From 21c7d1643fa155cf76ce59b63ff15046d6530c39 Mon Sep 17 00:00:00 2001 From: Damian Rouson Date: Tue, 12 May 2026 20:35:17 -0700 Subject: [PATCH] feat(burgers): add default RK4, animate solutions This commit 1. Adds scalar_1D_t operators to support 4th-order Runge-Kutta (RK4) time advancement for the Burgers equation solver, 2. Defaults the Burgers solver to RK4, 3. Saves the solver output to example/scripts/burgers-order-4.dat, and 4. Adds example/scripts/animate-burgers.gnuplot, which uses gnuplot to create an animated GIF of the analytical & numerical solutions. --- example/burgers-1D.F90 | 110 +++++++++++-- example/scripts/animate-burgers.gnuplot | 132 +++++++++++++++ example/scripts/burgers-order-4.dat | 207 ++++++++++++++++++++++++ src/formal/scalar_1D_s.F90 | 12 ++ src/formal/tensor_1D_s.f90 | 3 + src/formal/tensors_1D_m.F90 | 28 +++- 6 files changed, 475 insertions(+), 17 deletions(-) create mode 100644 example/scripts/animate-burgers.gnuplot create mode 100644 example/scripts/burgers-order-4.dat diff --git a/example/burgers-1D.F90 b/example/burgers-1D.F90 index 6002e1a..a62b191 100644 --- a/example/burgers-1D.F90 +++ b/example/burgers-1D.F90 @@ -1,6 +1,8 @@ ! Copyright (c) 2026, The Regents of the University of California ! Terms of use are as specified in LICENSE.txt +#include "julienne-assert-macros.h" + module initial_condition_m implicit none @@ -26,8 +28,9 @@ program burgers_1D !! * Corbino & Castillo (2020) https://doi.org/10.1016/j.cam.2019.06.042. !! * Dumett & Castillo (2022) https://doi.org/10.13140/RG.2.2.26630.14400 use initial_condition_m, only : initial_condition - use julienne_m, only : command_line_t + use julienne_m, only : command_line_t, csv, call_julienne_assert_, operator(.equalsExpected.), string_t use formal_m, only : scalar_1D_t, scalar_1D_initializer_i, d_dx, d2_dx2 + use iso_fortran_env, only : output_unit implicit none #ifdef __GFORTRAN__ @@ -48,37 +51,102 @@ program burgers_1D // 'where square brackets indicate optional arguments and angular brackets indicate user input values.' // new_line('') end if - print *, new_line('') - print *," Initial condition" - print *," =================" + print '(a)', new_line('') + print '(a)',"# Initial condition" + print '(a)',"# =================" + write(output_unit,'(a)', advance="no") call execute_command_line("grep 'initial_condition =' example/burgers-1D.F90 | grep -v execute_command", wait=.true.) order_string = command_line%flag_value("--order") if (len(order_string)==0) then - order = 2 + order = 4 else read(order_string,"(i1)") order end if - print *, "order = ", order block #ifndef __GFORTRAN__ procedure(scalar_1D_initializer_i), pointer :: scalar_1D_initializer #endif - double precision, parameter :: dt = 1D0, pi = acos(-1D0) + double precision, parameter :: pi = acos(-1D0), nu=1D0, t_final=0.6D0 + double precision, allocatable :: u_surface(:,:), time(:) + double precision dt type(scalar_1D_t) u + integer step, n scalar_1D_initializer => initial_condition - u = scalar_1D_t(scalar_1D_initializer, order, x_min=0D0, x_max=2*pi, cells=20) - - runge_kutta_2nd_order: & - associate(u_half => u + d_dt(u)*dt/2) ! first substep - u = u + d_dt(u_half)*dt ! second substep - end associate runge_kutta_2nd_order - + u = scalar_1D_t(scalar_1D_initializer, order, x_min=0D0, x_max=2*pi, cells=199) + dt = diffusion_stability_limit(nu, u%dx(), order) + + associate(steps => ceiling(t_final/dt)) + associate(initial_condition => u%values()) + allocate(u_surface(size(initial_condition), steps + 1)) + u_surface(:,1) = initial_condition + end associate + + runge_kutta: & + do step = 1, steps + select case(order) + case(2) + associate(u_half => u + d_dt(u,nu)*dt/2) ! first substep + u = u + d_dt(u_half,nu)*dt ! second substep + u_surface(:,step) = u%values() + end associate + case(4) + associate(k1 => d_dt(u , nu)) + associate(k2 => d_dt(u + dt*k1/2, nu)) + associate(k3 => d_dt(u + dt*k1/2, nu)) + associate(k4 => d_dt(u + dt*k2 , nu)) + u = u + (k1 + 2*k2 + 2*k3 + k4)*dt/6 + u_surface(:,step) = u%values() + end associate + end associate + end associate + end associate + end select + end do runge_kutta + + block + character(len=64) scratch_pad + character(len=:), allocatable :: file_name + character(len=*), parameter :: path = "example/scripts/" + integer file_unit + + write(scratch_pad,'(a,i1,a)') "burgers-order-", order, ".dat" + file_name = trim(scratch_pad) + open(newunit=file_unit, file = path // file_name, status="unknown") + write(file_unit,'(a)' ) "# 1D Burgers equation solver results" + write(file_unit,'(a)' ) "# ==================================" + write(file_unit,'(a,i2)' ) "# spatial order of accuracy = ", order + write(file_unit,'(a,g0)' ) "# nu = " , nu + write(file_unit,'(a,g0)' ) "# dt = " , dt + write(file_unit,'(a,i4,a)') "# steps = ", steps + + associate(x => u%grid()) + do n = 1, size(x) + write(file_unit,"(*(G13.6,:,' '))"), x(n), u_surface(n,:) ! write space-separated values + end do + end associate + + close(file_unit) + + write(*,*) + write(*,'(a)') "To animate the results, set your present working directory to formal/example/scripts." + write(*,'(a)') "Then execute the following command:" + associate(dt_ => string_t(dt), frames => string_t(steps+1)) + write(*,'(a)') new_line('') & + // 'gnuplot -e "results_file=' // "'" // file_name // "'" // '"' & + // ' -e "animation_file=' // "'" // "animated-burgers.gif" // "'" // '"' & + // ' -e "dt=' // dt_%string() // '"' & + // ' -e "frames=' // frames%string() // '"' & + // " animate-burgers.gnuplot" // new_line('') + end associate + + end block + end associate end block #ifdef __GFORTRAN__ @@ -87,11 +155,21 @@ program burgers_1D contains - pure function d_dt(u) result(du_dt) + pure function d_dt(u, nu) result(du_dt) type(scalar_1D_t), intent(in) :: u + double precision, intent(in) :: nu type(scalar_1D_t) du_dt - double precision, parameter :: nu=1D0 du_dt = nu*d2_dx2(u) - d_dx((u**2)/2) end function + pure function diffusion_stability_limit(diffusivity,delta_x,order_of_accuracy) result(stable_time_step) + double