From 5751900b8896aedd4f57e07709fb315dfffe1431 Mon Sep 17 00:00:00 2001 From: Lucas Esclapez <13371051+esclapez@users.noreply.github.com> Date: Wed, 1 Mar 2023 13:27:39 -0800 Subject: [PATCH] Extend validation section with EBchannelFlow and 1D PMF. (#180) * Add EBChannelFlow validation test case. LES results are still in process. * Add data from a laminar premixed flame case and comparisons with Cantera. * A fresh pass on the doc. * Add a couple of missing files. * Add the Re_t = 934 case to the validation and stop there for now. * Trailing whitespace. --- Docs/source/manual/Model.rst | 12 +- Docs/source/manual/Performances.rst | 4 +- Docs/source/manual/Tutorials_FlowPastCyl.rst | 22 +- Docs/source/manual/Validation.rst | 309 +++++++++++++++++- Docs/source/manual/_static/theme.css | 8 + Docs/source/manual/conf.py | 6 +- .../EBChannelFlow/Uplus_Re180_DNS_LMeX.png | Bin 0 -> 52691 bytes .../EBChannelFlow/Uplus_Re395_LES_LMeX.png | Bin 0 -> 51311 bytes .../EBChannelFlow/Uplus_Re934_LES_LMeX.png | Bin 0 -> 51400 bytes .../VelRMSplus_Re180_DNS_LMeX.png | Bin 0 -> 65196 bytes .../VelRMSplus_Re395_LES_LMeX.png | Bin 0 -> 71547 bytes .../VelRMSplus_Re934_LES_LMeX.png | Bin 0 -> 74443 bytes .../EBChannelFlow/nu_t_Re934_LES_LMeX.png | Bin 0 -> 37489 bytes .../PremixedFlame/LMeX_DRM19_Phi0p9.png | Bin 0 -> 167837 bytes .../PremixedFlame/LMeX_FinevsCoarse.png | Bin 0 -> 177502 bytes 15 files changed, 327 insertions(+), 34 deletions(-) create mode 100644 Docs/source/manual/_static/theme.css create mode 100644 Docs/source/manual/images/validations/EBChannelFlow/Uplus_Re180_DNS_LMeX.png create mode 100644 Docs/source/manual/images/validations/EBChannelFlow/Uplus_Re395_LES_LMeX.png create mode 100644 Docs/source/manual/images/validations/EBChannelFlow/Uplus_Re934_LES_LMeX.png create mode 100644 Docs/source/manual/images/validations/EBChannelFlow/VelRMSplus_Re180_DNS_LMeX.png create mode 100644 Docs/source/manual/images/validations/EBChannelFlow/VelRMSplus_Re395_LES_LMeX.png create mode 100644 Docs/source/manual/images/validations/EBChannelFlow/VelRMSplus_Re934_LES_LMeX.png create mode 100644 Docs/source/manual/images/validations/EBChannelFlow/nu_t_Re934_LES_LMeX.png create mode 100644 Docs/source/manual/images/validations/PremixedFlame/LMeX_DRM19_Phi0p9.png create mode 100644 Docs/source/manual/images/validations/PremixedFlame/LMeX_FinevsCoarse.png diff --git a/Docs/source/manual/Model.rst b/Docs/source/manual/Model.rst index b548754e..19bc01ed 100644 --- a/Docs/source/manual/Model.rst +++ b/Docs/source/manual/Model.rst @@ -176,11 +176,11 @@ An overview of `PeleLMeX` time-advance function is provided in the figure below .. figure:: images/model/PeleLMeX_Algorithm.png :align: center - :figwidth: 70% + :figwidth: 50% -The three steps of the low Mach number projection scheme described in Section `ssec:projScheme`_ are referenced to better emphasize how the thermodynamic solve is -closely weaved into the fractional step appraoch. Striped boxes indicate where the Godunov procedure described in Section `ssec:advScheme`_ is employed while -the four different linear solves are highlighted. +The three steps of the low Mach number projection scheme described :ref:`below ` are referenced to better +emphasize how the thermodynamic solve is closely weaved into the fractional step appraoch. Striped boxes indicate where the +:ref:`Godunov procedure ` is employed while the four different linear solves are highlighted. Low Mach number projection scheme ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ @@ -345,7 +345,7 @@ This difference is illustrated in the figure below comparing the multi-level tim .. figure:: images/model/PeleLMeX_Subcycling.png :align: center - :figwidth: 90% + :figwidth: 60% * `PeleLM` will recursively advance finer levels, halving the time step size (when using a refinement ratio of 2) at each level. For instance, considering a 3 levels