks in the advection field.
+       * The KXRCF indicator is used by the WENO limiter.
+       *
+       * This function is implemented in
+       * <code>source/simulator/limiters.cc</code>.
+       */
+      template <typename T>
+      void compute_KXRCF_indicators(Vector<T> &KXRCF_indicators,
+                                    const AdvectionField &advection_field) const;
 
       /**
        * Compute the reactions in case of operator splitting: