From 2e02a887f0bdc012c9df8ed77d64474c39ce89dd Mon Sep 17 00:00:00 2001 From: Mahesh Natarajan Date: Sat, 15 Jul 2023 15:18:21 -0700 Subject: [PATCH] Adding verification for 2d terrain - potential flow over a semi-cylinder (#1158) * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Adding 2d cylinder verification * Fixing white spaces and tabs --------- Co-authored-by: Mahesh Natarajan Co-authored-by: Aaron M. Lattanzi <103702284+AMLattanzi@users.noreply.github.com> Co-authored-by: Ann Almgren --- Docs/sphinx_doc/Verification.rst | 64 ++++++------------ .../sphinx_doc/figures/Terrain2d_Cylinder.png | Bin 0 -> 181306 bytes 2 files changed, 22 insertions(+), 42 deletions(-) create mode 100644 Docs/sphinx_doc/figures/Terrain2d_Cylinder.png diff --git a/Docs/sphinx_doc/Verification.rst b/Docs/sphinx_doc/Verification.rst index 43bd24c8d..e10a83777 100644 --- a/Docs/sphinx_doc/Verification.rst +++ b/Docs/sphinx_doc/Verification.rst @@ -11,52 +11,16 @@ The following tests are used to verify the correct behavior of different algorit Scalar Advection ---------------- -Here we present spatial and temporal convergence studies for simple scalar advection with a uniform velocity field. -The initial data has constant density and pressure, constant velocity :math:`u=10` in the x-direction, +Here we present a convergence study of the advection stencils in ERF for second through sixth order. +The initial data is constant density and pressure, constant velocity :math:`u=10` in the x-direction, and a scalar initialized with profile :math:`cos(\pi x)` in a domain that is 2 units wide and periodic in the lateral directions with slip walls on top and bottom. -The simulation is run for one period, i.e. until time :math:`t=0.2` -The first study, shown below on the left, tests the horizontal centered/upwind advection stencils for -second through sixth order. The study on the right tests the WENO 3rd and 5th order stencils, -with and without the ``smoothing'' contributions in the stencil. In all of these cases, -the time step was held fixed at :math:`\Delta t = 0.0000078125` to ensure that the spatial error dominates -the temporal error. +The simulation is run for one period, i.e. until time :math:`t=0.2` For all cases shown here, the time step +was held fixed at :math:`\Delta t = 0.0000078125` to ensure that the spatial error dominates the temporal error. -.. |aconv| image:: figures/conv_plot_spatial.png - :width: 300 - -.. |bconv| image:: figures/conv_plot_spatial_WENO.png - :width: 300 - -.. _fig:convergence_spatial - -.. table:: Convergence studies of spatial error - - +-----------------------------------------------------+------------------------------------------------------+ - | |aconv| | |bconv| | - +-----------------------------------------------------+------------------------------------------------------+ - | Spatial convergence study (centered/upwind) | Spatial convergence study (WENO) | - +-----------------------------------------------------+------------------------------------------------------+ - -The second study tests the temporal accuracy by first setting :math:`\Delta t = 0.0005` -and :math:`\Delta x = 1/8`, then reducing both :math:`\Delta t` and :math:`\Delta x` by a factor of two, keeping -the ratio of :math:`\Delta t` to :math:`\Delta x` constant. These tests were run with the 6th order accurate -spatial stencil so that the temporal error dominated the spatial error. Here we recover the expected 3rd order -accuracy of the RK3 scheme. - -.. |tconv| image:: figures/conv_plot_temporal.png - :width: 300 - -.. _fig:convergence_temporal - -.. table:: Convergence study of temporal error - - +-----------------------------------------------------+ - | |tconv| | - +-----------------------------------------------------+ - | Temporal convergence study | - +-----------------------------------------------------+ +.. image:: figures/conv_plot.png + :width: 400 Nonlinear Density Current @@ -109,3 +73,19 @@ The steady solution is shown below, as well as a log-log plot showing the error +-----------------------------------------------------+------------------------------------------------------+ | Flow profiles | Convergence study | +-----------------------------------------------------+------------------------------------------------------+ + +Potential flow over a semi-cylinder +---------------------------------------- +The potential flow over a semi-cylinder problem tests the terrain feature in two dimensions and the +effectiveness of sponge zones in preventing spurious reflections. This is a classic text book problem which +has an `exact solution`_. The density is constant and the streamwise velocity is 10 m/s, and sponge zones +are used on both the streamwise boundaries as well as the top boundary. The bottom wall is an inviscid, +slip wall. The schematic of the computational domain and the comparison of the steady state velocity profiles +with the exact solution at two different horizontal and vertical locations are shown below. + +.. _`exact solution`: https://en.wikipedia.org/wiki/Potential_flow_around_a_circular_cylinder + +.. image:: figures/Terrain2d_Cylinder.png + :width: 600 + + diff --git a/Docs/sphinx_doc/figures/Terrain2d_Cylinder.png b/Docs/sphinx_doc/figures/Terrain2d_Cylinder.png new file mode 100644 index 0000000000000000000000000000000000000000..d3fb09f10ffa03c81b4dae8ff7764218148d7e69 GIT binary patch literal 181306 zcmeFZRajih);5X;2q8fdNYKVZu;A|6cp!Li3m&9tT!V!mL4!2z8r&rbPH^|&PUF@P z&Sb5{+WY^%@8VpZi__23%wo=2Rij3Y8a3pt4pmW-!Ffph5D5th2P`Y8iiCvLjf8~i zi}?V!Gia>ri-h#Z#8N^+1uP)}QgO65x3n=sLXr)QOTc)i1}11bk9&)+142<1x6hQt z0nvUW6ca53y`sdTiG7am{|RS!<*8s}h%w)=8r~BjA!I&mDwii63s10L^}1<&%Q&)? z6&*zM!b!Xl3nG=3l^j3!J?xQ(wtn}S*5|Vzxs9N>y>oqSEiU&e?BqG<;0cCw+ecQF 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