add Navier-Stokes Characteristic Boundary Conditions (#352)

* add updated cloud problem

* add coolinglength and mmw functions

* fix cloud problem

* update param file

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* add option to read cloudy tables even if disabled

* remove old code

* removed unnecessary params

* silence clang-tidy warnings

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* fix integratorOrder = 1

* add hydro debugging output

* update cloud settings

* revert shockcloud to development

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* revert CloudyCooling.hpp

* add NSCBC test problem

* fix ascent includes

* fix typo

* fix channel problem

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* allow build in 1d

* remove table_data

* Update src/simulation.hpp

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* move globals to namespace

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* clean-up channel problem

* add sympy notebook

* add prototype implementation

* fix unicode error

* fix cxxcode output

* re-derive eigensystem

* working prototype

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* update problem params to match paper

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* use target temperature for inflow

* add ChannelFlow to test suite

* add passive scalar

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* update error tolerance

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* remove shock-cloud param file

* refactor

* add convecting vortex test

* add transverse terms

* add all transverse terms, eliminate explicit gamma

* add permutations

* fix dependent type shadow

* add option to outflow along y-axis

* removed unused vars

* only build vortex test in 2D/3D

* fix typo

* fix loop indices

* fix const

* stricter tolerance

* fix typo

* fix CMakeLists

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src/CMakeLists.txt

@@ -153,3 +153,4 @@ add_subdirectory(ShockCloud)
 add_subdirectory(PassiveScalar)
 add_subdirectory(FCQuantities)
 add_subdirectory(SphericalCollapse)
+add_subdirectory(NSCBC)

src/NSCBC/CMakeLists.txt

@@ -0,0 +1,15 @@
+add_executable(test_channel_flow channel.cpp ${QuokkaObjSources} ../fextract.cpp)
+
+if(AMReX_GPU_BACKEND MATCHES "CUDA")
+    setup_target_for_cuda_compilation(test_channel_flow)
+endif(AMReX_GPU_BACKEND MATCHES "CUDA")
+
+add_test(NAME ChannelFlow COMMAND test_channel_flow NSCBC_Channel.in WORKING_DIRECTORY ${CMAKE_SOURCE_DIR}/tests)
+
+if (AMReX_SPACEDIM GREATER_EQUAL 2)
+    add_executable(test_vortex vortex.cpp ${QuokkaObjSources})
+
+    if(AMReX_GPU_BACKEND MATCHES "CUDA")
+        setup_target_for_cuda_compilation(test_vortex)
+    endif(AMReX_GPU_BACKEND MATCHES "CUDA")
+endif(AMReX_SPACEDIM GREATER_EQUAL 2)

