Add UpdateFunctionsOfTime action

src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/CMakeLists.txt

@@ -20,4 +20,5 @@ spectre_target_headers(
   ReceiveElementData.hpp
   SendToElements.hpp
   UpdateAcceleration.hpp
+  UpdateFunctionsOfTime.hpp
 )

src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/InitializeEvolvedVariables.hpp

@@ -33,6 +33,7 @@ struct InitializeEvolvedVariables {
 
   using simple_tags =
       tmpl::list<variables_tag, dt_variables_tag, Tags::CurrentIteration,
+                 Tags::ExpirationTime, Tags::WorldtubeRadius,
                  ::Tags::HistoryEvolvedVariables<variables_tag>>;
   using return_tags = simple_tags;
 
@@ -41,7 +42,8 @@ struct InitializeEvolvedVariables {
   using mutable_global_cache_tags = tmpl::list<>;
   using simple_tags_from_options = tmpl::list<Tags::InitialPositionAndVelocity>;
   using argument_tags = tmpl::list<::Tags::TimeStepper<TimeStepper>,
-                                   Tags::InitialPositionAndVelocity>;
+                                   Tags::InitialPositionAndVelocity,
+                                   ::Tags::Time, Tags::ExcisionSphere<Dim>>;
   static void apply(
       const gsl::not_null<Variables<
           tmpl::list<Tags::EvolvedPosition<Dim>, Tags::EvolvedVelocity<Dim>>>*>
@@ -51,11 +53,20 @@ struct InitializeEvolvedVariables {
                                ::Tags::dt<Tags::EvolvedVelocity<Dim>>>>*>
           dt_evolved_vars,
       const gsl::not_null<size_t*> current_iteration,
+      const gsl::not_null<double*> expiration_time,
+      const gsl::not_null<double*> worldtube_radius,
       const gsl::not_null<::Tags::HistoryEvolvedVariables<variables_tag>::type*>
           time_stepper_history,
       const TimeStepper& time_stepper,
-      const std::array<tnsr::I<double, Dim>, 2>& initial_pos_and_vel) {
+      const std::array<tnsr::I<double, Dim>, 2>& initial_pos_and_vel,
+      const double initial_time, const ExcisionSphere<Dim>& excision_sphere) {
     *current_iteration = 0;
+
+    // the functions of time should be ready during the first step but not the
+    // second. We choose the arbitrary value of 1e-10 here to ensure this.
+    *expiration_time = initial_time + 1e-10;
+    *worldtube_radius = excision_sphere.radius();
+
     const size_t starting_order =
         time_stepper.number_of_past_steps() == 0 ? time_stepper.order() : 1;
     *time_stepper_history =

src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/ReceiveElementData.hpp

@@ -102,7 +102,7 @@ struct ReceiveElementData {
     for (const auto& [_, element_ylm_coefs] : inbox.at(time_step_id)) {
       external_ylm_coefs += element_ylm_coefs;
     }
-    const double wt_radius = db::get<Tags::ExcisionSphere<Dim>>(box).radius();
+    const double wt_radius = db::get<Tags::WorldtubeRadius>(box);
     external_ylm_coefs /= wt_radius * wt_radius;
 
     DataVector& psi_ylm_coefs =

src/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/UpdateFunctionsOfTime.hpp