precision, intent(in) :: diffusivity, delta_x + integer, intent(in) :: order_of_accuracy + double precision stable_time_step + double precision, parameter, dimension(*) :: stability_limit=[2.,2.,2.5,2.79] ! third value needs to be checked + double precision, parameter :: safety_factor = 0.9 + ! See Moin, P. (2010) Fundamentals of Engineering Numerical Analysis, 2nd ed., pp. 111-116. + stable_time_step = safety_factor*stability_limit(order_of_accuracy)*(delta_x**2)/(4*diffusivity) + end function + end program diff --git a/example/scripts/animate-burgers.gnuplot b/example/scripts/animate-burgers.gnuplot new file mode 100644 index 0000000..bde8a81 --- /dev/null +++ b/example/scripts/animate-burgers.gnuplot @@ -0,0 +1,132 @@ +# ============================================================================= +# Generate an GIF animated at 20 fps showing the mimetic and analytical +# solutions of the 1D Burgers Equation: +# +# du/dt + u du/dx = ν d^2u/dx^2 +# +# where ν is the diffusivity. +# +# Domain : x in [0, 2π] (periodic) +# Initial Condition : u(x,0) = 10*sin(x) +# Boundary Conditions : u^(n)(0,t) = u^(n)(2π,t) for n^{th} derivative +# +# Usage: +# +# gnuplot -e "dt=6.258068143677011E-4; frames=959; nu=1.0; results_file='burgers-order-4.dat'; animation_file='animated-burgers.gif'; order=4" animate-burgers.gnuplot +# +# where each command-line option has the default value shown above if the option is not specified. +# +# Expected results-file format: +# +# column 1 : abscissa (x) +# columns 2... M : numerical solution at successive times separated by dt + +if (!exists("dt")) dt = 6.258068143677011E-4 +t_end = 0.6 # final time +if (!exists("frames")) frames = int(t_end / dt) +if (!exists("nu")) nu = 1.0 +if (!exists("results_file")) results_file = "burgers-order-4.dat" +if (!exists("animation_file")) animation_file = "animated-burgers.gif" +if (!exists("order")) order = 4 + +# Obtain the exact solution via the Cole–Hopf transformation: +# +# phi(x,0) = exp( A*cos(x) ), A = 10/(2*nu) = 5 +# +# phi(x,t) = I_0(A) + 2 * sum_{n=1}^{N} I_n(A)*cos(n*x)*exp(-nu*n^2*t) +# +# u(x,t) = 4*nu * [sum_{n=1}^{N} n*I_n(A)*sin(n*x)*exp(-nu*n^2*t)] +# / [I_0(A) + 2*sum_{n=1}^{N} I_n(A)*cos(n*x)*exp(-nu*n^2*t)] +# +# I_n(A) are modified Bessel functions computed via Miller's backward +# recurrence and normalised with exp(A) = I_0 + 2*(I_1 + I_2 + ...). + +# Solution parameters: +# +A = 10.0 / (2.0*nu) +N = 40 # Fourier terms (ample convergence for nu=1) + +# ---------- Bessel function pre-computation ---------------------------------- +# Miller backward recurrence: I_{n-1} = (2n/A)*I_n + I_{n+1} +# Start from n = N+2 with seed values, then normalise. + +array IV[N+3] +IV[N+3] = 0.0 +IV[N+2] = 1.0 +do for [k = N+1 : 1 : -1] { + IV[k] = (2.0*k / A) * IV[k+1] + IV[k+2] +} + +# Normalise: exp(A) = I_0(A) + 2 * sum_{n>=1} I_n(A) +norm_sum = IV[1] +do for [k = 1 : N+1] { + norm_sum = norm_sum + 2.0 * IV[k+1] +} +scale = exp(A) / norm_sum + +array I_n[N+1] # I_n[n+1] = I_n(A), n = 0 … N +do for [k = 0 : N] { + I_n[k+1] = scale * IV[k+1] +} + +# ---------- solution --------------------------------------------------------- +num(x,t) = sum [k=1:N] ( k * I_n[k+1] * sin(k*x) * exp(-nu*k*k*t) ) +den(x,t) = 0.5*I_n[1] + sum [k=1:N] ( I_n[k+1] * cos(k*x) * exp(-nu*k*k*t) ) +u(x,t) = 2.0*nu * num(x,t) / den(x,t) + +# Determine the number of columns in the data file. +# total_cols includes the abscissa column; num_time_cols is the number of +# numerical solution snapshots (columns 2 … total_cols). +stats results_file nooutput +total_cols = STATS_columns +num_time_cols = total_cols - 1 + +print sprintf("Read '%s': %d abscissa column + %d numerical solution columns.", \ + results_file, 1, num_time_cols) + +# ---------- animated GIF terminal -------------------------------------------- +set terminal gif animate delay 5 loop 0 size 900,600 +# delay 5 → 5/100 s per frame = 20 fps +# loop 0 → loop forever +set output animation_file + +# ---------- fixed plot cosmetics --------------------------------------------- +set title "1D Burgers Equation Solutions \n\nu_t + u u_x = νu_{xx}\n\n IC: u(x,0) = 10 sin(x), BC: u^{(n)}(x,t) = u^{(n)}(x+2π,t), ν = 1" font "Arial,13" + +set xlabel "x" font "Arial,12" +set ylabel "u(x,t)" font "Arial,12" +set xrange [0 : 2*pi] +set yrange [-10 : 10] +set xtics ("0" 0, "pi/2" pi/2, "pi" pi, \ + "3pi/2" 3*pi/2, "2pi" 2*pi) +set grid lc rgb "#cccccc" +set key top right font "Arial,11" + +# Solid blue line for the exact solution +set style line 10 lc rgb "#1A5276" lw 2.5 + +# Red circles for the numerical solution +set style line 20 lc rgb "#C0392B" pt 7 ps 0.6 + +ordinal = (order == 1) ? "st" : \ + (order == 2) ? "nd" : \ + (order == 3) ? "rd" : "th" + +# ---------- animation loop --------------------------------------------------- +do for [frame = 0 : frames-1] { + t = frame * dt + + # Colour-map current time: blue + set style line 10 lc rgb int(255) lw 2.5 # blue + + set label 1 sprintf("t = %.4f", t) \ + at graph 0.04, graph 0.93 \ + font "Arial Bold,13" tc rgb "black" \ + front + + plot u(x, t) ls 10 title sprintf("Analytical solution", t), \ + results_file using 1:(column(frame+2)) ls 20 title "Mimetic (" . sprintf("%d", order). ordinal . "-order, RK" . sprintf("%d", order) . ")" +} + +set output # flush / close GIF +print sprintf("Done – %d frames written to animated-burgers.gif", frames) diff --git a/example/scripts/burgers-order-4.dat b/example/scripts/burgers-order-4.dat new file mode 100644 index 0000000..d52201a --- /dev/null +++ b/example/scripts/burgers-order-4.dat @@ -0,0 +1,207 @@ +# 1D Burgers equation solver results +# ================================== +# spatial order of accuracy = 4 +# nu = 1. +# dt = .6258068143677011E-3 +# steps = 959 + 0.00000 0.607962E-07 0.184383E-06 0.370505E-06 0.616983E-06 0.920316E-06 0.127610E-05 0.167928E-05 0.212443E-05 0.260584E-05 0.311764E-05 0.365394E-05 0.420885E-05 0.477655E-05 0.535134E-05 0.592767E-05 0.650012E-05 0.706350E-05 0.761278E-05 0.814318E-05 0.865009E-05 