From ec55fffd1a328a9e53ab6d4551a18e46a6aa1e5d Mon Sep 17 00:00:00 2001 From: ChongChong He Date: Fri, 5 Jan 2024 15:57:45 +1100 Subject: [PATCH] add tests to sphinx docs (#483) ### Description Add a few pages to the Sphinx docs under the tests section. ### Related issues N/A ### Checklist _Before this pull request can be reviewed, all of these tasks should be completed. Denote completed tasks with an `x` inside the square brackets `[ ]` in the Markdown source below:_ - [x] I have added a description (see above). - [ ] I have added a link to any related issues see (see above). - [x] I have read the [Contributing Guide](https://github.com/quokka-astro/quokka/blob/development/CONTRIBUTING.md). - [ ] I have added tests for any new physics that this PR adds to the code. - [ ] I have tested this PR on my local computer and all tests pass. - [ ] I have manually triggered the GPU tests with the magic comment `/azp run`. - [x] I have requested a reviewer for this PR. --- docs/references.bib | 17 ++++ docs/tests/{ => attach}/hydro_shuosher.png | Bin docs/tests/{ => attach}/hydro_sms.png | Bin docs/tests/{ => attach}/radcoupling.png | Bin docs/tests/{ => attach}/radcoupling_rsla.png | Bin .../tests/attach/radhydro_pulse_density-1.png | Bin 0 -> 48766 bytes docs/tests/attach/radhydro_pulse_density.png | Bin 0 -> 46474 bytes .../attach/radhydro_pulse_temperature-1.png | Bin 0 -> 61146 bytes .../attach/radhydro_pulse_temperature.png | Bin 0 -> 55031 bytes .../attach/radhydro_pulse_velocity-1.png | Bin 0 -> 61676 bytes docs/tests/attach/radhydro_pulse_velocity.png | Bin 0 -> 63418 bytes ...o_uniform_advecting_temperature-nobeta.png | Bin 0 -> 31581 bytes ...radhydro_uniform_advecting_temperature.png | Bin 0 -> 30782 bytes ...ydro_uniform_advecting_velocity-nobeta.png | Bin 0 -> 26027 bytes .../radhydro_uniform_advecting_velocity.png | Bin 0 -> 25212 bytes .../{ => attach}/radshock_cgs_temperature.png | Bin docs/tests/energy_exchange.rst | 4 +- docs/tests/index.rst | 2 + docs/tests/radhydro_pulse.rst | 83 +++++++++++++++ docs/tests/radhydro_uniform_adv.rst | 95 ++++++++++++++++++ docs/tests/radshock.rst | 2 +- docs/tests/shu_osher.rst | 2 +- docs/tests/sms.rst | 2 +- 23 files changed, 202 insertions(+), 5 deletions(-) rename docs/tests/{ => attach}/hydro_shuosher.png (100%) rename docs/tests/{ => attach}/hydro_sms.png (100%) rename docs/tests/{ => attach}/radcoupling.png (100%) rename docs/tests/{ => attach}/radcoupling_rsla.png (100%) create mode 100644 docs/tests/attach/radhydro_pulse_density-1.png create mode 100644 docs/tests/attach/radhydro_pulse_density.png create mode 100644 docs/tests/attach/radhydro_pulse_temperature-1.png create mode 100644 docs/tests/attach/radhydro_pulse_temperature.png create mode 100644 docs/tests/attach/radhydro_pulse_velocity-1.png create mode 100644 docs/tests/attach/radhydro_pulse_velocity.png create mode 100644 docs/tests/attach/radhydro_uniform_advecting_temperature-nobeta.png create mode 100644 docs/tests/attach/radhydro_uniform_advecting_temperature.png create mode 100644 docs/tests/attach/radhydro_uniform_advecting_velocity-nobeta.png create mode 100644 docs/tests/attach/radhydro_uniform_advecting_velocity.png rename docs/tests/{ => attach}/radshock_cgs_temperature.png (100%) create mode 100644 docs/tests/radhydro_pulse.rst create mode 100644 docs/tests/radhydro_uniform_adv.rst diff --git a/docs/references.bib b/docs/references.bib index 3a6bcc5d6..0cc7df648 100644 --- a/docs/references.bib +++ b/docs/references.bib @@ -263,3 +263,20 @@ @ARTICLE{Jin_1996 adsnote = {Provided by the SAO/NASA Astrophysics Data System} } +@article{Krumholz_2007, + title = {Equations and {{Algorithms}} for {{Mixed-frame Flux-limited Diffusion Radiation Hydrodynamics}}}, + author = {{Krumholz}, Mark R. and {Klein}, Richard I. and {McKee}, Christopher F. and {Bolstad}, John}, + year = {2007}, + month = sep, + journal = {The Astrophysical Journal}, + volume = {667}, + pages = {626--643}, + issn = {0004-637X}, + doi = {10.1086/520791}, + url = {https://ui.adsabs.harvard.edu/abs/2007ApJ...667..626K}, + urldate = {2023-10-18}, + abstract = {We analyze the mixed-frame equations of radiation hydrodynamics under the approximations of flux-limited diffusion and a thermal radiation field and derive the minimal set of evolution equations that includes all terms that are of leading order in any regime of nonrelativistic radiation hydrodynamics. Our equations are accurate to first order in v/c in the static diffusion regime. In contrast, we show that previous lower order derivations of these equations omit leading terms in at least some regimes. In comparison to comoving-frame formulations of radiation hydrodynamics, our equations have the advantage that they manifestly conserve total energy, making them very well suited to numerical simulations, particularly with adaptive meshes. For systems in the static diffusion regime, our analysis also suggests an algorithm that is both simpler and faster than earlier comoving-frame methods. We implement this algorithm in the Orion adaptive mesh refinement code and show that it performs well in a range of test problems.}, + keywords = {Astrophysics,Hydrodynamics,Methods: Numerical,Radiative Transfer}, + annotation = {ADS Bibcode: 2007ApJ...667..626K}, + file = {/Users/cche/Googledrive2/Academic/Zotero/Code/QUOKKA/Krumholz_plus_2007_Equations_and_Algorithms_for_Mixed-frame2.pdf} +} diff --git a/docs/tests/hydro_shuosher.png b/docs/tests/attach/hydro_shuosher.png similarity index 100% rename from docs/tests/hydro_shuosher.png rename to docs/tests/attach/hydro_shuosher.png diff --git a/docs/tests/hydro_sms.png b/docs/tests/attach/hydro_sms.png similarity index 100% rename from docs/tests/hydro_sms.png rename to docs/tests/attach/hydro_sms.png diff --git a/docs/tests/radcoupling.png b/docs/tests/attach/radcoupling.png similarity index 100% rename from docs/tests/radcoupling.png rename to docs/tests/attach/radcoupling.png diff --git a/docs/tests/radcoupling_rsla.png b/docs/tests/attach/radcoupling_rsla.png similarity index 100% rename from docs/tests/radcoupling_rsla.png rename to docs/tests/attach/radcoupling_rsla.png diff --git a/docs/tests/attach/radhydro_pulse_density-1.png b/docs/tests/attach/radhydro_pulse_density-1.png new file mode 100644 index 0000000000000000000000000000000000000000..73b9c3b41f7b40fe7988704201f1acf6373e62f5 GIT binary patch literal 48766 zcmcG$1yEIQ6fe4I5NQcX0R`#qQdFc-q(MLd>25frV1Sf#D=7`qeGnz3OB$r4;n4lQ z1N`s1cjnET`|ix!GtO4ej_+H&erv7$@tN{dyc?7^APB;flYOiTK^Wk#XmD&)a9U`1 z#0gF~cCy-z5JdX}`3J?O*I5#R?m%*nAF8>HtxdY?>Fs^JxFFzu@W+)GUi^lh>Mc*- z{f|tPpP0rHHFVj2dRXSY9Q?VTRbWtbkoe(DeSE5@f~TZJ$Fsh|H>6xp;9~+Ii2%LK zBQn|F-8U_n_|~`y4Gq10KBb7_4bzQ}3(|fBU zod(YezkD$~JKl?oOKdmRY4kn|=4uc={5ml)aWLhn^7YxL;?vv3G% z348Gc1&Wkmg(yQ>#Cojvi_vB7=efAe_+bSF2S0WD(Go&6?R~QT{rh(!kE|Etn;p?? 