src/NSCBC/channel.cpp

@@ -0,0 +1,299 @@
+//==============================================================================
+// TwoMomentRad - a radiation transport library for patch-based AMR codes
+// Copyright 2020 Benjamin Wibking.
+// Released under the MIT license. See LICENSE file included in the GitHub repo.
+//==============================================================================
+/// \file channel.cpp
+/// \brief Implements a subsonic channel flow problem with Navier-Stokes
+///        Characteristic Boundary Conditions (NSCBC).
+///
+#include <random>
+#include <tuple>
+#include <vector>
+
+#include "AMReX.H"
+#include "AMReX_Array.H"
+#include "AMReX_BC_TYPES.H"
+#include "AMReX_BLProfiler.H"
+#include "AMReX_BLassert.H"
+#include "AMReX_FabArray.H"
+#include "AMReX_Geometry.H"
+#include "AMReX_GpuDevice.H"
+#include "AMReX_IntVect.H"
+#include "AMReX_MultiFab.H"
+#include "AMReX_ParallelContext.H"
+#include "AMReX_ParallelDescriptor.H"
+#include "AMReX_ParmParse.H"
+#include "AMReX_REAL.H"
+#include "AMReX_SPACE.H"
+
+#include "ArrayUtil.hpp"
+#include "EOS.hpp"
+#include "HydroState.hpp"
+#include "NSCBC_inflow.hpp"
+#include "NSCBC_outflow.hpp"
+#include "RadhydroSimulation.hpp"
+#include "channel.hpp"
+#include "fextract.hpp"
+#include "fundamental_constants.H"
+#include "hydro_system.hpp"
+#include "radiation_system.hpp"
+#include "valarray.hpp"
+#ifdef HAVE_PYTHON
+#include "matplotlibcpp.h"
+#endif
+
+using amrex::Real;
+
+struct Channel {
+}; // dummy type to allow compile-type polymorphism via template specialization
+
+template <> struct quokka::EOS_Traits<Channel> {
+	static constexpr double gamma = 1.1;
+	static constexpr double mean_molecular_weight = 28.96 * C::m_u; // air
+	static constexpr double boltzmann_constant = C::k_B;
+};
+
+template <> struct Physics_Traits<Channel> {
+	static constexpr bool is_hydro_enabled = true;
+	static constexpr bool is_chemistry_enabled = false;
+	static constexpr bool is_mhd_enabled = false;
+	static constexpr int numMassScalars = 0;		     // number of mass scalars
+	static constexpr int numPassiveScalars = numMassScalars + 1; // number of passive scalars
+	static constexpr bool is_radiation_enabled = false;
+};
+
+// global variables needed for Dirichlet boundary condition and initial conditions
+namespace
+{
+Real rho0 = NAN;									 // NOLINT(cppcoreguidelines-avoid-non-const-global-variables)
+Real u0 = NAN;										 // NOLINT(cppcoreguidelines-avoid-non-const-global-variables)
+Real s0 = NAN;										 // NOLINT(cppcoreguidelines-avoid-non-const-global-variables)
+AMREX_GPU_MANAGED Real Tgas0 = NAN;							 // NOLINT(cppcoreguidelines-avoid-non-const-global-variables)
+AMREX_GPU_MANAGED Real P_outflow = NAN;							 // NOLINT(cppcoreguidelines-avoid-non-const-global-variables)
+AMREX_GPU_MANAGED Real u_inflow = NAN;							 // NOLINT(cppcoreguidelines-avoid-non-const-global-variables)
+AMREX_GPU_MANAGED Real v_inflow = NAN;							 // NOLINT(cppcoreguidelines-avoid-non-const-global-variables)
+AMREX_GPU_MANAGED Real w_inflow = NAN;							 // NOLINT(cppcoreguidelines-avoid-non-const-global-variables)
+AMREX_GPU_MANAGED GpuArray<Real, Physics_Traits<Channel>::numPassiveScalars> s_inflow{}; // NOLINT(cppcoreguidelines-avoid-non-const-global-variables)
+};											 // namespace
+
+template <> void RadhydroSimulation<Channel>::setInitialConditionsOnGrid(quokka::grid grid_elem)
+{
+	// set initial conditions
+	const amrex::Box &indexRange = grid_elem.indexRange_;
+	const amrex::Array4<double> &state_cc = grid_elem.array_;
+
+	Real const rho = rho0;
+	Real const xmom = rho0 * u0;
+	Real const ymom = 0;
+	Real const zmom = 0;
+	Real const Eint = quokka::EOS<Channel>::ComputeEintFromTgas(rho0, Tgas0);
+	Real const Egas = RadSystem<Channel>::ComputeEgasFromEint(rho, xmom, ymom, zmom, Eint);
+	Real const scalar = s0;
+
+	amrex::ParallelFor(indexRange, [=] AMREX_GPU_DEVICE(int i, int j, int k) {
+		state_cc(i, j, k, HydroSystem<Channel>::density_index) = rho;
+		state_cc(i, j, k, HydroSystem<Channel>::x1Momentum_index) = xmom;
+		state_cc(i, j, k, HydroSystem<Channel>::x2Momentum_index) = ymom;