@@ -0,0 +1,153 @@
+// Distributed under the MIT License.
+// See LICENSE.txt for details.
+
+#pragma once
+
+#include <cstddef>
+#include <memory>
+#include <unordered_map>
+#include <utility>
+
+#include "ControlSystem/UpdateFunctionOfTime.hpp"
+#include "DataStructures/DataBox/DataBox.hpp"
+#include "DataStructures/DataBox/Prefixes.hpp"
+#include "Domain/Creators/Tags/Domain.hpp"
+#include "Evolution/Systems/CurvedScalarWave/Worldtube/Inboxes.hpp"
+#include "Evolution/Systems/CurvedScalarWave/Worldtube/RadiusFunctions.hpp"
+#include "Evolution/Systems/CurvedScalarWave/Worldtube/Tags.hpp"
+#include "Evolution/Systems/CurvedScalarWave/Worldtube/Worldtube.hpp"
+#include "Parallel/AlgorithmExecution.hpp"
+#include "Parallel/GlobalCache.hpp"
+#include "ParallelAlgorithms/EventsAndTriggers/Tags.hpp"
+#include "ParallelAlgorithms/Initialization/MutateAssign.hpp"
+#include "Time/Tags/TimeStepId.hpp"
+#include "Time/TimeStepId.hpp"
+#include "Time/TimeSteppers/TimeStepper.hpp"
+#include "Utilities/Gsl.hpp"
+#include "Utilities/TMPL.hpp"
+
+namespace control_system {
+// forward declare
+struct UpdateMultipleFunctionsOfTime;
+}  // namespace control_system
+
+namespace CurvedScalarWave::Worldtube::Actions {
+
+/*!
+ * \brief Updates the functions of time according to the motion of the
+ * worldtube.
+ *
+ * \details We demand that the scalar charge is always in the center of the
+ * worldtube and therefore deform the grid to the track the particle's motion.
+ * In addition, the worldtube and black hole excision sphere radii are adjusted
+ * according to smooth_broken_power_law.
+ */
+struct UpdateFunctionsOfTime {
+  template <typename DbTagsList, typename... InboxTags, typename Metavariables,
+            typename ArrayIndex, typename ActionList,
+            typename ParallelComponent>
+  static Parallel::iterable_action_return_t apply(
+      db::DataBox<DbTagsList>& box,
+      tuples::TaggedTuple<InboxTags...>& /*inboxes*/,
+      Parallel::GlobalCache<Metavariables>& cache,
+      const ArrayIndex& /*array_index*/, ActionList /*meta*/,
+      const ParallelComponent* const /*meta*/) {
+    const double current_expiration_time = db::get<Tags::ExpirationTime>(box);
+    const double time = db::get<::Tags::Time>(box);
+    const auto& particle_pos_vel =
+        db::get<Tags::ParticlePositionVelocity<3>>(box);
+    const double& x = get<0>(particle_pos_vel[0]);
+    const double& y = get<1>(particle_pos_vel[0]);
+    const double& xdot = get<0>(particle_pos_vel[1]);
+    const double& ydot = get<1>(particle_pos_vel[1]);
+    const double r = hypot(x, y);
+    const double radial_vel = (xdot * x + ydot * y) / r;
+    const auto& excision_sphere = db::get<Tags::ExcisionSphere<3>>(box);
+    const double grid_radius_particle =
+        get(magnitude(excision_sphere.center()));
+
+    const DataVector angular_update{atan2(y, x),
+                                    (x * ydot - y * xdot) / square(r)};
+    const DataVector expansion_update{r / grid_radius_particle,
+                                      radial_vel / grid_radius_particle};
+
+    const auto& wt_radius_params =
+        db::get<Tags::WorldtubeRadiusParameters>(box);
+    const auto& bh_radius_params =
+        db::get<Tags::BlackHoleRadiusParameters>(box);
+    const double wt_radius_grid = excision_sphere.radius();
+    const double wt_radius_inertial =
+        smooth_broken_power_law(r, wt_radius_params[0], wt_radius_params[1],
+                                wt_radius_params[2], wt_radius_params[3]);
+    const double wt_radius_derivative = smooth_broken_power_law_derivative(
+        r, wt_radius_params[0], wt_radius_params[1], wt_radius_params[2],
+        wt_radius_params[3]);
+    const double wt_radius_time_derivative = wt_radius_derivative * radial_vel;
+
+    const auto& bh_excision_sphere =
+        db::get<domain::Tags::Domain<3>>(box).excision_spheres().at(
+            "ExcisionSphereB");
+    const double bh_excision_radius_grid = bh_excision_sphere.radius();
+    const double bh_excision_radius_inertial =
+        smooth_broken_power_law(r, bh_radius_params[0], bh_radius_params[1],
+                                bh_radius_params[2], bh_radius_params[3]);
+    const double bh_excision_radius_derivative =
+        smooth_broken_power_law_derivative(
+            r, bh_radius_params[0], bh_radius_params[1], bh_radius_params[2],
+            bh_radius_params[3]);
+    const double bh_excision_radius_time_derivative =
+        bh_excision_radius_derivative * radial_vel;
+
+    const double sqrt_4_pi = sqrt(4. * M_PI);
+    // The expansion map has already stretched the excision spheres and we need
+    // to account for that.
+    const DataVector size_a_update{
+        sqrt_4_pi * (wt_radius_grid - wt_radius_inertial / expansion_update[0]),
+        sqrt_4_pi *
+            (wt_radius_inertial * expansion_update[1] -
+             wt_radius_time_derivative * expansion_update[0]) /
+            square(expansion_update[0])};
+
+    const DataVector size_b_update{
+        sqrt_4_pi * (bh_excision_radius_grid -
+                     bh_excision_radius_inertial / expansion_update[0]),
+        sqrt_4_pi *
+            (bh_excision_radius_inertial * expansion_update[1] -
+             bh_excision_radius_time_derivative * expansion_update[0]) /
+            square(expansion_update[0])};
+
+    // we set the new expiration time to 1/100th of a time step next to the
+    // current time. This is small enough that it can handle rapid time step
+    // decreases but large enough to avoid floating point precision issues.
+    const double new_expiration_time =
+        time +
+        0.01 * (db::get<::Tags::Next<::Tags::TimeStepId>>(box).substep_time() -
+                time);
+
+    db::mutate<Tags::ExpirationTime>(
+        [&new_expiration_time](const auto expiration_time) {
+          *expiration_time = new_expiration_time;
+        },
+        make_not_null(&box));
+    db::mutate<Tags::WorldtubeRadius>(
+        [&wt_radius_inertial](const auto wt_radius) {
+          *wt_radius = wt_radius_inertial;
+        },
+        make_not_null(&box));
+    std::unordered_map<std::string, std::pair<DataVector, double>>
+        all_updates{};
+    all_updates["Rotation"] =
+        std::make_pair(angular_update, new_expiration_time);
+    all_updates["Expansion"] =
+        std::make_pair(expansion_update, new_expiration_time);
+    all_updates["SizeA"] = std::make_pair(size_a_update, new_expiration_time);
+    all_updates["SizeB"] = std::make_pair(size_b_update, new_expiration_time);
+
+    Parallel::mutate<::domain::Tags::FunctionsOfTime,
+                     control_system::UpdateMultipleFunctionsOfTime>(
+        cache, current_expiration_time, all_updates);
+
+    return {Parallel::AlgorithmExecution::Continue, std::nullopt};
+  }
+};
+}  // namespace CurvedScalarWave::Worldtube::Actions