0.912913E-05 0.957616E-05 0.998722E-05 0.103586E-04 0.106868E-04 0.109684E-04 0.112005E-04 0.113800E-04 0.115042E-04 0.115707E-04 0.115771E-04 0.115212E-04 0.114009E-04 0.112145E-04 0.109602E-04 0.106365E-04 0.102421E-04 0.977548E-05 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2.60283 2.59905 2.59528 2.59152 2.58777 2.58403 2.58030 2.57658 2.57288 2.56918 2.56549 2.56182 2.55815 2.55450 2.55086 2.54722 2.54360 2.53999 2.53638 2.53279 2.52921 2.52564 2.52207 2.51852 2.51498 2.51145 2.50792 2.50441 2.50091 2.49741 2.49393 2.49046 2.48699 2.48354 2.48009 2.47666 2.47323 2.46981 2.46641 2.46301 2.45962 2.45624 2.45287 2.44951 2.44616 2.44281 2.43948 2.43615 2.43284 2.42953 2.42623 2.42295 2.41967 2.41639 2.41313 2.40988 2.40663 2.40340 2.40017 2.39695 2.39374 2.39054 2.38735 2.38416 2.38098 2.37782 2.37466 2.37151 2.36836 2.36523 2.36210 2.35898 2.35587 2.35277 2.34968 2.34659 2.34352 2.34045 2.33738 2.33433 2.33128 2.32825 2.32522 2.32220 2.31918 2.31617 2.31318 2.31019 2.30720 2.30423 2.30126 2.29830 2.29535 2.29240 2.28946 2.28653 2.28361 2.28069 2.27779 2.27489 2.27199 2.26911 2.26623 2.26336 2.26049 2.25764 2.25479 2.25194 2.24911 2.24628 2.24346 2.24064 2.23784 2.23504 2.23224 2.22946 2.22668 2.22391 2.22114 2.21838 2.21563 2.21288 2.21015 2.20741 2.20469 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1.90770 1.90566 1.90362 1.90159 1.89957 1.89754 1.89553 1.89351 1.89150 1.88950 1.88750 1.88550 1.88351 1.88152 1.87953 1.87755 1.87558 1.87360 1.87164 1.86967 1.86771 1.86576 1.86381 1.86186 1.85991 1.85797 1.85604 1.85411 1.85218 1.85025 1.84833 1.84642 1.84451 1.84260 1.84069 1.83879 1.83690 1.83501 1.83312 1.83123 1.82935 1.82747 1.82560 1.82373 1.82186 1.82000 1.81814 1.81629 1.81444 1.81259 1.81075 1.80891 1.80707 1.80524 1.80341 1.80159 1.79976 1.79795 1.79613 1.79432 1.79251 1.79071 1.78891 1.78711 1.78532 1.78353 1.78175 1.77996 1.77819 1.77641 1.77464 1.77287 1.77111 1.76934 1.76759 1.76583 1.76408 1.76233 1.76059 1.75885 1.75711 1.75538 1.75365 1.75192 1.75020 1.74847 1.74676 1.74504 1.74333 1.74163 1.73992 1.73822 1.73652 1.73483 1.73314 1.73145 1.72976 1.72808 1.72640 1.72473 1.72306 1.72139 1.71972 1.71806 1.71640 1.71475 1.71309 1.71144 1.70980 1.70815 1.70651 1.70488 1.70324 1.70161 1.69998 1.69836 1.69673 1.69512 1.69350 1.69189 1.69028 1.68867 1.68707 1.68546 1.68387 1.68227 1.68068 1.67909 1.67750 1.67592 1.67434 1.67276 1.67119 1.66962 1.66805 1.66648 1.66492 1.66336 1.66180 1.66024 1.65869 1.65714 1.65560 1.65405 1.65251 1.65098 1.64944 1.64791 1.64638 1.64485 1.64333 1.64181 1.64029 1.63878 1.63726 1.63575 1.63424 1.63274 1.63124 1.62974 1.62824 1.62675 1.62526 1.62377 1.62228 1.62080 1.61932 1.61784 1.61636 1.61489 1.61342 1.61195 1.61049 1.60903 1.60757 1.60611 1.60465 1.60320 1.60175 1.60030 1.59886 1.59742 1.59598 1.59454 1.59311 1.59167 1.59024 1.58882 1.58739 1.58597 1.58455 1.58313 1.58172 1.58031 1.57890 1.57749 1.57608 1.57468 1.57328 0.00000 + 1.15244 9.10860 9.07952 9.05037 9.02116 8.99188 8.96255 8.93318 8.90376 