{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "# Tutorial-IllinoisGRMHD: A_i_rhs_no_gauge_terms.C\n", "\n", "## Authors: Leo Werneck & Zach Etienne\n", "\n", "**This module is currently under development**\n", "\n", "## This notebook explains the construction of the right-hand side of the evolution equations of $A_{i}$.\n", "\n", "### Required and recommended citations:\n", "\n", "* **(Required)** Etienne, Z. B., Paschalidis, V., Haas R., Mösta P., and Shapiro, S. L. IllinoisGRMHD: an open-source, user-friendly GRMHD code for dynamical spacetimes. Class. Quantum Grav. 32 (2015) 175009. ([arxiv:1501.07276](http://arxiv.org/abs/1501.07276)).\n", "* **(Required)** Noble, S. C., Gammie, C. F., McKinney, J. C., Del Zanna, L. Primitive Variable Solvers for Conservative General Relativistic Magnetohydrodynamics. Astrophysical Journal, 641, 626 (2006) ([astro-ph/0512420](https://arxiv.org/abs/astro-ph/0512420)).\n", "* **(Recommended)** Del Zanna, L., Bucciantini N., Londrillo, P. An efficient shock-capturing central-type scheme for multidimensional relativistic flows - II. Magnetohydrodynamics. A&A 400 (2) 397-413 (2003). DOI: 10.1051/0004-6361:20021641 ([astro-ph/0210618](https://arxiv.org/abs/astro-ph/0210618))." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Table of Contents\n", "$$\\label{toc}$$\n", "\n", "This module is organized as follows\n", "\n", "0. [Step 0](#src_dir): **Source directory creation**\n", "1. [Step 1](#introduction): **Introduction**\n", "1. [Step 2](#a_i_rhs_no_gauge_terms__c): **`A_i_rhs_no_gauge_terms.C`**\n", "1. [Step n-1](#code_validation): **Code validation**\n", "1. [Step n](#latex_pdf_output): **Output this notebook to $\\LaTeX$-formatted PDF file**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Step 0: Source directory creation \\[Back to [top](#toc)\\]\n", "$$\\label{src_dir}$$\n", "\n", "We will now use the [cmdline_helper.py NRPy+ module](Tutorial-Tutorial-cmdline_helper.ipynb) to create the source directory within the `IllinoisGRMHD` NRPy+ directory if it does not exist yet." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "# Step 0: Creation of the IllinoisGRMHD source directory\n", "# Step 0a: Add NRPy's directory to the path\n", "# https://stackoverflow.com/questions/16780014/import-file-from-parent-directory\n", "import os,sys\n", "nrpy_dir_path = os.path.join(\"..\",\"..\")\n", "if nrpy_dir_path not in sys.path:\n", " sys.path.append(nrpy_dir_path)\n", "\n", "# Step 0b: Load up cmdline_helper and create the directory\n", "import cmdline_helper as cmd\n", "IGM_src_dir_path = os.path.join(\"..\",\"src\")\n", "cmd.mkdir(IGM_src_dir_path)\n", "\n", "# Step 0c: Create the output file path\n", "outfile_path__A_i_rhs_no_gauge_terms__C = os.path.join(IGM_src_dir_path,\"A_i_rhs_no_gauge_terms.C\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Step 1: Introduction \\[Back to [top](#toc)\\]\n", "$$\\label{introduction}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Step 2: `A_i_rhs_no_gauge_terms.C` \\[Back to [top](#toc)\\]\n", "$$\\label{a_i_rhs_no_gauge_terms__c}$$" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Writing ../src/A_i_rhs_no_gauge_terms.C\n" ] } ], "source": [ "%%writefile $outfile_path__A_i_rhs_no_gauge_terms__C\n", "/* Compute the part of A_i_rhs that excludes the gauge terms. I.e., we set\n", " * A_i_rhs = \\partial_t A_i = \\psi^{6} (v^z B^x - v^x B^z) here.