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a/docs/tests/energy_exchange.rst b/docs/tests/energy_exchange.rst index 655a4c969..b69957e74 100644 --- a/docs/tests/energy_exchange.rst +++ b/docs/tests/energy_exchange.rst @@ -33,13 +33,13 @@ The exact time-dependent solution for the matter temperature :math:`T` is: We show the numerical results below: -.. figure:: radcoupling_rsla.png +.. figure:: attach/radcoupling_rsla.png :alt: A figure showing the radiation temperature and material temperature as a function of time. The radiation temperature and matter temperatures in the reduced speed-of-light approximation, along with the exact solution for the matter temperature. -.. figure:: radcoupling.png +.. figure:: attach/radcoupling.png :alt: A figure showing the radiation temperature and material temperature as a function of time. The radiation temperature and matter temperatures, along with the exact solution for the matter temperature. \ No newline at end of file diff --git a/docs/tests/index.rst b/docs/tests/index.rst index 46b7da098..7b3afa926 100644 --- a/docs/tests/index.rst +++ b/docs/tests/index.rst @@ -10,4 +10,6 @@ Listed here are the test problems that are included with Quokka. *This page is s shu_osher sms energy_exchange + radhydro_uniform_adv + radhydro_pulse \ No newline at end of file diff --git a/docs/tests/radhydro_pulse.rst b/docs/tests/radhydro_pulse.rst new file mode 100644 index 000000000..63f2d8e52 --- /dev/null +++ b/docs/tests/radhydro_pulse.rst @@ -0,0 +1,83 @@ +.. Advecting radiation pulse test + +Advecting radiation pulse test +========================= + +This test demonstrates the code’s ability to deal with the relativistic +correction source terms that arise from the mixed frame formulation of +the RHD moment equations, in a fully-coupled RHD problem. The problems +involve the advection of the a pulse of radiation energy in an optically +thick (:math:`\tau \gg 1`) gas in both static (:math:`\beta \tau \ll 1`) +and dynamic (:math:`\beta \tau \gg 1`) diffusion regimes, with a uniform +background flow velocity :cite:`Krumholz_2007`. + +Parameters +---------- + +Initial condition of the problem in static diffusion regime: + +.. math:: + + + \begin{align} + T = T_0 + (T_1 - T_0) \exp \left( - \frac{x^2}{2 w^2} \right), \\ + w = 24 ~{\rm cm}, T_0 = 10^7 ~{\rm K}, T_1 = 2 \times 10^7 ~{\rm K} \\ + \rho=\rho_0 \frac{T_0}{T}+\frac{a_{\mathrm{R}} \mu}{3 k_{\mathrm{B}}}\left(\frac{T_0^4}{T}-T^3\right) \\ + \rho_0 = 1.2 ~{\rm g~cm^{-3}}, \mu = 2.33 ~m_{\rm H} \\ + \kappa_P=\kappa_R=\kappa = 100 \mathrm{~cm}^2 \mathrm{~g}^{-1} \\ + v = 10 ~{\rm km~s^{-1}} \\ + \tau = \rho \kappa w = 3 \times 10^3, \beta = v/c = 3 \times 10^{-5}, \beta \tau = 9 \times 10^{-2} + \end{align} + +The simulation is run till +:math:`t_{\rm end} = 2 w/v = 4.8 \times 10^{-5} ~{\rm s}`. + +Initial condition of the problem in dynamic diffusion regime: same +parameters as in the static diffusion regime except + +.. math:: + + + \begin{align} + \kappa_P=\kappa_R=\kappa=1000 \mathrm{~cm}^2 \mathrm{~g}^{-1} \\ + v = 1000 ~{\rm km~s^{-1}} \\ + t_{\rm end} = 2 w/v = 1.2 \times 10^{-4} ~{\rm s} \\ + \tau = \rho \kappa w = 3 \times 10^4, \beta = v/c = 3 \times 10^{-3}, \beta \tau = 90 + \end{align} + +Results +------- + +Static diffusion regime: + +.. figure:: attach/radhydro_pulse_temperature-1.png + :alt: radhydro_pulse_temperature-static-diffusion + + radhydro_pulse_temperature-static-diffusion + +.. figure:: attach/radhydro_pulse_density-1.png + :alt: radhydro_pulse_density-static-diffusion + + radhydro_pulse_density-static-diffusion + +.. figure:: attach/radhydro_pulse_velocity-1.png + :alt: radhydro_pulse_velocity-static-diffusion + + radhydro_pulse_velocity-static-diffusion + +Dynamic diffusion regime: + +.. figure:: attach/radhydro_pulse_temperature.png + :alt: radhydro_pulse_temperature-dynamic-diffusion + + radhydro_pulse_temperature-dynamic-diffusion + +.. figure:: attach/radhydro_pulse_density.png + :alt: radhydro_pulse_density-dynamic-diffusion + + radhydro_pulse_density-dynamic-diffusion + +.. figure:: attach/radhydro_pulse_velocity.png + :alt: radhydro_pulse_velocity-dynamic-diffusion + + radhydro_pulse_velocity-dynamic-diffusion diff --git a/docs/tests/radhydro_uniform_adv.rst b/docs/tests/radhydro_uniform_adv.rst new file mode 100644 index 000000000..b52e8278e --- /dev/null +++ b/docs/tests/radhydro_uniform_adv.rst @@ -0,0 +1,95 @@ +Uniform advecting radiation in diffusive limit +============================================== + +In this test, we simulation an advecting uniform gas where radiation and +matter are in thermal equilibrium in the co-moving frame. Following the +Lorentz tranform, the initial radiation energy and flux in the lab frame +to first order in :math:`v/c` are :math:`E_r = a_r T^4` and +:math:`F_r = \frac{4}{3} v E_r`. + +Parameters +---------- + +.. math:: + + + \begin{align} + T_0 = 10^7~{\rm K} \\ + \rho_0 = 1.2 ~{\rm g~cm^{-3}}, \mu = 2.33 ~m_{\rm H} \\ + \kappa_P=\kappa_R=100 \mathrm{~cm}^2 \mathrm{~g}^{-1} \\ + v_{x,0} = 10 ~{\rm km~s^{-1}} \\ + E_{r,0} = a_r T_0^4 \\ + F_{x,0} = \frac{4}{3} v_{x,0} E_{r,0} \\ + t_{\rm end} = 4.8 \times 10^{-5} ~{\rm s} + \end{align} + +Results +------- + +With :math:`O(\beta \tau)` terms: + +.. figure:: attach/radhydro_uniform_advecting_temperature.png + :alt: A figure showing the radiation temperature and material temperature as a function of time. + + The radiation temperature and matter temperatures, along with the exact solution. + +.. figure:: attach/radhydro_uniform_advecting_velocity.png + :alt: A figure showing the radiation velocity and material velocity as a function of time. + + The matter velocity, along with the exact solution. + +Without :math:`O(\beta \tau)` terms: + +.. figure:: attach/radhydro_uniform_advecting_temperature-nobeta.png + :alt: A figure showing the radiation temperature and material temperature as a function of time. + + The radiation temperature and matter temperatures, along with the exact solution. + +.. figure:: attach/radhydro_uniform_advecting_velocity-nobeta.png + :alt: A figure showing the radiation velocity and material velocity as a function of time. + + The matter velocity, along with the exact solution. + + +Physics +------- + +In the transport equation, both the radiation energy and flux are +unchanged because the radiation flux and pressure are uniform. In the +matter-radiation exchange step, the source term is zero since the +radiation and matter are in equilibrium. Finally, the flux is updated +following + +.. math:: + + + \mathbf{F}_{r}^{(t+1)} = \frac{\mathbf{F}_{r}^{(t)} + \Delta t \left[ \rho \kappa_P \left(\frac{4 \pi B}{c}\right) \boldsymbol{v}c + \rho \kappa_F (\boldsymbol{v} :\boldsymbol{P}_r) c \right] }{1+\rho \kappa_{F} {c} \Delta t}. + +With :math:`F_{r}^{(t)} = 4 v E_{r}^{(t)} / 3`, and +:math:`\kappa_P=\kappa_R=\kappa`, we have + +.. math:: + + + \mathbf{F}_{r}^{(t+1)} = \frac{\frac{4}{3} v E_r^{(t)} + \Delta t \left[ \rho \kappa E_r^{(t)} \boldsymbol{v}c + \rho \kappa \boldsymbol{v} (\frac{1}{3}E_r^{(t)}) c \right] }{1+\rho \kappa {c} \Delta t} = \frac{4}{3} v E_r^{(t)} = F_{r}^{(t)} + +Therefore, :math:`F_r` remains constant. This demonstrates that the code +is invariant under Lorentz transformation. + +We can also show that, with the :math:`O(\beta \tau)` terms in the +matter-radiation exchange step, the space-like component of the +radiation four-force vanishes: + +.. math:: + + + \begin{align} + -G &= -\rho \kappa_F \frac{\boldsymbol{F}_r}{c} + \rho \kappa_P\left(\frac{4 \pi B}{c}\right) \frac{\boldsymbol{v}}{c}+\rho \kappa_F \frac{\boldsymbol{v} :\boldsymbol{P}_r}{c} \\ + &= -\rho \kappa \frac{4}{3} E_r v / c + \rho \kappa E_r v / c+ \rho \kappa \frac{1}{3} E_r v / c \\ + &= 0 + \end{align} + +.. |radhydro_uniform_advecting_temperature| image:: attach/radhydro_uniform_advecting_temperature.png +.. |radhydro_uniform_advecting_velocity| image:: attach/radhydro_uniform_advecting_velocity.png +.. |radhydro_uniform_advecting_temperature-nobeta| image:: attach/radhydro_uniform_advecting_temperature-nobeta.png +.. |radhydro_uniform_advecting_velocity-nobeta| image:: attach/radhydro_uniform_advecting_velocity-nobeta.png diff --git a/docs/tests/radshock.rst b/docs/tests/radshock.rst index d651a86a8..b91d561cf 100644 --- a/docs/tests/radshock.rst +++ b/docs/tests/radshock.rst @@ -53,7 +53,7 @@ Since the solution is given assuming radiation diffusion, we set the Eddington f We use the RK2 integrator with a CFL number of 0.2 and a mesh of 256 equally-spaced zones. After 3 shock crossing times, we obtain a solution for the radiation temperature and matter temperature that agrees to better than 0.5% (in relative L1 norm) with the steady-state ODE solution to the radiation hydrodynamics equations: -.. figure:: radshock_cgs_temperature.png +.. figure:: attach/radshock_cgs_temperature.png :alt: A figure showing the radiation temperature and material temperature as a function of position. The radiation temperature is shown in the black solid and dashed lines, with the dashed line showing the semi-analytic solution. The material temperature is shown in the red lines, with the semi-analytic solution shown with the dashed line. \ No newline at end of file diff --git a/docs/tests/shu_osher.rst b/docs/tests/shu_osher.rst index 774d9f7cf..5d0af44c0 100644 --- a/docs/tests/shu_osher.rst +++ b/docs/tests/shu_osher.rst @@ -36,7 +36,7 @@ the interface states in the characteristic variables, as done in §4 of :cite:`S The reference solution is computed using Athena++ with PPM reconstruction in the characteristic variables on a grid of 1600 zones. -.. figure:: hydro_shuosher.png +.. figure:: attach/hydro_shuosher.png :alt: A figure showing the numerical solution to the Shu-Osher test. The density is shown as the solid blue line. There is no exact solution for this problem. \ No newline at end of file diff --git a/docs/tests/sms.rst b/docs/tests/sms.rst index 35606eb99..aa733de7f 100644 --- a/docs/tests/sms.rst +++ b/docs/tests/sms.rst @@ -35,7 +35,7 @@ We use the RK2 integrator with a fixed timestep of :math:`10^{-3}` and a mesh of 100 equally-spaced cells. The contact discontinuity is initially placed at :math:`x=0.5`. -.. figure:: hydro_sms.png +.. figure:: attach/hydro_sms.png :alt: A figure showing the numerical solution to the slow-moving shock test. The density is shown as the solid blue line. The exact solution is the solid orange line. \ No newline at end of file