From db8e02b0cd991023d611209eeea72c45c3710d79 Mon Sep 17 00:00:00 2001 From: Emily Boudreaux Date: Thu, 12 Feb 2026 07:53:26 -0500 Subject: [PATCH] feat(rotating-polytrope): initial commit --- .gitignore | 552 +++ default.toml | 10 + main.cpp | 782 ++++ makefile | 20 + readme.md | 27 + stroid.mesh | 12028 +++++++++++++++++++++++++++++++++++++++++++++++++ 6 files changed, 13419 insertions(+) create mode 100644 .gitignore create mode 100644 default.toml create mode 100644 main.cpp create mode 100644 makefile create mode 100644 readme.md create mode 100644 stroid.mesh diff --git a/.gitignore b/.gitignore new file mode 100644 index 0000000..e3f5a51 --- /dev/null +++ b/.gitignore @@ -0,0 +1,552 @@ +### C++ template +# Prerequisites +*.d + +# Compiled Object files +*.slo +*.lo +*.o +*.obj + +# Precompiled Headers +*.gch +*.pch + +# Compiled Dynamic libraries +*.so +*.dylib +*.dll + +# Fortran module files +*.mod +*.smod + +# Compiled Static libraries +*.lai +*.la +*.a +*.lib + +# Executables +*.exe +*.out +*.app + +### TeX template +## Core latex/pdflatex auxiliary files: +*.aux +*.lof +*.log +*.lot +*.fls +*.out +*.toc +*.fmt +*.fot +*.cb +*.cb2 +.*.lb + +## Intermediate documents: +*.dvi +*.xdv +*-converted-to.* +# these rules might exclude image files for figures etc. +# *.ps +# *.eps +# *.pdf + +## Generated if empty string is given at "Please type another file name for output:" +.pdf + +## Bibliography auxiliary files (bibtex/biblatex/biber): +*.bbl +*.bcf +*.blg +*-blx.aux +*-blx.bib +*.run.xml + +## Build tool auxiliary files: +*.fdb_latexmk +*.synctex +*.synctex(busy) +*.synctex.gz +*.synctex.gz(busy) +*.pdfsync +*.rubbercache +rubber.cache + +## Build tool directories for auxiliary files +# latexrun +latex.out/ + +## Auxiliary and intermediate files from other packages: +# algorithms +*.alg +*.loa + +# achemso +acs-*.bib + +# amsthm +*.thm + +# beamer +*.nav +*.pre +*.snm +*.vrb + +# changes +*.soc + +# comment +*.cut + +# cprotect +*.cpt + +# elsarticle (documentclass of Elsevier journals) +*.spl + +# endnotes +*.ent + +# fixme +*.lox + +# feynmf/feynmp +*.mf +*.mp +*.t[1-9] +*.t[1-9][0-9] +*.tfm + +#(r)(e)ledmac/(r)(e)ledpar +*.end +*.?end +*.[1-9] +*.[1-9][0-9] +*.[1-9][0-9][0-9] +*.[1-9]R +*.[1-9][0-9]R +*.[1-9][0-9][0-9]R +*.eledsec[1-9] +*.eledsec[1-9]R +*.eledsec[1-9][0-9] +*.eledsec[1-9][0-9]R +*.eledsec[1-9][0-9][0-9] +*.eledsec[1-9][0-9][0-9]R + +# glossaries +*.acn +*.acr +*.glg +*.glo +*.gls +*.glsdefs +*.lzo +*.lzs +*.slg +*.slo +*.sls + +# uncomment this for glossaries-extra (will ignore makeindex's style files!) +# *.ist + +# gnuplot +*.gnuplot +*.table + +# gnuplottex +*-gnuplottex-* + +# gregoriotex +*.gaux +*.glog +*.gtex + +# htlatex +*.4ct +*.4tc +*.idv +*.lg +*.trc +*.xref + +# hypdoc +*.hd + +# hyperref +*.brf + +# knitr +*-concordance.tex +# TODO Uncomment the next line if you use knitr and want to ignore its generated tikz files +# *.tikz +*-tikzDictionary + +# listings +*.lol + +# luatexja-ruby +*.ltjruby + +# makeidx +*.idx +*.ilg +*.ind + +# minitoc +*.maf +*.mlf +*.mlt +*.mtc[0-9]* +*.slf[0-9]* +*.slt[0-9]* +*.stc[0-9]* + +# minted +_minted* +*.pyg + +# morewrites +*.mw + +# newpax +*.newpax + +# nomencl +*.nlg +*.nlo +*.nls + +# pax +*.pax + +# pdfpcnotes +*.pdfpc + +# sagetex +*.sagetex.sage +*.sagetex.py +*.sagetex.scmd + +# scrwfile +*.wrt + +# svg +svg-inkscape/ + +# sympy +*.sout +*.sympy +sympy-plots-for-*.tex/ + +# pdfcomment +*.upa +*.upb + +# pythontex +*.pytxcode +pythontex-files-*/ + +# tcolorbox +*.listing + +# thmtools +*.loe + +# TikZ & PGF +*.dpth +*.md5 +*.auxlock + +# titletoc +*.ptc + +# todonotes +*.tdo + +# vhistory +*.hst +*.ver + +# easy-todo +*.lod + +# xcolor +*.xcp + +# xmpincl +*.xmpi + +# xindy +*.xdy + +# xypic precompiled matrices and outlines +*.xyc +*.xyd + +# endfloat +*.ttt +*.fff + +# Latexian +TSWLatexianTemp* + +## Editors: +# WinEdt +*.bak +*.sav + +# Texpad +.texpadtmp + +# LyX +*.lyx~ + +# Kile +*.backup + +# gummi +.*.swp + +# KBibTeX +*~[0-9]* + +# TeXnicCenter +*.tps + +# auto folder when using emacs and auctex +./auto/* +*.el + +# expex forward references with \gathertags +*-tags.tex + +# standalone packages +*.sta + +# Makeindex log files +*.lpz + +# xwatermark package +*.xwm + +# REVTeX puts footnotes in the bibliography by default, unless the nofootinbib +# option is specified. 