\n", " */\n", "static void A_i_rhs_no_gauge_terms(const int A_dirn,const cGH *cctkGH,const int *cctk_lsh,const int *cctk_nghostzones,gf_and_gz_struct *out_prims_r,gf_and_gz_struct *out_prims_l,\n", " CCTK_REAL *phi_interped,CCTK_REAL *cmax_1,CCTK_REAL *cmin_1,CCTK_REAL *cmax_2,CCTK_REAL *cmin_2, CCTK_REAL *A3_rhs) {\n", " // If A_dirn=1, then v1_offset=1 (v1=VY) and v2_offset=2 (v2=VZ)\n", " // If A_dirn=2, then v1_offset=2 (v1=VZ) and v2_offset=0 (v2=VX)\n", " // If A_dirn=3, then v1_offset=0 (v1=VX) and v2_offset=1 (v2=VY)\n", " int v1_offset = ((A_dirn-1)+1)%3, v2_offset = ((A_dirn-1)+2)%3;\n", "\n", " CCTK_REAL *v1rr=out_prims_r[VXR+v1_offset].gf, *v2rr=out_prims_r[VXR+v2_offset].gf;\n", " CCTK_REAL *v1rl=out_prims_l[VXR+v1_offset].gf, *v2rl=out_prims_l[VXR+v2_offset].gf;\n", " CCTK_REAL *v1lr=out_prims_r[VXL+v1_offset].gf, *v2lr=out_prims_r[VXL+v2_offset].gf;\n", " CCTK_REAL *v1ll=out_prims_l[VXL+v1_offset].gf, *v2ll=out_prims_l[VXL+v2_offset].gf;\n", "\n", " CCTK_REAL *B1r=out_prims_r[BX_STAGGER+v1_offset].gf, *B1l=out_prims_l[BX_STAGGER+v1_offset].gf;\n", " CCTK_REAL *B2r=out_prims_r[BX_STAGGER+v2_offset].gf, *B2l=out_prims_l[BX_STAGGER+v2_offset].gf;\n", "\n", " /**** V DEPENDENCIES ****/\n", " /* In the case of Ax_rhs, we need v{y,z}{r,l} at (i,j+1/2,k+1/2).\n", " * However, v{y,z}{r,l}{r,l} are defined at (i,j-1/2,k-1/2), so\n", " * v{y,z}{r,l} at (i,j+1/2,k+1/2) is stored at v{y,z}{r,l}{r,l}(i,j+1,k+1).\n", " * In the case of Ay_rhs, we need v{x,z}{r,l} at (i+1/2,j,k+1/2).\n", " * However, v{x,z}{r,l}{r,l} are defined at (i-1/2,j,k-1/2), so\n", " * v{x,z}{r,l} at (i+1/2,j,k+1/2) is stored at v{x,z}{r,l}{r,l}(i+1,j,k+1).\n", " * In the case of Az_rhs, we need v{x,y}{r,l} at (i+1/2,j+1/2,k).\n", " * However, v{x,y}{r,l}{r,l} are defined at (i-1/2,j-1/2,k), so\n", " * v{x,y}{r,l} at (i+1/2,j+1/2,k) is stored at v{x,y}{r,l}{r,l}(i+1,j+1,k). */\n", " static const int vs_ijk_offset[4][3] = { {0,0,0} , {0,1,1} , {1,0,1} , {1,1,0} };\n", "\n", " /**** B DEPENDENCIES ****/\n", " /* In the case of Ax_rhs, we need B{y,z}{r,l} at (i,j+1/2,k+1/2).\n", " * However, By_stagger{r,l} is defined at (i,j+1/2,k-1/2), and\n", " * Bz_stagger{r,l} is defined at (i,j-1/2,k+1/2), so\n", " * By_stagger{r,l} at (i,j+1/2,k+1/2) is stored at By_stagger{r,l}(i,j,k+1), and\n", " * Bz_stagger{r,l} at (i,j+1/2,k+1/2) is stored at Bz_stagger{r,l}(i,j+1,k).\n", " * In the case of Ay_rhs, we need B{z,x}_stagger{r,l} at (i+1/2,j,k+1/2).\n", " * However, Bz_stagger{r,l} is defined at (i-1/2,j,k+1/2), and\n", " * Bx_stagger{r,l} is defined at (i+1/2,j,k-1/2), so\n", " * Bz_stagger{r,l} at (i+1/2,j,k+1/2) is stored at Bz_stagger{r,l}(i+1,j,k), and\n", " * Bx_stagger{r,l} at (i+1/2,j,k+1/2) is stored at Bx_stagger{r,l}(i,j,k+1).