+		state_cc(i, j, k, HydroSystem<Channel>::x3Momentum_index) = zmom;
+		state_cc(i, j, k, HydroSystem<Channel>::energy_index) = Egas;
+		state_cc(i, j, k, HydroSystem<Channel>::internalEnergy_index) = Eint;
+		state_cc(i, j, k, HydroSystem<Channel>::scalar0_index) = scalar;
+	});
+}
+
+template <>
+AMREX_GPU_DEVICE AMREX_FORCE_INLINE void AMRSimulation<Channel>::setCustomBoundaryConditions(const amrex::IntVect &iv, amrex::Array4<Real> const &consVar,
+											     int /*dcomp*/, int /*numcomp*/, amrex::GeometryData const &geom,
+											     const Real /*time*/, const amrex::BCRec * /*bcr*/, int /*bcomp*/,
+											     int /*orig_comp*/)
+{
+	auto [i, j, k] = iv.dim3();
+	amrex::Box const &box = geom.Domain();
+	const auto &domain_lo = box.loVect3d();
+	const auto &domain_hi = box.hiVect3d();
+	const int ilo = domain_lo[0];
+	const int ihi = domain_hi[0];
+
+	if (i < ilo) {
+		NSCBC::setInflowX1Lower<Channel>(iv, consVar, geom, ::Tgas0, ::u_inflow, ::v_inflow, ::w_inflow, ::s_inflow);
+	} else if (i > ihi) {
+		NSCBC::setOutflowBoundary<Channel, FluxDir::X1, NSCBC::BoundarySide::Upper>(iv, consVar, geom, P_outflow);
+	}
+}
+
+auto problem_main() -> int
+{
+	// Problem initialization
+	constexpr int ncomp_cc = Physics_Indices<Channel>::nvarTotal_cc;
+	amrex::Vector<amrex::BCRec> BCs_cc(ncomp_cc);
+	for (int n = 0; n < ncomp_cc; ++n) {
+		BCs_cc[n].setLo(0, amrex::BCType::ext_dir); // NSCBC inflow
+		BCs_cc[n].setHi(0, amrex::BCType::ext_dir); // NSCBC outflow
+
+		if constexpr (AMREX_SPACEDIM >= 2) {
+			BCs_cc[n].setLo(1, amrex::BCType::int_dir); // periodic
+			BCs_cc[n].setHi(1, amrex::BCType::int_dir);
+		} else if (AMREX_SPACEDIM == 3) {
+			BCs_cc[n].setLo(2, amrex::BCType::int_dir);
+			BCs_cc[n].setHi(2, amrex::BCType::int_dir);
+		}
+	}
+
+	RadhydroSimulation<Channel> sim(BCs_cc);
+
+	amrex::ParmParse const pp("channel");
+	// initial condition parameters
+	pp.query("rho0", ::rho0);   // initial density [g/cc]
+	pp.query("Tgas0", ::Tgas0); // initial temperature [K]
+	pp.query("u0", ::u0);	    // initial velocity [cm/s]
+	pp.query("s0", ::s0);	    // initial passive scalar [dimensionless]
+	// boundary condition parameters
+	pp.query("u_inflow", ::u_inflow);    // inflow velocity along x-axis [cm/s]
+	pp.query("v_inflow", ::v_inflow);    // transverse inflow velocity (v_y) [cm/s]
+	pp.query("w_inflow", ::w_inflow);    // transverse inflow velocity (v_z) [cm/s]
+	pp.query("s_inflow", ::s_inflow[0]); // inflow passive scalar [dimensionless]
+
+	// compute derived parameters
+	const Real Eint0 = quokka::EOS<Channel>::ComputeEintFromTgas(rho0, Tgas0);
+	::P_outflow = quokka::EOS<Channel>::ComputePressure(rho0, Eint0);
+	amrex::Print() << "Derived outflow pressure is " << ::P_outflow << " erg/cc.\n";
+
+	// Set initial conditions
+	sim.setInitialConditions();
+
+	// run simulation
+	sim.evolve();
+
+	// extract slice
+	auto [position, values] = fextract(sim.state_new_cc_[0], sim.geom[0], 0, 0., true);
+	int const nx = static_cast<int>(position.size());
+	std::vector<double> const xs = position;
+	std::vector<double> xs_exact = position;
+
+	// extract solution
+	std::vector<double> d(nx);
+	std::vector<double> vx(nx);
+	std::vector<double> P(nx);
+	std::vector<double> s(nx);
+	std::vector<double> density_exact(nx);
+	std::vector<double> velocity_exact(nx);
+	std::vector<double> Pexact(nx);
+	std::vector<double> sexact(nx);
+
+	for (int i = 0; i < nx; ++i) {
+		{
+			amrex::Real const rho = values.at(HydroSystem<Channel>::density_index)[i];
+			amrex::Real const xmom = values.at(HydroSystem<Channel>::x1Momentum_index)[i];
+			amrex::Real const Egas = values.at(HydroSystem<Channel>::energy_index)[i];
+			amrex::Real const scalar = values.at(HydroSystem<Channel>::scalar0_index)[i];
+			amrex::Real const Eint = Egas - (xmom * xmom) / (2.0 * rho);
+			amrex::Real const gamma = quokka::EOS_Traits<Channel>::gamma;
+			d.at(i) = rho;
+			vx.at(i) = xmom / rho;
+			P.at(i) = ((gamma - 1.0) * Eint);
+			s.at(i) = scalar;
+		}
+		{
+			density_exact.at(i) = rho0;
+			velocity_exact.at(i) = u_inflow;
+			Pexact.at(i) = P_outflow;
+			sexact.at(i) = s_inflow[0];
+		}
+	}
+	std::vector<std::vector<double>> const sol{d, vx, P, s};