src/Evolution/Systems/CurvedScalarWave/Worldtube/Tags.hpp

@@ -430,6 +430,21 @@ struct CurrentIteration : db::SimpleTag {
   using type = size_t;
 };
 
+/*!
+ * \brief The current expiration time of the functions of time which are
+ * controlled by the worldtube singleton.
+ */
+struct ExpirationTime : db::SimpleTag {
+  using type = double;
+};
+
+/*!
+ * \brief The current worldtube radius held by the singleton.
+ */
+struct WorldtubeRadius : db::SimpleTag {
+  using type = double;
+};
+
 /*!
  * \brief The initial position and velocity of the scalar charge in inertial
  * coordinates.

tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/CMakeLists.txt

@@ -20,13 +20,15 @@ set(LIBRARY_SOURCES
   SingletonActions/Test_InitializeEvolvedVariables.cpp
   SingletonActions/Test_ObserveWorldtubeSolution.cpp
   SingletonActions/Test_UpdateAcceleration.cpp
+  SingletonActions/Test_UpdateFunctionsOfTime.cpp
   )
 
 add_test_library(${LIBRARY} "${LIBRARY_SOURCES}")
 
 target_link_libraries(
   ${LIBRARY}
   PRIVATE
+  ControlSystem
   CurvedScalarWave
   CurvedScalarWaveHelpers
   DataStructures

tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/ElementActions/Test_Iterations.cpp

@@ -120,8 +120,8 @@ struct MockMetavariables {
   using const_global_cache_tags = tmpl::list<
       domain::Tags::Domain<Dim>,
       CurvedScalarWave::Tags::BackgroundSpacetime<gr::Solutions::KerrSchild>,
-      Tags::ExcisionSphere<Dim>, Tags::ExpansionOrder, Tags::MaxIterations,
-      Tags::Charge, Tags::Mass>;
+      Tags::ExcisionSphere<Dim>, Tags::WorldtubeRadius, Tags::ExpansionOrder,
+      Tags::MaxIterations, Tags::Charge, Tags::Mass>;
 };
 
 void test_iterations(const size_t max_iterations) {
@@ -166,10 +166,15 @@ void test_iterations(const size_t max_iterations) {
     tuples::TaggedTuple<
         domain::Tags::Domain<Dim>,
         CurvedScalarWave::Tags::BackgroundSpacetime<gr::Solutions::KerrSchild>,
-        Tags::ExcisionSphere<Dim>, Tags::ExpansionOrder, Tags::MaxIterations,
-        Tags::Charge, Tags::Mass>
-        tuple_of_opts{shell.create_domain(),   kerr_schild,    excision_sphere,
-                      expansion_order,         max_iterations, charge,
+        Tags::ExcisionSphere<Dim>, Tags::WorldtubeRadius, Tags::ExpansionOrder,
+        Tags::MaxIterations, Tags::Charge, Tags::Mass>
+        tuple_of_opts{shell.create_domain(),
+                      kerr_schild,
+                      excision_sphere,
+                      excision_sphere.radius(),
+                      expansion_order,
+                      max_iterations,
+                      charge,
                       std::make_optional(mass)};
     ActionTesting::MockRuntimeSystem<metavars> runner{std::move(tuple_of_opts)};
     const auto element_ids = initial_element_ids(initial_refinements);

tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/ElementActions/Test_SendToWorldtube.cpp