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For a more nuclear +# option (not recommended) you can uncomment the following to ignore the entire idea folder. +#.idea/ + + +run +run_debug +.idea/ \ No newline at end of file diff --git a/default.toml b/default.toml new file mode 100644 index 0000000..467b617 --- /dev/null +++ b/default.toml @@ -0,0 +1,10 @@ +[main] +core_steepness = 1.0 +flattening = 0.0 +include_external_domain = false +order = 2 +r_core = 0.1 +r_infinity = 6.0 +r_instability = 1e-14 +r_star = 1.0 +refinement_levels = 2 diff --git a/main.cpp b/main.cpp new file mode 100644 index 0000000..6b46a0e --- /dev/null +++ b/main.cpp @@ -0,0 +1,782 @@ +#include +#include +#include +#include +#include +#include +#include +#include + +#include + +constexpr double G = 1.0; +constexpr double MASS = 1.0; +constexpr double RADIUS = 1.0; +constexpr double CENTRAL_DENSITY = 0.9550104783; +constexpr double mP = 1.0; +constexpr double kB = 0.28; + +constexpr char HOST[10] = "localhost"; +constexpr int PORT = 19916; + + +/***************************** +* +* Types +* +* ***************************/ + +class MassContinuitySolver { + private: + mfem::FiniteElementSpace &m_fes; + std::unique_ptr m_laplacian; + public: + explicit MassContinuitySolver(mfem::FiniteElementSpace& fes); + void Solve(mfem::Coefficient& rho, mfem::GridFunction& phi_gf, const mfem::Array& ess_tdof_list) const; +}; + +struct FEM { + std::unique_ptr mesh_ptr; + + std::unique_ptr H1_fec; + std::unique_ptr L2_fec; + + std::unique_ptr H1_fes; + std::unique_ptr L2_fes; + + std::unique_ptr Vec_H1_fes; + + std::unique_ptr rho_gf; + std::unique_ptr phi_gf; + std::unique_ptr H_gf; + std::unique_ptr P_gf; + + [[nodiscard]] bool okay() const; +}; + +struct FixedPoint { + std::unique_ptr rho; + std::unique_ptr h; + std::unique_ptr phi; + + [[nodiscard]] FixedPoint clone() const; +}; + +enum class FixedPointErrors : uint8_t { + UNBOUNDED, + MAX_ITERS +}; + +static const std::map FixedPointErrorMessages = { + {FixedPointErrors::UNBOUNDED, "The system appears to be unbounded. Try reducing the rotation rate or increasing the polytropic index."}, + {FixedPointErrors::MAX_ITERS, "Maximum number of iterations reached without convergence. Try increasing max iterations or relaxing the convergence criteria."} +}; + +enum class Verbosity : uint8_t { + SILENT, + PER_DEFORMATION, + PER_ITERATION, + FULL, + VERBOSE +}; + +static const std::map> VerbosityNames = { + {Verbosity::SILENT, {"S", "SILENT"}}, + {Verbosity::PER_DEFORMATION, {"D", "PER_DEFORMATION"}}, + {Verbosity::PER_ITERATION, {"I", "PER_ITERATION"}}, + {Verbosity::FULL, {"F", "FULL"}}, + {Verbosity::VERBOSE, {"V", "VERBOSE"}} +}; + +struct Point { + double x; + double y; + double z; + double r; + size_t IR_ID; + size_t BE_ID; +}; + +struct Envelope { + std::vector points; +}; + + +struct Args { + bool visualize = false; + bool rotation = true; + Verbosity verbosity = Verbosity::PER_DEFORMATION; + double index = 1; + double alpha = 0.1; + std::string mesh = "stroid.mesh"; + size_t max_iters = 500; + double tol = 1e-8; + double omega = 1.0; + double relax_rate = 0.1; + bool allow_deformation = true; + size_t max_deformation_iters = 50; + double deformation_rtol = 1e-4; + double deformation_atol = 1e-6; + int env_ref_levels = 2; +}; + + +/***************************** +* +* Functions +* +* ***************************/ +FEM setup_fem(const std::string& filename, bool verbose=true); + +void ViewMesh(const std::string& host, int port, const mfem::Mesh& mesh, const mfem::GridFunction& gf, const std::string& title); + +double initial_density(const mfem::Vector& x); + +double get_current_mass(const FEM& fem, const mfem::GridFunction& gf); + +double centrifugal_potential(const mfem::Vector& x, double omega); + +void project_scalar_function(mfem::GridFunction& gf, const std::function &g); + +std::unique_ptr get_potential(const FEM& fem, const mfem::GridFunction& rho, const Args& args); + +std::unique_ptr get_enthalpy(const FEM& fem, const mfem::GridFunction& phi); + +double get_polar_value(const mfem::GridFunction& gf, mfem::Mesh& mesh, double radius); + +double gamma(double n); + +double rho_from_enthalpy_barotropic(double