8.87432 8.84484 8.81535 8.78585 8.75634 8.72682 8.69731 8.66781 8.63832 8.60885 8.57940 8.54998 8.52060 8.49125 8.46194 8.43268 8.40347 8.37432 8.34522 8.31618 8.28720 8.25829 8.22945 8.20069 8.17200 8.14339 8.11486 8.08641 8.05805 8.02978 8.00160 7.97351 7.94552 7.91763 7.88983 7.86213 7.83454 7.80705 7.77966 7.75238 7.72521 7.69814 7.67119 7.64434 7.61761 7.59099 7.56449 7.53810 7.51182 7.48566 7.45962 7.43370 7.40789 7.38220 7.35663 7.33118 7.30585 7.28064 7.25555 7.23058 7.20573 7.18100 7.15639 7.13190 7.10753 7.08328 7.05916 7.03515 7.01127 6.98751 6.96387 6.94034 6.91694 6.89366 6.87050 6.84746 6.82453 6.80173 6.77904 6.75648 6.73403 6.71170 6.68948 6.66739 6.64541 6.62354 6.60180 6.58016 6.55865 6.53724 6.51596 6.49478 6.47372 6.45277 6.43193 6.41121 6.39059 6.37009 6.34970 6.32941 6.30924 6.28917 6.26921 6.24936 6.22962 6.20998 6.19045 6.17102 6.15170 6.13248 6.11337 6.09436 6.07545 6.05664 6.03793 6.01933 6.00082 5.98242 5.96411 5.94590 5.92779 5.90977 5.89186 5.87404 5.85631 5.83868 5.82114 5.80370 5.78635 5.76909 5.75193 5.73485 5.71787 5.70097 5.68417 5.66746 5.65083 5.63429 5.61784 5.60148 5.58520 5.56901 5.55290 5.53688 5.52095 5.50509 5.48932 5.47363 5.45803 5.44250 5.42706 5.41169 5.39641 5.38121 5.36608 5.35103 5.33606 5.32117 5.30636 5.29162 5.27695 5.26236 5.24785 5.23341 5.21904 5.20475 5.19053 5.17638 5.16231 5.14830 5.13437 5.12051 5.10671 5.09299 5.07934 5.06575 5.05223 5.03878 5.02540 5.01208 4.99883 4.98565 4.97253 4.95947 4.94648 4.93356 4.92069 4.90790 4.89516 4.88249 4.86988 4.85733 4.84484 4.83241 4.82004 4.80773 4.79549 4.78330 4.77117 4.75910 4.74708 4.73513 4.72323 4.71139 4.69960 4.68787 4.67620 4.66458 4.65302 4.64151 4.63006 4.61866 4.60731 4.59602 4.58478 4.57359 4.56246 4.55138 4.54035 4.52937 4.51844 4.50756 4.49673 4.48595 4.47522 4.46454 4.45391 4.44333 4.43280 4.42231 4.41187 4.40148 4.39114 4.38084 4.37059 4.36039 4.35023 4.34012 4.33005 4.32003 4.31005 4.30012 4.29023 4.28039 4.27059 4.26083 4.25112 4.24144 4.23182 4.22223 4.21268 4.20318 4.19372 4.18430 4.17492 4.16558 4.15629 4.14703 4.13781 4.12863 4.11950 4.11040 4.10134 4.09232 4.08333 4.07439 4.06548 4.05662 4.04779 4.03899 4.03024 4.02152 4.01284 4.00419 3.99558 3.98701 3.97847 3.96997 3.96150 3.95307 3.94467 3.93631 3.92798 3.91969 3.91143 3.90321 3.89502 3.88686 3.87874 3.87065 3.86259 3.85456 3.84657 3.83861 3.83068 3.82279 3.81492 3.80709 3.79929 3.79152 3.78378 3.77607 3.76840 3.76075 3.75314 3.74555 3.73799 3.73047 3.72297 3.71551 3.70807 3.70066 3.69328 3.68593 3.67861 3.67132 3.66405 3.65682 3.64961 3.64243 3.63527 3.62815 3.62105 3.61398 3.60694 3.59992 3.59293 3.58597 3.57903 3.57212 3.56524 3.55838 3.55155 3.54474 3.53796 3.53121 3.52448 3.51777 3.51109 3.50444 3.49781 3.49120 3.48462 3.47807 3.47154 3.46503 3.45854 3.45208 3.44565 3.43924 3.43285 3.42648 3.42014 3.41382 3.40753 3.40125 3.39500 3.38877 3.38257 3.37639 3.37023 3.36409 3.35797 3.35188 3.34580 3.33975 3.33372 3.32772 3.32173 3.31576 3.30982 3.30390 3.29800 3.29211 3.28625 3.28041 3.27459 