\n", " * In the case of Az_rhs, we need B{x,y}_stagger{r,l} at (i+1/2,j+1/2,k).\n", " * However, Bx_stagger{r,l} is defined at (i+1/2,j-1/2,k), and\n", " * By_stagger{r,l} is defined at (i-1/2,j+1/2,k), so\n", " * Bx_stagger{r,l} at (i+1/2,j+1/2,k) is stored at Bx_stagger{r,l}(i,j+1,k), and\n", " * By_stagger{r,l} at (i+1/2,j+1/2,k) is stored at By_stagger{r,l}(i+1,j,k).\n", " */\n", " static const int B1_ijk_offset[4][3] = { {0,0,0} , {0,0,1} , {1,0,0} , {0,1,0} };\n", " static const int B2_ijk_offset[4][3] = { {0,0,0} , {0,1,0} , {0,0,1} , {1,0,0} };\n", "\n", "#pragma omp parallel for\n", " for(int k=cctk_nghostzones[2];k\n", "\n", "# Step n-1: Code validation \\[Back to [top](#toc)\\]\n", "$$\\label{code_validation}$$\n", "\n", "First, we download the original `IllinoisGRMHD` source code and then compare it to the source code generated by this tutorial notebook." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Validation test for A_i_rhs_no_gauge_terms.C: FAILED!\n", "Diff:\n", "20c20\n", "< /* In the case of Ax_rhs, we need v{y,z}{r,l} at (i,j+1/2,k+1/2). \n", "---\n", "> /* In the case of Ax_rhs, we need v{y,z}{r,l} at (i,j+1/2,k+1/2).\n", "23c23\n", "< * In the case of Ay_rhs, we need v{x,z}{r,l} at (i+1/2,j,k+1/2). \n", "---\n", "> * In the case of Ay_rhs, we need v{x,z}{r,l} at (i+1/2,j,k+1/2).\n", "26c26\n", "< * In the case of Az_rhs, we need v{x,y}{r,l} at (i+1/2,j+1/2,k). \n", "---\n", "> * In the case of Az_rhs, we need v{x,y}{r,l} at (i+1/2,j+1/2,k).\n", "33c33\n", "< * However, By_stagger{r,l} is defined at (i,j+1/2,k-1/2), and \n", "---\n", "> * However, By_stagger{r,l} is defined at (i,j+1/2,k-1/2), and\n", "43c43\n", "< * However, Bx_stagger{r,l} is defined at (i+1/2,j-1/2,k), and \n", "---\n", "> * However, Bx_stagger{r,l} is defined at (i+1/2,j-1/2,k), and\n", "86c86\n", "< * Implement 2D HLL flux \n", "---\n", "> * Implement 2D HLL flux\n", "89c89\n", "< * Note that cmax/cmin (\\alpha^{\\pm} as defined in that paper) is at a slightly DIFFERENT \n", "---\n", "> * Note that cmax/cmin (\\alpha^{\\pm} as defined in that paper) is at a slightly DIFFERENT\n", "96,97c96,97\n", "< /( (cmax_1L+cmin_1L)*(cmax_2L+cmin_2L) ) \n", "< - cmax_1L*cmin_1L*(B2tilder_minus_B2tildel)/(cmax_1L+cmin_1L) \n", "---\n", "> /( (cmax_1L+cmin_1L)*(cmax_2L+cmin_2L) )\n", "> - cmax_1L*cmin_1L*(B2tilder_minus_B2tildel)/(cmax_1L+cmin_1L)\n", "100a101\n", "> \n" ] } ], "source": [ "# Verify if the code generated by this tutorial module\n", "# matches the original IllinoisGRMHD source code\n", "\n", "# First download the original IllinoisGRMHD source code\n", "import urllib\n", "from os import path\n", "\n", "original_IGM_file_url = \"https://bitbucket.org/zach_etienne/wvuthorns/raw/5611b2f0b17135538c9d9d17c7da062abe0401b6/IllinoisGRMHD/src/A_i_rhs_no_gauge_terms.C\"\n", "original_IGM_file_name = \"A_i_rhs_no_gauge_terms-original.C\"\n", "original_IGM_file_path = os.path.join(IGM_src_dir_path,original_IGM_file_name)\n", "\n", "# Then download the original IllinoisGRMHD source code\n", "# We try it here in a couple of ways in an attempt to keep\n", "# the code more portable\n", "try:\n", " original_IGM_file_code = urllib.request.urlopen(original_IGM_file_url).read().decode(\"utf-8\")\n", " # Write down the file the original IllinoisGRMHD source code\n", " with open(original_IGM_file_path,\"w\") as file:\n", " file.write(original_IGM_file_code)\n", "except:\n", " try:\n", " original_IGM_file_code = urllib.urlopen(original_IGM_file_url).read().decode(\"utf-8\")\n", " # Write down the file the original IllinoisGRMHD source code\n", " with open(original_IGM_file_path,\"w\") as file:\n", " file.write(original_IGM_file_code)\n", " except:\n", " # If all else fails, hope wget does the job\n", " !wget -O $original_IGM_file_path $original_IGM_file_url\n", "\n", "# Perform validation\n", "Validation__A_i_rhs_no_gauge_terms__C = !diff $original_IGM_file_path $outfile_path__A_i_rhs_no_gauge_terms__C\n", "\n", "if Validation__A_i_rhs_no_gauge_terms__C == []:\n", " # If the validation passes, we do not need to store the original IGM source code file\n", " !rm $original_IGM_file_path\n", " print(\"Validation test for A_i_rhs_no_gauge_terms.C: PASSED!\")\n", "else:\n", " # If the validation fails, we keep the original IGM source code file\n", " print(\"Validation test for A_i_rhs_no_gauge_terms.C: FAILED!\")\n", " # We also print out the difference between the code generated\n", " # in this tutorial module and the original IGM source code\n", " print(\"Diff:\")\n", " for diff_line in Validation__A_i_rhs_no_gauge_terms__C:\n", " print(diff_line)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "# Step n: Output this notebook to $\\LaTeX$-formatted PDF file \\[Back to [top](#toc)\\]\n", "$$\\label{latex_pdf_output}$$\n", "\n", "The following code cell converts this Jupyter notebook into a proper, clickable $\\LaTeX$-formatted PDF file. After the cell is successfully run, the generated PDF may be found in the root NRPy+ tutorial directory, with filename\n", "[Tutorial-IllinoisGRMHD__A_i_rhs_no_gauge_terms.pdf](Tutorial-IllinoisGRMHD__A_i_rhs_no_gauge_terms.pdf) (Note that clicking on this link may not work; you may need to open the PDF file through another means)." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "latex_nrpy_style_path = os.path.join(nrpy_dir_path,\"latex_nrpy_style.tplx\")\n", "#!jupyter nbconvert --to latex --template $latex_nrpy_style_path --log-level='WARN' Tutorial-IllinoisGRMHD__A_i_rhs_no_gauge_terms.ipynb\n", "#!pdflatex -interaction=batchmode Tutorial-IllinoisGRMHD__A_i_rhs_no_gauge_terms.tex\n", "#!pdflatex -interaction=batchmode Tutorial-IllinoisGRMHD__A_i_rhs_no_gauge_terms.tex\n", "#!pdflatex -interaction=batchmode Tutorial-IllinoisGRMHD__A_i_rhs_no_gauge_terms.tex\n", "!rm -f Tut*.out Tut*.aux Tut*.log" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.11" } }, "nbformat": 4, "nbformat_minor": 4 }