h, double n); + +double mix_density(double rho_0, double rho_1, double alpha); + +std::unique_ptr update_density(const FEM& fem, const FixedPoint& fp_old, const FixedPoint& fp_new, double n, double alpha); + +std::unique_ptr conserve_mass(const FEM& fem, const mfem::GridFunction& gf, double target_mass); + +FixedPoint init_fp(const FEM& fem, const Args& args); + +FixedPoint step(const FEM& fem, const FixedPoint& fp, const Args& args); + +void VisualizeFP(const FEM& fem, const FixedPoint& fp, const std::string& prefix); + +double L2RelativeResidual(const FixedPoint& fp_old, const FixedPoint& fp_new); + +std::expected iterate_for_constant_shape(const FEM &fem, const Args &args); + +double clip(double h, double relax); + +void radial(const mfem::Vector& x, mfem::Vector &r_hat); + +bool is_system_bound(const FEM& fem, const FixedPoint& fp, const Args& args); + +std::unique_ptr get_nodal_displacement(const FEM& fem, const FixedPoint &fp, const Args& args); + +void deform_mesh(const FEM& fem, const mfem::GridFunction& displacement, const Args& args); + +Args setup_cli(int argc, char** argv); + +void print_options(const Args& args); + +Envelope extract_envelope(const FEM& fem, const Args& args); + +std::map make_verbosity_map(); + + +/***************************** +* +* Entry Point +* +* ***************************/ + +int main(const int argc, char** argv) { + const Args args = setup_cli(argc, argv); + print_options(args); + + FEM fem = setup_fem(args.mesh, args.verbosity == Verbosity::VERBOSE); + + double last_displacement_norm = std::numeric_limits::infinity(); + for (int i = 0; i < args.max_deformation_iters; ++i) { + std::print("Deformation Step {:3}{}", i, args.verbosity > Verbosity::PER_DEFORMATION ? "\n" : " -- "); + std::cout << std::flush; + const auto solution = iterate_for_constant_shape(fem, args); + if (!solution) { + std::cerr << "Error: " << FixedPointErrorMessages.at(solution.error()) << std::endl; + exit(1); + } + const auto boundary_displacement = get_nodal_displacement(fem, solution.value(), args); + + double displacement_norm = std::numeric_limits::infinity(); + if (i > 0) { + displacement_norm = boundary_displacement->Norml2(); + } + + double rel_displacement = std::numeric_limits::infinity(); + if (i > 3) { + rel_displacement = (last_displacement_norm > 1e-18) ? (displacement_norm / last_displacement_norm) : displacement_norm; + } + + if (args.verbosity >= Verbosity::PER_DEFORMATION) { + std::println("||Da|| = {:5.3E}, ||Dr|| = {:5.3E}", (i > 0) ? displacement_norm : 0.0, (i > 3) ? rel_displacement : 0.0); + } + + if (displacement_norm <= args.deformation_atol || rel_displacement <= args.deformation_rtol) { + if (args.verbosity >= Verbosity::PER_DEFORMATION) { + std::println("Deformation convergence reached in {} steps!", i); + } + break; + } + + last_displacement_norm = displacement_norm; + + deform_mesh(fem, *boundary_displacement, args); + fem.rho_gf = std::make_unique(*solution.value().rho); + + + } + auto solution = iterate_for_constant_shape(fem, args); + if (!solution) { + std::cerr << "Error: " << FixedPointErrorMessages.at(solution.error()) << std::endl; + exit(1); + } + + ViewMesh(HOST, PORT, *fem.mesh_ptr, *solution.value().phi, "Final Potential"); + ViewMesh(HOST, PORT, *fem.mesh_ptr, *solution.value().h, "Final Enthalpy"); + ViewMesh(HOST, PORT, *fem.mesh_ptr, *solution.value().rho, "Final Density"); +} + + +/***************************** +* +* Implementations +* +* ***************************/ + +FEM setup_fem(const std::string& filename, bool verbose) { + FEM fem_setup; + fem_setup.mesh_ptr = std::make_unique(filename, 0, 0); + fem_setup.mesh_ptr->EnsureNodes(); + + int dim = fem_setup.mesh_ptr->Dimension(); + + fem_setup.H1_fec = std::make_unique(2, dim); + fem_setup.L2_fec = std::make_unique(2, dim); + + fem_setup.H1_fes = std::make_unique(fem_setup.mesh_ptr.get(), fem_setup.H1_fec.get()); + fem_setup.L2_fes = std::make_unique(fem_setup.mesh_ptr.get(), fem_setup.L2_fec.get()); + + fem_setup.Vec_H1_fes = std::make_unique(fem_setup.mesh_ptr.get(), fem_setup.H1_fec.get(), dim, mfem::Ordering::byNODES); + + fem_setup.rho_gf = std::make_unique(fem_setup.H1_fes.get()); + fem_setup.phi_gf = std::make_unique(fem_setup.H1_fes.get()); + fem_setup.H_gf = std::make_unique(fem_setup.H1_fes.get()); + fem_setup.P_gf = std::make_unique(fem_setup.H1_fes.get()); + + project_scalar_function(*fem_setup.rho_gf, initial_density); + fem_setup.rho_gf = conserve_mass(fem_setup, *fem_setup.rho_gf, MASS); + + if (verbose) { + std::println("Setup {}", fem_setup.okay() ? "OK" : "FAIL"); + } + if (!fem_setup.okay()) { + exit(1); + } + + return fem_setup; +} + +bool FEM::okay() const { + const bool has_mesh = mesh_ptr != nullptr; + + const bool has_fec = (H1_fec != nullptr) && (L2_fec != nullptr); + const bool has_fes = (H1_fes != nullptr) && (L2_fes != nullptr); + + const bool has_vec_fes = Vec_H1_fes != nullptr; + + const bool has_gf = (rho_gf != nullptr) && (phi_gf != nullptr) && (H_gf != nullptr) && (P_gf != nullptr); + + return has_mesh && has_fec && has_fes && has_gf && has_vec_fes; + +} + +FixedPoint FixedPoint::clone() const { + FixedPoint fp; + if (rho) fp.rho = std::make_unique(*rho); + if (h) fp.h = std::make_unique(*h); + if (phi) fp.phi = std::make_unique(*phi); + + return fp; +} + +double initial_density(const mfem::Vector& x) { + const double r = x.Norml2(); + const double rho = MASS * CENTRAL_DENSITY * (1.0 - r / RADIUS); + return rho; +} + +double get_current_mass(const FEM& fem, const mfem::GridFunction& gf) { + mfem::ConstantCoefficient one(1.0); + mfem::LinearForm mass_lf(fem.H1_fes.get()); + mfem::GridFunctionCoefficient rho_coeff(&gf); + + mass_lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(rho_coeff)); + mass_lf.Assemble(); + + const double current_mass = mass_lf.Sum(); + + return current_mass; +} + +double centrifugal_potential(const mfem::Vector& x, double omega) { + const double s2 = std::pow(x(0), 2) + std::pow(x(1), 2); + return -0.5 * s2 * std::pow(omega, 2); +} + + +MassContinuitySolver::MassContinuitySolver(mfem::FiniteElementSpace& fes): m_fes(fes) { + m_laplacian = std::make_unique(&m_fes); + m_laplacian->AddDomainIntegrator(new mfem::DiffusionIntegrator()); + m_laplacian->Assemble(); + m_laplacian->Finalize(); +} + +void MassContinuitySolver::Solve(mfem::Coefficient& rho, mfem::GridFunction& phi_gf, const mfem::Array& ess_tdof_list) const { + mfem::ConstantCoefficient fourPiG (-4.0 * M_PI * G); + mfem::ProductCoefficient rhsCoeff(fourPiG, rho); + mfem::LinearForm b(&m_fes); + + b.AddDomainIntegrator(new mfem::DomainLFIntegrator(rhsCoeff)); + b.Assemble(); + + mfem::OperatorPtr A; + mfem::Vector B, X; + + m_laplacian -> FormLinearSystem(ess_tdof_list, phi_gf, b, A, X, B); + + mfem::GSSmoother prec; + mfem::CGSolver cg; + cg.SetRelTol(1e-12); + cg.SetMaxIter(2000); + cg.SetPrintLevel(0); + cg.SetPreconditioner(prec); + cg.SetOperator(*A); + + cg.Mult(B, X); + m_laplacian->RecoverFEMSolution(X, b, phi_gf); +} + +void ViewMesh(const std::string& host, int port, const mfem::Mesh& mesh, const mfem::GridFunction& gf, const std::string& title) { + mfem::socketstream sol_sock(host.c_str(), port); + if (!sol_sock.is_open()) { + std::cerr << "Unable to connect to GLVis Server running at " << host << ":" << port << std::endl; + return; + } + + sol_sock.precision(8); + sol_sock << "solution\n" << mesh << gf; + sol_sock << "window_title '" << title << "'\n"; + sol_sock << "keys 'iIzzMaagpmtppcizzz'"; + sol_sock << std::flush; +} + +std::unique_ptr get_potential(const FEM& fem, const mfem::GridFunction& rho, const Args& args) { + auto phi = std::make_unique(fem.H1_fes.get()); + + mfem::Array ess_bdr(fem.mesh_ptr->bdr_attributes.Max()); + ess_bdr = 1; + + mfem::LinearForm mass_lf(fem.H1_fes.get()); + mfem::GridFunctionCoefficient rho_coeff(&rho); + mass_lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(rho_coeff)); + mass_lf.Assemble(); + + const double target_mass = mass_lf.Sum(); + // const double polar_potential = -G * target_mass / RADIUS; + + auto grav_potential = [&target_mass](const mfem::Vector& x) { + const double r = x.Norml2(); + return (r > 1e-12) ? (-G * target_mass / r) : 0.0; + }; + + // mfem::ConstantCoefficient phi_bdr_coeff(polar_potential); + mfem::FunctionCoefficient phi_bdr_coeff(grav_potential); + mfem::Array ess_tdof_list; + fem.H1_fes->GetEssentialTrueDofs(ess_bdr, ess_tdof_list); + + MassContinuitySolver gravPotentialSolver(*fem.H1_fes); + phi->ProjectBdrCoefficient(phi_bdr_coeff, ess_tdof_list); + gravPotentialSolver.Solve(rho_coeff, *phi, ess_tdof_list); + + if (args.rotation) { + auto rot = [&args](const mfem::Vector& x) { + return centrifugal_potential(x, args.omega); + }; + + mfem::FunctionCoefficient centrifugal_coeff(rot); + mfem::GridFunction centrifugal_gf(fem.H1_fes.get()); + centrifugal_gf.ProjectCoefficient(centrifugal_coeff); + (*phi) += centrifugal_gf; + } + return phi; +} + +void project_scalar_function(mfem::GridFunction& gf, const std::function &g) { + mfem::FunctionCoefficient coeff(g); + gf.ProjectCoefficient(coeff); +} + +std::unique_ptr get_enthalpy(const FEM& fem, const mfem::GridFunction& phi) { + const double polar_potential = get_polar_value(phi, *fem.mesh_ptr, RADIUS); + + auto H = std::make_unique(fem.H1_fes.get()); + mfem::ConstantCoefficient bernoulli(polar_potential); + + mfem::GridFunctionCoefficient potentialCoeff(&phi); + mfem::SumCoefficient enthalpyCoeff(bernoulli, potentialCoeff, 1.0, -1.0); + + H->ProjectCoefficient(enthalpyCoeff); + + return H; +} + +double get_polar_value(const mfem::GridFunction& gf, mfem::Mesh& mesh, const double radius) { + mfem::DenseMatrix pole(3, 1); + pole(0, 0) = 0; + pole(1, 0) = 0; + pole(2, 0) = radius; + + mfem::Array elementIds(1); + mfem::Array ips(1); + mesh.FindPoints(pole, elementIds, ips); + + if (elementIds[0] > 0) { + const double value = gf.GetValue(elementIds[0], ips[0]); + return value; + } else { + std::cerr << "Unable to locate pole..." << std::endl; + exit(1); + } +} + +double gamma(double n) { + if (n <= 0.0) { + const std::string errMsg = std::format("polytropic index but be finite, non-zero, and positive. Got {}", n); + std::cerr << errMsg << std::endl; + exit(1); + } + + return 1.0 + (1.0/n); + +} + +double rho_from_enthalpy_barotropic(double h, double n) { + if (h <= 0.0) return 0.0; + + const double g = gamma(n); + constexpr double K = 1.0; + const double K_prime = (g * K) / (g - 1.0); + + return std::pow(h / K_prime, 1.0 / (g - 1.0)); +} + +double mix_density(const double rho_0, const double rho_1, const double alpha) { + return alpha * rho_1 + (1-alpha) * rho_0; +} + +std::unique_ptr update_density(const FEM& fem, const FixedPoint& fp_old, const FixedPoint& fp_new, double n, double alpha) { + mfem::GridFunctionCoefficient h_coeff(fp_new.h.get()); + + auto trans = [&n](double h) { + return rho_from_enthalpy_barotropic(h, n); + }; + + mfem::TransformedCoefficient rho_map_coeff(&h_coeff, trans); + mfem::GridFunctionCoefficient rho_0_coeff(fp_old.rho.get()); + + auto mixer = [&alpha](const double rho_0, const double rho_1) { + return mix_density(rho_0, rho_1, alpha); + }; + + mfem::TransformedCoefficient rho_mixed(&rho_0_coeff, &rho_map_coeff, mixer); + + auto rho_new = std::make_unique(fem.H1_fes.get()); + rho_new->ProjectCoefficient(rho_mixed); + return rho_new; +} + +std::unique_ptr conserve_mass(const FEM& fem, const mfem::GridFunction& gf, double target_mass) { + const double current_mass = get_current_mass(fem, gf); + const double global_scaling_factor = target_mass / current_mass; + + auto new_rho = std::make_unique(fem.H1_fes.get()); + mfem::GridFunctionCoefficient orig_rho_coeff(&gf); + mfem::ConstantCoefficient scale_coeff(global_scaling_factor); + + mfem::ProductCoefficient scaled_rho(orig_rho_coeff, scale_coeff); + + + new_rho->ProjectCoefficient(scaled_rho); + + return new_rho; +} + +FixedPoint init_fp(const FEM& fem, const Args& args) { + FixedPoint fp; + fp.phi = get_potential(fem, *fem.rho_gf, args); + fp.h = get_enthalpy(fem, *fp.phi); + fp.rho = std::make_unique(*fem.rho_gf); + return fp; + +} + +FixedPoint step(const FEM& fem, const FixedPoint& fp, const Args& args) { + FixedPoint nfp; + nfp.phi = get_potential(fem, *fp.rho, args); + nfp.h = get_enthalpy(fem, *nfp.phi); + + const auto new_density = update_density(fem, fp, nfp, args.index, args.alpha); + nfp.rho = conserve_mass(fem, *new_density, MASS); + + return nfp; +} + +void VisualizeFP(const FEM& fem, const FixedPoint& fp, const std::string& prefix) { + auto titler = [&prefix](const std::string& name) -> std::string { + return std::format("{}: {}", prefix, name); + }; + ViewMesh(HOST, PORT, *fem.mesh_ptr, *fp.rho, titler("Density")); + ViewMesh(HOST, PORT, *fem.mesh_ptr, *fp.phi, titler("Potential")); + ViewMesh(HOST, PORT, *fem.mesh_ptr, *fp.h, titler("Enthalpy")); +} + +double