simulation, `PeleLM` advances the coarse `Level0` over a :math:`\Delta t_0` step, then `Level1` over a :math:`\Delta t_1` step and `Level2` over two :math:`\Delta t_2` steps, performing an interpolation of the `Level1` data after the first `Level2` step. At this point, a synchronization step is performed to ensure that the fluxes are conserved at coarse-fine interface and a second `Level1` step is performed, followed by the same two `Level2` steps. At this point, two synchronizations are needed between the two pairs of levels. * In order to get to the same physical time, `PeleLMeX` will perform 4 time steps of size similar to `PeleLM`'s :math:`\Delta t_2`, advancing all the levels at once. The coarse-fine fluxes consistency is this time ensured by averaging down the face-centered fluxes from fine to coarse levels. Additionnally, the state itself is averaged down at the end of each SDC iteration. @@ -361,7 +361,7 @@ mesh is uniform and block-structured, but the boundary of the irregular-shaped c through this mesh. Each cell in the mesh becomes labeled as regular, cut or covered, and the finite-volume based discretization methods traditionally used in AMReX applications need to be modified to incorporate these cell shapes. AMReX provides the necessary EB data structures, including volume and area fractions, surface normals and centroids, -as well as local connectivity information. The fluxes described in Section `ssec:projScheme`_ are then modified to account +as well as local connectivity information. The fluxes described in :ref:`the projection scheme section ` are then modified to account for the apperture opening between adjacent cells and the additional EB-fluxes are included when constructing the cell flux divergences. A common problem arising with EB is the presence of the small cut-cells which can either introduce undesirable constraint on diff --git a/Docs/source/manual/Performances.rst b/Docs/source/manual/Performances.rst index 122a403d..cafccb5d 100644 --- a/Docs/source/manual/Performances.rst +++ b/Docs/source/manual/Performances.rst @@ -106,7 +106,7 @@ of the stiff chemistry integration, especially on the GPU. Results on Crusher (ORNL) ^^^^^^^^^^^^^^^^^^^^^^^^^ -Crusher is the testbed for DOE's first ExaScale platform Frontier. Crusher's `nodes `_ consists of a single AMD EPYC 7A53 (Trento), 64 cores CPU connected to 4 AMD MI250X, +Crusher is the testbed for DOE's first ExaScale platform Frontier. `Crusher's nodes `_ consists of a single AMD EPYC 7A53 (Trento), 64 cores CPU connected to 4 AMD MI250X, each containing 2 Graphics Compute Dies (GCDs) for a total of 8 GCDs per node. When running with GPU acceleration, `PeleLMeX` will use 8 MPI ranks with each access to one GCD, while when running on flat MPI, we will use 64 MPI-ranks. The FlameSheet case is ran using 2 levels of refinement (3 levels total) and the following domain size and cell count: @@ -149,7 +149,7 @@ Results on Summit (ORNL) ^^^^^^^^^^^^^^^^^^^^^^^^ Summit was launched in 2018 as the first DOE's fully GPU-accelerated platform. -Summit's `nodes `_ consists +`Summit's nodes `_ consists of a two IBM Power9 CPU connected to 6 NVIDIA V100 GPUs. When running with GPU acceleration, `PeleLMeX` will use 6 MPI ranks with each access to one V100, while when running on flat MPI, we will use 42 MPI-ranks. Note that in contrast with newer GPUs available on Perlmutter or Crusher, Summit's V100s only have 16GBs of diff --git a/Docs/source/manual/Tutorials_FlowPastCyl.rst b/Docs/source/manual/Tutorials_FlowPastCyl.rst index 6b318d29..6f0b73a0 100644 --- a/Docs/source/manual/Tutorials_FlowPastCyl.rst +++ b/Docs/source/manual/Tutorials_FlowPastCyl.rst @@ -33,25 +33,25 @@ Follow the steps listed below to get to this point: #. Move into the Exec folder containing the ``FlowPastCylinder``. To do so: :: - cd PeleLMeX/Exec/RegTests/EB_FlowPastCylinder + cd PeleLMeX/Exec/RegTests/EB_FlowPastCylinder #. Finally, setup the environment variables providing paths to `PeleLMeX` and its dependencies. This can done in one of two ways: #. Directly into the `GNUmakefile` by updating the top-most lines as follows: :: - PELELMEX_HOME = - AMREX_HOME =${PELELMEX_HOME}/Submodules/amrex - AMREX_HYDRO_HOME =${PELELMEX_HOME}/Submodules/AMReX-Hydro - PELE_PHYSICS_HOME =${PELELMEX_HOME}/Submodules/PelePhysics + PELELMEX_HOME = + AMREX_HOME =${PELELMEX_HOME}/Submodules/amrex + AMREX_HYDRO_HOME =${PELELMEX_HOME}/Submodules/AMReX-Hydro + PELE_PHYSICS_HOME =${PELELMEX_HOME}/Submodules/PelePhysics #. Exporting shell environement variables (using *bash* for instance): :: - export PELELMEX_HOME= - export AMREX_HOME=${PELELMEX_HOME}/Submodules/amrex - export AMREX_HYDRO_HOME=${PELELMEX_HOME}/Submodules/AMReX-Hydro - export PELE_PHYSICS_HOME=${PELELMEX_HOME}/Submodules/PelePhysics + export PELELMEX_HOME= + export AMREX_HOME=${PELELMEX_HOME}/Submodules/amrex + export AMREX_HYDRO_HOME=${PELELMEX_HOME}/Submodules/AMReX-Hydro + export PELE_PHYSICS_HOME=${PELELMEX_HOME}/Submodules/PelePhysics Both options require to provide the path to where you cloned `PeleLMeX`. Note that using the first option will overwrite any environement variables you might have previously defined when using this `GNUmakefile`. @@ -61,7 +61,7 @@ You're good to go ! Numerical setup --------------- -In this section we review the content of the various input files for the flow past cylinder test case. To get additional information about the keywords discussed, the user is referred to section :ref:`sec:control`. +In this section we review the content of the various input files for the flow past cylinder test case. To get additional information about the keywords discussed, the user is referred to :doc:`LMeXControls`. Test case and boundary conditions ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ @@ -173,7 +173,7 @@ This initial solution is constructed via the routine ``pelelm_initdata()``, in t Numerical scheme ^^^^^^^^^^^^^^^^ -The ``NUMERICS CONTROL`` block can be modified by the user to increase the number of SDC iterations. Note that there are many other parameters controlling the numerical algorithm that the advanced user can tweak, but we will not talk about them in the present Tutorial. The interested user can refer to section :ref:`sec:control`. +The ``NUMERICS CONTROL`` block can be modified by the user to increase the number of SDC iterations. Note that there are many other parameters controlling the numerical algorithm that the advanced user can tweak, but we will not talk about them in the present Tutorial. The interested user can refer to :doc:`LMeXControls`. Building the executable diff --git a/Docs/source/manual/Validation.rst b/Docs/source/manual/Validation.rst index 69b41d4c..8765b214 100644 --- a/Docs/source/manual/Validation.rst +++ b/Docs/source/manual/Validation.rst @@ -1,7 +1,83 @@ PeleLMeX Verification & Validations =================================== -This section is work-in-progress. +This section assembles results of `PeleLMeX` simulations on a set a test cases +for which a reference solution can be obtained from the litterature or an +analytical solution exists. + +Laminar premixed flame +~~~~~~~~~~~~~~~~~~~~~~ + +The case of a laminar premixed flame is a foundational test case for a reactive +flow solver. A laminar premixed flame setup is available in ``Exec/RegTests/FlameSheet``. +The case reported hereafter is that of a planar laminar methane/air flame at +atmospheric conditions and a lean equivalence ratio of 0.9. The initial condition +is obtained from a Cantera simulation using +the DRM19 mechanism and the simulation is conducted starting with a coarse resolution +:math:`d_{l,0}/\delta_x = 3.5` (3.5 grid cells in the flame thermal thickness) and progressively +refined to :math:`d_{l,0}/\delta_x = 110` using AMR. Note that the