3.26879 3.26302 3.25726 3.25152 3.24580 3.24010 3.23442 3.22876 3.22312 3.21750 3.21190 3.20632 3.20076 3.19521 3.18969 3.18418 3.17870 3.17323 3.16778 3.16235 3.15694 3.15154 3.14617 3.14081 3.13547 3.13015 3.12484 3.11955 3.11429 3.10904 3.10380 3.09859 3.09339 3.08821 3.08304 3.07789 3.07276 3.06765 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3.99867 3.99248 3.98631 3.98015 3.97401 3.96790 3.96180 3.95571 3.94965 3.94360 3.93758 3.93157 3.92558 3.91960 3.91364 3.90771 3.90178 3.89588 3.88999 3.88413 3.87827 3.87244 3.86662 3.86082 3.85504 3.84927 3.84352 3.83779 3.83207 3.82637 3.82069 3.81502 3.80937 3.80374 3.79812 3.79252 3.78693 3.78136 3.77581 3.77027 3.76475 3.75924 3.75375 3.74827 3.74282 3.73737 3.73194 3.72653 3.72113 3.71575 3.71038 3.70503 3.69969 3.69437 3.68906 3.68377 3.67849 3.67323 3.66798 3.66275 3.65753 3.65233 3.64714 3.64196 3.63680 3.63165 3.62652 3.62140 3.61630 3.61121 3.60613 3.60107 3.59602 3.59099 3.58597 3.58096 3.57597 3.57099 3.56602 3.56107 3.55613 3.55120 3.54629 3.54139 3.53650 3.53163 3.52677 3.52192 3.51709 3.51227 3.50746 3.50267 3.49788 3.49312 3.48836 3.48361 3.47888 3.47416 3.46946 3.46476 3.46008 3.45541 3.45076 3.44611 3.44148 3.43686 3.43225 3.42766 3.42307 3.41850 3.41394 3.40939 3.40485 3.40033 3.39582 3.39132 3.38683 3.38235 3.37788 3.37343 3.36899 3.36455 3.36013 3.35572 3.35133 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0.596942E-02 0.597794E-02 0.598648E-02 0.599502E-02 0.600357E-02 0.601213E-02 0.602069E-02 0.00000 diff --git a/src/formal/scalar_1D_s.F90 b/src/formal/scalar_1D_s.F90 index 645f0dd..cabd16f 100644 --- a/src/formal/scalar_1D_s.F90 +++ b/src/formal/scalar_1D_s.F90 @@ -99,12 +99,24 @@ pure function cell_center_locations(x_min, x_max, cells) result(x) tensor_1D_t(values = lhs*rhs%values_, x_min = rhs%x_min_, x_max = rhs%x_max_, cells = rhs%cells_, order = rhs%order_) end procedure + module procedure premultiply_integer + lhs_x_rhs%gradient_operator_1D_ = rhs%gradient_operator_1D_ + lhs_x_rhs%tensor_1D_t = & + tensor_1D_t(values = lhs*rhs%values_, x_min = rhs%x_min_, x_max = rhs%x_max_, cells = rhs%cells_, order = rhs%order_) + end procedure + module procedure postmultiply_double lhs_x_rhs%gradient_operator_1D_ = lhs%gradient_operator_1D_ lhs_x_rhs%tensor_1D_t = & tensor_1D_t(values = rhs*lhs%values_, x_min = lhs%x_min_, x_max = lhs%x_max_, cells = lhs%cells_, order = lhs%order_) end procedure + module procedure postmultiply_integer + lhs_x_rhs%gradient_operator_1D_ = lhs%gradient_operator_1D_ + lhs_x_rhs%tensor_1D_t = & + tensor_1D_t(values = rhs*lhs%values_, x_min = lhs%x_min_, x_max = lhs%x_max_, cells = lhs%cells_, order = lhs%order_) + end procedure + module procedure exponentiate power%tensor_1D_t = tensor_1D_t( & values = self%values_**exponent, x_min = self%x_min_, x_max = self%x_max_, cells = self%cells_, order = self%order_ & diff --git a/src/formal/tensor_1D_s.f90 b/src/formal/tensor_1D_s.f90 index c085da3..79dd3e3 100644 --- a/src/formal/tensor_1D_s.f90 +++ b/src/formal/tensor_1D_s.f90 @@ -32,5 +32,8 @@ dx = (self%x_max_ - self%x_min_)/self%cells_ end procedure + module procedure cells + cells = self%cells_ + end procedure end submodule tensor_1D_s diff --git a/src/formal/tensors_1D_m.F90 b/src/formal/tensors_1D_m.F90 index eecd06f..42b2823 100644 --- a/src/formal/tensors_1D_m.F90 +++ b/src/formal/tensors_1D_m.F90 @@ -60,6 +60,7 @@ pure function vector_1D_initializer_i(x) result(v) procedure, non_overridable, private :: divergence_1D_weights generic :: dV => dx procedure, non_overridable :: dx + procedure, non_overridable :: cells end type interface tensor_1D_t @@ -87,7 +88,7 @@ pure module function construct_1D_tensor_from_components(values, x_min, x_max, c generic :: operator(-) => subtract_scalar_1D generic :: operator(+) => add_scalar_1D generic :: operator(/) => divide_by_integer - generic :: operator(*) => premultiply_double, postmultiply_double + generic :: operator(*) => premultiply_double, postmultiply_double, premultiply_integer, postmultiply_integer generic :: operator(**) => exponentiate generic :: operator(.grad.) => grad generic :: operator(.laplacian.) => laplacian @@ -98,6 +99,8 @@ pure module function construct_1D_tensor_from_components(values, x_min, x_max, c procedure, non_overridable, private :: divide_by_integer procedure, non_overridable, private, pass(rhs) :: premultiply_double procedure, non_overridable, private :: postmultiply_double + procedure, non_overridable, private, pass(rhs) :: premultiply_integer + procedure, non_overridable, private :: postmultiply_integer procedure, non_overridable, private :: exponentiate procedure, non_overridable, private :: grad procedure, non_overridable, private :: laplacian @@ -250,6 +253,13 @@ pure module function dA(self) double precision dA end function + pure module function cells(self) + !! Result is the number of cells + implicit none + class(tensor_1D_t), intent(in) :: self + integer cells + end function + pure module function dx(self) !! Result is the uniform cell width implicit none @@ -328,6 +338,14 @@ pure module function premultiply_double(lhs, rhs) result(lhs_x_rhs) type(scalar_1D_t) lhs_x_rhs end function + pure module function premultiply_integer(lhs, rhs) result(lhs_x_rhs) + !! Result is the product of lhs and rhs + implicit none + integer, intent(in) :: lhs + class(scalar_1D_t), intent(in) :: rhs + type(scalar_1D_t) lhs_x_rhs + end function + pure module function postmultiply_double(lhs, rhs) result(lhs_x_rhs) !! Result is the product of lhs and rhs implicit none @@ -336,6 +354,14 @@ pure module function postmultiply_double(lhs, rhs) result(lhs_x_rhs) type(scalar_1D_t) lhs_x_rhs end function + pure module function postmultiply_integer(lhs, rhs) result(lhs_x_rhs) + !! Result is the product of lhs and rhs + implicit none + class(scalar_1D_t), intent(in) :: lhs + integer, intent(in) :: rhs + type(scalar_1D_t) lhs_x_rhs + end function + pure module function add_scalar_1D(lhs, rhs) result(total) !! Result is the sum of scalar_1D_t lhs and rhs implicit none