L2RelativeResidual(const FixedPoint& fp_old, const FixedPoint& fp_new) { + mfem::GridFunctionCoefficient old_rho_coeff(fp_old.rho.get()); + + const double l2_diff = fp_new.rho->ComputeL2Error(old_rho_coeff); + const double l2_norm = fp_new.rho->Norml2(); + + return (l2_norm > 1e-18) ? (l2_diff/l2_norm) : l2_diff; +} + +std::expected iterate_for_constant_shape(const FEM &fem, const Args &args) { + FixedPoint fp = init_fp(fem, args); + if (args.visualize && args.verbosity == Verbosity::VERBOSE) {VisualizeFP(fem, fp, "Initial");} + + for (int i = 0; i < args.max_iters; ++i) { + FixedPoint new_fp = step(fem, fp, args); + double err = L2RelativeResidual(fp, new_fp); + + if (args.verbosity >= Verbosity::PER_ITERATION) std::println("Iteration {:4} -- ||r|| = {:7.5E}", i, err); + + fp = new_fp.clone(); + if (args.visualize && args.verbosity == Verbosity::VERBOSE) {VisualizeFP(fem, fp, std::format("Step Number {}", i));} + if (err <= args.tol) { + if (args.verbosity >= Verbosity::PER_ITERATION) std::println("Convergence reached in {} steps!", i); + break; + } + } + + if (args.visualize) {VisualizeFP(fem, fp, "Final");} + return fp; +} + +double clip(const double h, const double relax) { + return std::max(h, 0.0) * relax; +} + +void radial(const mfem::Vector& x, mfem::Vector &r_hat) { + r_hat = x; + if (const double norm = r_hat.Norml2(); norm > 1e-12) { + r_hat /= norm; + } else { + r_hat = 0.0; + } +} + +bool is_system_bound(const FEM& fem, const FixedPoint& fp, const Args& args) { + mfem::GridFunctionCoefficient rho_coeff(fp.rho.get()); + mfem::GridFunctionCoefficient h_coeff(fp.h.get()); + + auto cent_func = [&args](const mfem::Vector& x) { + return centrifugal_potential(x, args.omega); + }; + mfem::FunctionCoefficient cent_coeff(cent_func); + + mfem::GridFunction phi_grav_gf(*fp.phi); + mfem::GridFunction cent_gf(fem.H1_fes.get()); + cent_gf.ProjectCoefficient(cent_coeff); + phi_grav_gf -= cent_gf; + + mfem::GridFunctionCoefficient phi_grav_coeff(&phi_grav_gf); + + mfem::ProductCoefficient rho_phi_coeff(rho_coeff, phi_grav_coeff); + mfem::LinearForm w_lf(fem.H1_fes.get()); + w_lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(rho_phi_coeff)); + w_lf.Assemble(); + double W = 0.5 * w_lf.Sum(); + + mfem::ProductCoefficient rho_cent_coeff(rho_coeff, cent_coeff); + mfem::LinearForm t_lf(fem.H1_fes.get()); + t_lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(rho_cent_coeff)); + t_lf.Assemble(); + double T = -1.0 * t_lf.Sum(); + + mfem::ProductCoefficient rho_h_coeff(rho_coeff, h_coeff); + mfem::LinearForm u_lf(fem.H1_fes.get()); + u_lf.AddDomainIntegrator(new mfem::DomainLFIntegrator(rho_h_coeff)); + u_lf.Assemble(); + double integral_rho_h = u_lf.Sum(); + double U = (args.index / (args.index + 1.0)) * integral_rho_h; + + double E_total = W + T + U; + + if (args.verbosity >= Verbosity::FULL) { + std::println("--- Energy Diagnostics ---"); + std::println(" W (Grav) : {:+.4E}", W); + std::println(" T (Rot) : {:+.4E}", T); + std::println(" U (Int) : {:+.4E}", U); + std::println(" Total E : {:+.4E}", E_total); + std::println("--------------------------"); + } + + return E_total < 0.0; +} + +std::unique_ptr get_nodal_displacement(const FEM& fem, const FixedPoint &fp, const Args& args) { + auto displacement = std::make_unique(fem.Vec_H1_fes.get()); + *displacement = 0.0; + + mfem::GridFunctionCoefficient h_coeff(fp.h.get()); + mfem::TransformedCoefficient mag_coeff(&h_coeff, [&args](double h){ return h * args.relax_rate; }); + mfem::VectorFunctionCoefficient dir_coeff(fem.mesh_ptr->Dimension(), radial); + mfem::ScalarVectorProductCoefficient total_dist_coeff(mag_coeff, dir_coeff); + + displacement->ProjectCoefficient(total_dist_coeff); + + mfem::BilinearForm a(fem.Vec_H1_fes.get()); + a.AddDomainIntegrator(new mfem::VectorDiffusionIntegrator()); + a.Assemble(); + + mfem::Array ess_bdr(fem.mesh_ptr->bdr_attributes.Max()); + ess_bdr = 1; // Mark the outer surface + mfem::Array ess_tdof_list; + fem.Vec_H1_fes->GetEssentialTrueDofs(ess_bdr, ess_tdof_list); + + mfem::LinearForm b(fem.Vec_H1_fes.get()); + b.Assemble(); + + mfem::OperatorPtr A; + mfem::Vector B, X; + a.FormLinearSystem(ess_tdof_list, *displacement, b, A, X, B); + + mfem::CGSolver