+	std::vector<std::vector<double>> const sol_exact{density_exact, velocity_exact, Pexact, sexact};
+
+	// compute error norm
+	amrex::Real err_sq = 0.;
+	for (size_t n = 0; n < sol.size(); ++n) {
+		amrex::Real dU_k = 0.;
+		amrex::Real U_k = 0;
+		for (int i = 0; i < nx; ++i) {
+			// Δ Uk = ∑i |Uk,in - Uk,i0| / Nx
+			const amrex::Real U_k0 = sol_exact.at(n)[i];
+			const amrex::Real U_k1 = sol.at(n)[i];
+			dU_k += std::abs(U_k1 - U_k0) / static_cast<double>(nx);
+			U_k += std::abs(U_k0) / static_cast<double>(nx);
+		}
+		amrex::Print() << "dU_" << n << " = " << dU_k << " U_k = " << U_k << "\n";
+		// ε = || Δ U / U || = [&sum_k (ΔU_k/U_k)^2]^{1/2}
+		err_sq += std::pow(dU_k / U_k, 2);
+	}
+	const amrex::Real epsilon = std::sqrt(err_sq);
+	amrex::Print() << "rms of component-wise relative L1 error norms = " << epsilon << "\n\n";
+
+#ifdef HAVE_PYTHON
+	if (amrex::ParallelDescriptor::IOProcessor()) {
+		// Plot results
+		const int skip = 4;	  // only plot every 8 elements of exact solution
+		const double msize = 5.0; // marker size
+		using mpl_arg = std::map<std::string, std::string>;
+		using mpl_sarg = std::unordered_map<std::string, std::string>;
+
+		matplotlibcpp::clf();
+		mpl_arg d_args;
+		mpl_sarg dexact_args;
+		d_args["label"] = "density";
+		d_args["color"] = "C0";
+		dexact_args["marker"] = "o";
+		dexact_args["color"] = "C0";
+		matplotlibcpp::plot(xs, d, d_args);
+		matplotlibcpp::scatter(strided_vector_from(xs_exact, skip), strided_vector_from(density_exact, skip), msize, dexact_args);
+		matplotlibcpp::legend();
+		matplotlibcpp::xlabel("length x");
+		matplotlibcpp::tight_layout();
+		matplotlibcpp::save("./channel_flow_density.pdf");
+
+		matplotlibcpp::clf();
+		std::map<std::string, std::string> vx_args;
+		vx_args["label"] = "velocity";
+		vx_args["color"] = "C3";
+		matplotlibcpp::plot(xs, vx, vx_args);
+		mpl_sarg vexact_args;
+		vexact_args["marker"] = "o";
+		vexact_args["color"] = "C3";
+		matplotlibcpp::scatter(strided_vector_from(xs_exact, skip), strided_vector_from(velocity_exact, skip), msize, vexact_args);
+		matplotlibcpp::legend();
+		matplotlibcpp::xlabel("length x");
+		matplotlibcpp::tight_layout();
+		matplotlibcpp::save("./channel_flow_velocity.pdf");
+
+		matplotlibcpp::clf();
+		std::map<std::string, std::string> P_args;
+		P_args["label"] = "pressure";
+		P_args["color"] = "C4";
+		matplotlibcpp::plot(xs, P, P_args);
+		mpl_sarg Pexact_args;
+		Pexact_args["marker"] = "o";
+		Pexact_args["color"] = "C4";
+		matplotlibcpp::scatter(strided_vector_from(xs_exact, skip), strided_vector_from(Pexact, skip), msize, Pexact_args);
+		matplotlibcpp::legend();
+		matplotlibcpp::xlabel("length x");
+		matplotlibcpp::tight_layout();
+		matplotlibcpp::save("./channel_flow_pressure.pdf");
+
+		matplotlibcpp::clf();
+		std::map<std::string, std::string> s_args;
+		s_args["label"] = "passive scalar";
+		s_args["color"] = "C4";
+		matplotlibcpp::plot(xs, s, s_args);
+		mpl_sarg sexact_args;
+		sexact_args["marker"] = "o";
+		sexact_args["color"] = "C4";
+		matplotlibcpp::scatter(strided_vector_from(xs_exact, skip), strided_vector_from(sexact, skip), msize, sexact_args);
+		matplotlibcpp::legend();
+		matplotlibcpp::xlabel("length x");
+		matplotlibcpp::tight_layout();
+		matplotlibcpp::save("./channel_flow_scalar.pdf");
+	}
+#endif
+
+	// Compute test success condition
+	int status = 0;
+	const double error_tol = 3.0e-5;
+	if (epsilon > error_tol) {
+		status = 1;
+	}
+	return status;
+}

src/NSCBC/channel.hpp

@@ -0,0 +1,19 @@
+#ifndef CLOUD_HPP_ // NOLINT
+#define CLOUD_HPP_
+//==============================================================================
+// TwoMomentRad - a radiation transport library for patch-based AMR codes
+// Copyright 2020 Benjamin Wibking.
+// Released under the MIT license. See LICENSE file included in the GitHub repo.
+//==============================================================================
+/// \file cloud.hpp
+/// \brief Implements a shock-cloud problem with radiative cooling.
+///
+
+// external headers
+#include <fmt/format.h>
+
+// internal headers
+
+// function definitions
+
+#endif // CLOUD_HPP_