@@ -122,8 +122,8 @@ struct MockMetavariables {
   using dg_element_array = MockElementArray<MockMetavariables>;
   using const_global_cache_tags =
       tmpl::list<domain::Tags::Domain<Dim>, Tags::ExcisionSphere<Dim>,
-                 Tags::ExpansionOrder, Tags::MaxIterations, Tags::Charge,
-                 Tags::Mass>;
+                 Tags::WorldtubeRadius, Tags::ExpansionOrder,
+                 Tags::MaxIterations, Tags::Charge, Tags::Mass>;
 };
 
 // This test checks that `SendToWorldtube` integrates the regular field on the
@@ -165,10 +165,11 @@ SPECTRE_TEST_CASE("Unit.CurvedScalarWave.Worldtube.SendToWorldtube", "[Unit]") {
     const auto& initial_extents = shell.initial_extents();
     // self force and therefore iterative scheme is turned off
     tuples::TaggedTuple<domain::Tags::Domain<Dim>, Tags::ExcisionSphere<Dim>,
-                        Tags::ExpansionOrder, Tags::MaxIterations, Tags::Charge,
-                        Tags::Mass>
+                        Tags::WorldtubeRadius, Tags::ExpansionOrder,
+                        Tags::MaxIterations, Tags::Charge, Tags::Mass>
         tuple_of_opts{shell.create_domain(),
                       excision_sphere,
+                      excision_sphere.radius(),
                       expansion_order,
                       static_cast<size_t>(0),
                       0.1,

tests/Unit/Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/Test_InitializeEvolvedVariables.cpp

@@ -7,6 +7,7 @@
 #include "Evolution/Systems/CurvedScalarWave/Worldtube/SingletonActions/InitializeEvolvedVariables.hpp"
 #include "Framework/TestingFramework.hpp"
 #include "Time/Tags/HistoryEvolvedVariables.hpp"
+#include "Time/Tags/Time.hpp"
 #include "Time/Tags/TimeStepper.hpp"
 #include "Time/TimeSteppers/AdamsBashforth.hpp"
 #include "Time/TimeSteppers/TimeStepper.hpp"
@@ -19,21 +20,30 @@ SPECTRE_TEST_CASE(
       tmpl::list<Tags::EvolvedPosition<3>, Tags::EvolvedVelocity<3>>>;
   using dt_variables_tag = db::add_tag_prefix<::Tags::dt, variables_tag>;
   const tnsr::I<double, 3> initial_pos{{1., 2., 3.}};
+  const tnsr::I<double, 3, Frame::Grid> initial_excision_pos{{1., 2., 3.}};
   const tnsr::I<double, 3> initial_vel{{4., 5., 6.}};
   const size_t current_iteration = 77;
+  const double expiration_time = 1234.;
+  const double initial_time = 0.;
+  const double initial_wt_radius = 12345.;
+  const double wt_radius = 2.;
+  const ExcisionSphere<3> excision_sphere(wt_radius, initial_excision_pos, {});
   auto box =
       db::create<db::AddSimpleTags<
                      variables_tag, dt_variables_tag,
                      ::Tags::HistoryEvolvedVariables<variables_tag>,
                      ::Tags::ConcreteTimeStepper<TimeStepper>,
-                     Tags::InitialPositionAndVelocity, Tags::CurrentIteration>,
+                     Tags::InitialPositionAndVelocity, Tags::CurrentIteration,
+                     Tags::ExpirationTime, Tags::WorldtubeRadius, ::Tags::Time,
+                     Tags::ExcisionSphere<3>>,
                  time_stepper_ref_tags<TimeStepper>>(
           variables_tag::type{}, dt_variables_tag::type{},
           TimeSteppers::History<variables_tag::type>{},
           static_cast<std::unique_ptr<TimeStepper>>(
               std::make_unique<TimeSteppers::AdamsBashforth>(4)),
           std::array<tnsr::I<double, 3>, 2>{{initial_pos, initial_vel}},
-          current_iteration);
+          current_iteration, expiration_time, initial_wt_radius, initial_time,
+          excision_sphere);
 
   db::mutate_apply<Initialization::InitializeEvolvedVariables>(
       make_not_null(&box));
@@ -47,6 +57,8 @@ SPECTRE_TEST_CASE(
   CHECK(db::get<::Tags::HistoryEvolvedVariables<variables_tag>>(box) ==
         TimeSteppers::History<variables_tag::type>(1));
   CHECK(get<Tags::CurrentIteration>(box) == 0);
+  CHECK(get<Tags::ExpirationTime>(box) == initial_time + 1e-10);
+  CHECK(get<Tags::WorldtubeRadius>(box) == wt_radius);
 }
 }  // namespace
 }  // namespace CurvedScalarWave::Worldtube