cg; + cg.SetRelTol(1e-6); + cg.SetMaxIter(500); + cg.SetOperator(*A); + cg.Mult(B, X); + + a.RecoverFEMSolution(X, b, *displacement); + + return displacement; +} + +void deform_mesh(const FEM& fem, const mfem::GridFunction& displacement, const Args& args) { + if (args.allow_deformation) { + fem.mesh_ptr->MoveNodes(displacement); + fem.mesh_ptr->NodesUpdated(); + } +} + +void print_options(const Args& args) { + std::println("Options:"); + std::println(" Visualize: {}", args.visualize); + std::println(" Rotation: {}", args.rotation); + std::println(" Polytropic Index: {}", args.index); + std::println(" Density Mixing Alpha: {}", args.alpha); + std::println(" Mesh File: {}", args.mesh); + std::println(" Max Iterations: {}", args.max_iters); + std::println(" Tolerance: {:5.2E}", args.tol); + std::println(" Angular Velocity (Omega): {}", args.omega); + std::println(" Relaxation Rate: {}", args.relax_rate); + std::println(" Allow Deformation: {}", args.allow_deformation); + std::println(" Max Deformation Iterations: {}", args.max_deformation_iters); + std::println(" Deformation Relative Tolerance: {:5.2E}", args.deformation_rtol); + std::println(" Deformation Absolute Tolerance: {:5.2E}", args.deformation_atol); +} + +Args setup_cli(const int argc, char** argv) { + Args args; + + CLI::App app{"Simple Potential, Enthalpy, and Pressure Solver"}; + + bool no_rotate = false; + bool no_deform = false; + + app.add_flag("-v,--visualize", args.visualize, "Enable Visualizations"); + app.add_option("-n,--index", args.index, "polytropic index"); + app.add_option("-a,--alpha", args.alpha, "density mixing strength"); + app.add_option("-m,--mesh", args.mesh, "mesh file to read from"); + app.add_option("-i,--max-iters", args.max_iters, "Max number of iterations"); + app.add_option("-t,--tol", args.tol, "Relative tolerance to end on"); + app.add_flag("--no-rotate", no_rotate, "Enable or disable rotation"); + app.add_option("-w,--omega", args.omega, "Arbitrary Unit Angular Velocity"); + app.add_option("-r,--relax-rate", args.relax_rate, "Relaxation rate for boundary displacement"); + app.add_flag("--no-deform", no_deform, "Enable or disable mesh deformation"); + app.add_option("--max-deformation-iters", args.max_deformation_iters, "Max number of deformation steps to take"); + app.add_option("--deformation-rtol", args.deformation_rtol, "Relative tolerance for deformation convergence"); + app.add_option("--deformation-atol", args.deformation_atol, "Absolute tolerance for deformation convergence"); + + const auto verbosity_map = make_verbosity_map(); + + app.add_option("--verbosity", args.verbosity, "Set the verbosity level")->transform(CLI::CheckedTransformer(verbosity_map, CLI::ignore_case)); + + try { + app.parse(argc, argv); + } catch (const CLI::ParseError &e) { + exit(app.exit(e)); + } + + args.rotation = !no_rotate; + args.allow_deformation = !no_deform; + + return args; +} + +Envelope extract_envelope(const FEM& fem, const Args& args) { + Envelope env; + for (size_t i = 0; i < fem.mesh_ptr->GetNBE(); ++i) { + mfem::ElementTransformation *trans = fem.mesh_ptr->GetBdrElementTransformation(static_cast(i)); + const mfem::Geometry::Type geom = fem.mesh_ptr->GetBdrElementGeometry(static_cast(i)); + const mfem::RefinedGeometry *refiner = mfem::GeometryRefiner().Refine(geom, args.env_ref_levels); + const mfem::IntegrationRule *ir = &refiner->RefPts; + + for (size_t j = 0; j < ir->GetNPoints(); ++j) { + const mfem::IntegrationPoint &ip = ir->IntPoint(static_cast(j)); + + mfem::Vector phys_point; + trans->Transform(ip, phys_point); + + Point p{ + .x = phys_point(0), + .y = phys_point(1), + .z = phys_point(2), + .r = phys_point.Norml2(), + .IR_ID = j, + .BE_ID = i + + }; + + env.points.push_back(p); + } + } + return env; +} + +std::map make_verbosity_map() { + std::map verbosity_map; + for (const auto& [key, pair] : VerbosityNames) { + verbosity_map[pair.first] = key; + verbosity_map[pair.second] = key; + } + return verbosity_map; +} diff --git a/makefile b/makefile new file mode 100644 index 0000000..1d7625f --- /dev/null +++ b/makefile @@ -0,0 +1,20 @@ +default: all + +all: run + +run: main.cpp + clang++ -O3 -o run main.cpp -lmfem -std=c++23 + +run_debug: main.cpp + clang++ -g -O0 -o run_debug main.cpp -lmfem -std=c++23 + +clean: + rm -f run run_debug + +@.PHONY: all run run_debug clean + +test: run + ./run + +debug: run_debug + lldb run_debug diff --git a/readme.md b/readme.md new file mode 100644 index 0000000..3d70f6e --- /dev/null +++ b/readme.md @@ -0,0 +1,27 @@ +# FEM rotating polytrope + +A model of a rotating barotropic fluid including envelope deformation + +## Building +In order to build this you will need both MFEM and CLI11 installed on your system, follow the instructions on their respective websites to do so. Once you have those installed, you can build this project using GNU make. + +```bash +make +``` + +## Running +To run the program, you can use the following command: + +```bash +./run --help +``` + +select your desired options and run. If you wish to visualize the output you must have GLVis running on your local machine +at port 19916. + +## Notes +This is a very simple solver, though the physics should be mostly correct in the barotropic case. The primary issue +with this solver is the convergence rate. We have built this as a feasibility study and therefore no effort has been +made to optimize the solver. Specifically we use a seriese of nested picard iterations to solve the nonlinear system. These do +seem to converge reliably; however, they do so very slowly. + diff --git a/stroid.mesh b/stroid.mesh new file mode 100644 index 0000000..8dd8a18 --- /dev/null +++ b/stroid.mesh @@ -0,0 +1,12028 @@ +MFEM mesh v1.0 + +# +# MFEM Geometry Types (see fem/geom.hpp): +# +# POINT = 0 +# SEGMENT = 1 +# TRIANGLE = 2 +# SQUARE = 3 +# TETRAHEDRON = 4 +# CUBE = 5 +# PRISM = 6 +# PYRAMID = 7 +# + +dimension +3 + +elements +448 +1 5 0 79 281 82 87 282 461 285 +1 5 79 16 80 281 282 88 283 461 +1 5 281 80 48 81 461 283 89 284 +1 5 82 281 81 19 285 461 284 90 +1 5 87 282 461 285 24 83 286 86 +1 5 282 88 283 461 83 49 84 286 +1 5 461 283 89 284 286 84 72 85 +1 5 285 461 284 90 86 286 85 52 +1 5 16 91 287 80 88 288 462 283 +1 5 91 1 92 287 288 97 289 462 +1 5 287 92 17 93 462 289 98 290 +1 5 80 287 93 48 283 462 290 89 +1 5 88 288 462 283 49 94 291 84 +1 5 288 97 289 462 94 25 95 291 +1 5 462 289 98 290 291 95 50 96 +1 5 283 462 290 89 84 291 96 72 +1 5 48 93 292 101 89 290 463 295 +1 5 93 17 99 292 290 98 293 463 +1 5 292 99 3 100 463 293 105 294 +1 5 101 292 100 18 295 463 294 106 +1 5 89 290 463 295 72 96 296 104 +1 5 290 98 293 463 96 50 102 296 +1 5 463 293 105 294 296 102 26 103 +1 5 295 463 294 106 104 296 103 51 +1 5 19 81 297 108 90 284 464 299 +1 5 81 48 101 297 284 89 295 464 +1 5 297 101 18 107 464 295 106 298 +1 5 108 297 107 2 299 464 298 111 +1 5 90 284 464 299 52 85 300 110 +1 5 284 89 295 464 85 72 104 300 +1 5 464 295 106 298 300 104 51 109 +1 5 299 464 298 111 110 300 109 27 +1 5 24 83 286 86 116 301 465 304 +1 5 83 49 84 286 301 117 302 465 +1 5 286 84 72 85 465 302 118 303 +1 5 86 286 85 52 304 465 303 119 +1 5 116 301 465 304 4 112 305 115 +1 5 301 117 302 465 112 20 113 305 +1 5 465 302 118 303 305 113 53 114 +1 5 304 465 303 119 115 305 114 23 +1 5 49 94 291 84 117 306 466 302 +1 5 94 25 95 291 306 123 307 466 +1 5 291 95 50 96 466 307 124 308 +1 5 84 291 96 72 302 466 308 118 +1 5 117 306 466 302 20 120 309 113 +1 5 306 123 307 466 120 5 121 309 +1 5 466 307 124 308 309 121 21 122 +1 5 302 466 308 118 113 309 122 53 +1 5 72 96 296 104 118 308 467 312 +1 5 96 50 102 296 308 124 310 467 +1 5 296 102 26 103 467 310 128 311 +1 5 104 296 103 51 312 467 311 129 +1 5 118 308 467 312 53 122 313 127 +1 5 308 124 310 467 122 21 125 313 +1 5 467 310 128 311 313 125 7 126 +1 5 312 467 311 129 127 313 126 22 +1 5 52 85 300 110 119 303 468 315 +1 5 85 72 104 300 303 118 312 468 +1 5 300 104 51 109 468 312 129 314 +1 5 110 300 109 27 315 468 314 132 +1 5 119 303 468 315 23 114 316 131 +1 5 303 118 312 468 114 53 127 316 +1 5 468 312 129 314 316 127 22 130 +1 5 315 468 314 132 131 316 130 6 +2 5 8 133 317 136 141 318 469 321 +2 5 133 28 134 317 318 142 319 469 +2 5 317 134 54 135 469 319 143 320 +2 5 136 317 135 31 321 469 320 144 +2 5 141 318 469 321 32 137 322 140 +2 5 318 142 319 469 137 55 138 322 +2 5 469 319 143 320 322 138 73 139 +2 5 321 469 320 144 140 322 139 58 +2 5 28 145 323 134 142 324 470 319 +2 5 145 9 146 323 324 151 325 470 +2 5 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