simulation is carried for +about 30 :math:`\tau_f = d_{l,0} / S_{l,0}` before adding refinement levels ensuring that initial +numerical noise introduced by interpolating the Cantera solution onto the cartesian grid is +completely removed. + +The `PeleLMeX` results obtained with the finest grid are compared to that of Cantera in :numref:`PMFLMeXCantera`. +Profiles of major and intermediate species as well as temperature across the flame front are +displayed, with Cantera results shown as black ticked lined underlying each continuous line obtained +with `PeleLMeX`, demonstrating the solver accuracy. + +.. figure:: images/validations/PremixedFlame/LMeX_DRM19_Phi0p9.png + :name: PMFLMeXCantera + :align: center + :figwidth: 50% + + : One-dimentional flame profiles with PeleLMeX and Cantera (underlying black dashed lines) + +It is interesting to see how resolution affect the prediction of `PeleLMeX`. The :numref:`PMFTableResolution` +shows the laminar flame speed, obtained by numerically integrating the fuel consumption rate, at +increasing level of refinement. For each AMR level addition, simulation are conducted for about 10 :math:`\tau_f`, +until the flame speed stabilizes. With only a handful of cells across the flame thermal thickness, the flame +speed is recovered with an accuracy close to 1.5%. + +.. list-table:: Effect of resolution on the laminar flame speed + :name: PMFTableResolution + :align: center + :widths: 50 25 25 25 25 25 25 + :header-rows: 1 + + * - :math:`d_{l,0}/\delta_x` [-] + - 3.44 + - 6.88 + - 13.8 + - 27.5 + - 55 + - 110 + * - :math:`S_{l,0}` [m/s] + - 0.35696 + - 0.35144 + - 0.35408 + - 0.35473 + - 0.35488 + - 0.35494 + * - Error (vs. Cantera) [%] + - 0.02 + - 1.54 + - 0.8 + - 0.6 + - 0.58 + - 0.57 + +Additionally, :numref:`PMFLMeXCrseFine` compares profiles of major and intermediate species as well as +temperature across the flame front for the coarsest and the finest resolution employed. Results +indicates that major species (or temperature) are well captured whereas short lived species peak +values are locally off due to the lack of resolution but are stil reasonably well located within +the flame front. + +.. figure:: images/validations/PremixedFlame/LMeX_FinevsCoarse.png + :name: PMFLMeXCrseFine + :align: center + :figwidth: 50% + + : Comparison of a coarsed and finely resolved 1D flame in PeleLMeX Laminar Poiseuille flow ~~~~~~~~~~~~~~~~~~~~~~~ @@ -23,19 +99,25 @@ the input parameters are very similar to the PeleC counterpart of this case. The steady-state :math:`x`-velocity profiles accross the pipe diameter -at increasing resolution are plotted along with the theorerical profile: +at increasing resolution are plotted along with the theorerical profile in :numref:`PoiseuilleVelProf`: .. figure:: images/validations/Poiseuille3D/PoiseuilleVelProf.png + :name: PoiseuilleVelProf :align: center - :figwidth: 60% + :figwidth: 50% + + : Axial velocity profile at increasing resolution with PeleLMeX A more quantitative evaluation of PeleLMeX results is obtained by calculating the L2 norm of the error against the analytical profile: .. figure:: images/validations/Poiseuille3D/PoiseuilleConvergence.png + :name: PoiseuilleConvergence :align: center - :figwidth: 60% + :figwidth: 50% + + : L2-norm of the axial velocity profile as function of the number of cells across the pipe diameter showing second-order convergence for this diffusion dominated flow. @@ -72,17 +154,18 @@ to the results of a high-order spectral solver with a 512^3 resolution. that even though `PeleLMeX` uses a 2nd-order scheme, reasonable accuracy compared to the spectral results is obtained when the resolution is sufficient. -.. figure:: images/validations/TaylorGreen/KinEnergy.png - :align: center - :figwidth: 60% +.. |TGKinEnergy| image:: images/validations/TaylorGreen/KinEnergy.png + :width: 48% -.. figure:: images/validations/TaylorGreen/Dissipation.png - :align: center - :figwidth: 60% +.. |TGDiss| image:: images/validations/TaylorGreen/Dissipation.png + :width: 48% -.. figure:: images/validations/TaylorGreen/Enstrophy.png - :align: center - :figwidth: 60% +.. |TGEnstrophy| image:: images/validations/TaylorGreen/Enstrophy.png + :width: 48% + +|TGKinEnergy| |TGDiss| + +|TGEnstrophy| Additionnally, it is interesting to compare the different advection schemes available in `PeleLMeX` (namely, *Godunov_PLM*, *Godunov_PPM*, *Godunov_BDS*, @@ -90,7 +173,205 @@ available in `PeleLMeX` (namely, *Godunov_PLM*, *Godunov_PPM*, *Godunov_BDS*, .. figure:: images/validations/TaylorGreen/Enstrophy_AllSchemes.png :align: center - :figwidth: 60% + :figwidth: 48% On this particular case, the differences between the advection schemes are fairly marginal compared to those observed at different grid resolutions. + +Channel Flow using EB +~~~~~~~~~~~~~~~~~~~~~ + +We present results of the classical periodic channel flow, available in the +``Exec/RegTests/EB_PipeFlow`` folder. Simulations are performed at three +stress Reynold number :math:`Re_{\tau}` = 180, 395 and 934 corresponding +to the cases described in `Kim et al., 1986 `_, +`Moser et al., 1999 `_ and +`Hoyas and Jimenez, 2006 `_, respectively. A first +DNS is performed at :math:`Re_{\tau}` = 180, then the LES models implementation is tested +at higher Reynold numbers. + +For all cases, the configuration is periodic in the :math:`x` and :math:`z` directions and wall boundaries are +imposed in the :math:`y` direction using Embedded Boundaries. + +DNS results at :math:`Re_{\tau}` = 180 +###################################### + +The channel half width :math:`\delta` is set to 0.005 m, and the computational domain extend +in +/- 0.0052 m in :math:`y` with EB intersecting the domain at +/- :math:`\delta`. A background pressure gradient in +imposed in the :math:`x` to compensate wall friction. The base grid and two levels of refinement are described in :numref:`EBCDomain`: + +.. list-table:: DNS Channel flow domain + :name: EBCDomain + :align: center + :widths: 50 25 25 25 + :header-rows: 1 + + * - + - :math:`x` + - :math:`y` + - :math:`z` + * - Domain size + - 6.24 :math:`\delta` + - 2.08 :math:`\delta` + - 3.12 :math:`\delta` + * - Base grid L0 + - 384 + - 128 + - 192 + * - L1 + - 768 + - 256 + - 384 + * - L2 + - 1536 + - 512 + - 768 + +The fluid in the simulation is air at ambient pressure and a temperature of 750.0 K, the physical +property of which are summarized in :numref:`EBCFluidProp`: + +.. list-table:: Fluid properties + :name: EBCFluidProp + :align: center + :widths: 25 25 25 25 25 25 + :header-rows: 1 + + * - + - Pressure + - Temperature + - Density + - :math:`\mu` + - :math:`\nu` + * - Value [MKS] + - 102325.0 + - 750.0 + - 0.468793 + - 3.57816e-5 + - 7.63271e-5 + +The characteristics of the flows are reported in :numref:`EBCFlowChar`: + +.. list-table:: DNS Channel flow characteristics + :name: EBCFlowChar + :align: center + :widths: 25 25 25 25 35 + :header-rows: 1 + + * - :math:`Re_{\tau}` + - :math:`u_{\tau}` + - :math:`\tau_w` + - :math:`dp/dx` + - :math:`t^* = \delta/u_{\tau}` + * - 180.2 + - 2.75122 + - 3.5485 + - -709.79 + - 1.817e-3 + +Two levels of refinement, targeted on the EB, are employed in order to sufficiently resolve the boundary +layer. The mesh characteristics are summarized in :numref:`EBCMeshes`. The :math:`y^+` value is that of +the cell center of the first full cell (uncut by the EB). + +.. list-table:: Mesh characteristics + :name: EBCMeshes + :align: center + :widths: 25 25 25 25 35 + :header-rows: 1 + + * - :math:`Re_{\tau}` + - :math:`\Delta y^+ L0` + - :math:`\Delta y^+ Lmax` + - :math:`y^+` + - Cells count + * - 180.2 + - 2.93 + - 0.732 + - 0.479 + - 56.6 M + +Simulations are carried out for 20 eddy turn over time :math:`t^*` to reach statistically steady +conditions and data are then spatially averaged in the periodic directions and averaged in time over 10 :math:`t^*` +to get the velocity statistics in the direction normal to the wall. + +.. |DNS180Uplus| image:: images/validations/EBChannelFlow/Uplus_Re180_DNS_LMeX.png + :width: 48% + +.. |DNS180Urms| image:: images/validations/EBChannelFlow/VelRMSplus_Re180_DNS_LMeX.png + :width: 48% + +|DNS180Uplus| |DNS180Urms| + +Results indicate that `PeleLMeX` is able to reproduce accurately the DNS data obtained with +a high-order spectral solver, provided sufficient resolution at the wall. + +LES results at :math:`Re_{\tau}` = 395, 934 +########################################### + +The channel half width :math:`\delta` is set to 0.01 m, and the computational domain extend +in +/- 0.0101 m in :math:`y` with EB intersecting the domain at +/- :math:`\delta`. The base grid is coarser +than the DNS one by a factor of 2. A background pressure gradient in imposed in the :math:`x` to compensate +wall friction. The fluid conditions are similar to that of the DNS case and the flow +and mesh characteristics are summarized in :numref:`EBCLESFlowsChar`: + +.. list-table:: LES Channel flow characteristics + :name: EBCLESFlowsChar + :align: center + :widths: 25 25 25 25 25 25 25 + :header-rows: 1 + + * - :math:`Re_{\tau}` + - :math:`u_{\tau}` + - :math:`\tau_w` + - :math:`dp/dx` + - :math:`t^* = \delta/u_{\tau}` + - :math:`\Delta y^+ L0` + - :math:`\Delta y^+ Lmax` + * - 395 + - 3.01492 + - 4.26121 + - -426.121 + - 3.3317e-3 + - 12.467 + - 6.2336 + * - 934 + - 7.12895 + - 23.8250 + - -2382.50 + - 1.4027e-3 + - 29.479 + - 7.36984 + +Note that a single level of refinement is employed for the :math:`Re_{\tau}` = 395 while two are +used for :math:`Re_{\tau}` = 934 in order to provide sufficient (but still below :math:`y^+=1`) +resolution near the walls. + +Simulations are performed with the WALE LES SGS model. The plots below shows that `PeleLMeX` is +able to reproduce the normalized velocity profile reasonably well even though the resolution +requirements for a Wall Resolved LES are not quite attained with the grid employed here. + +.. |LES395Uplus| image:: images/validations/EBChannelFlow/Uplus_Re395_LES_LMeX.png + :width: 48% + +.. |LES395Urms| image:: images/validations/EBChannelFlow/VelRMSplus_Re395_LES_LMeX.png + :width: 48% + +|LES395Uplus| |LES395Urms| + +.. |LES934Uplus| image:: images/validations/EBChannelFlow/Uplus_Re934_LES_LMeX.png + :width: 48% + +.. |LES934Urms| image:: images/validations/EBChannelFlow/VelRMSplus_Re934_LES_LMeX.png + :width: 48% + +|LES934Uplus| |LES934Urms| + +The velocity variance in the plot above show distinctive drops around coarse/fine interfaces, +where the filter size change and a the subgrid-scale contribution increases as depicted on the figure below showing the +subgrid-scale viscosity for the :math:`Re_{\tau}` = 934 case. + +.. figure:: images/validations/EBChannelFlow/nu_t_Re934_LES_LMeX.png + :align: center + :figwidth: 48% + +Further work is ongoing to assess how to better handle large LES filter size changes in the context +of AMR-LES diff --git a/Docs/source/manual/_static/theme.css b/Docs/source/manual/_static/theme.css new file mode 100644 index 00000000..6242b5d2 --- /dev/null +++ b/Docs/source/manual/_static/theme.css @@ -0,0 +1,8 @@ +.wy-nav-content { + max-width: 1000px !important; +} +img.align-center { + margin-left: auto; + margin-right: auto; + display: block; +} diff --git a/Docs/source/manual/conf.py b/Docs/source/manual/conf.py index a173676d..8a5aaff7 100644 --- a/Docs/source/manual/conf.py +++ b/Docs/source/manual/conf.py @@ -61,7 +61,8 @@ html_logo = "_static/swirlH2Fast_OH_vort_256.png" numfig = True -numfig_format = {'figure': '%s', 'table': '%s', 'code-block': '%s'} +numfig_format = {'figure': 'Fig. %s', 'table': 'Table %s', 'code-block': '%s'} +numfig_secnum_depth=3 # -- Options for HTML 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