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This tutorial analyses the flow through an elbow discretized with a 3D tetrahedral unstructured mesh.
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* [Steady state flow](case_elbow.html#Steady_state_flow_2) : description of the problem
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* [Domain Boundaries](case_elbow.html#Domain_boundaries_2) : boundaries of the computational domain
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* [Case convergence](case_elbow.html#Convergence_2) : numerical convergence of the model
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* [Velocity field](case_elbow.html#Velocity_profiles_2) : post-processing of velocity field and pressure drop according to Re
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* [Pressure drop](case_elbow.html#Pressure_drop) : pressure drop vs. Reynolds number
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* [Input files](case_elbow.html#Input_files_2) : detailed description of case input files
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* [elbow.dat (case global parameters)](case_elbow.html#elbow_dat)
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* [elbow.dom.dat (domain input data)](case_elbow.html#elbow_dom_dat)
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* [elbow.geo.dat (mesh information)](case_elbow.html#elbow_geo_dat)
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* [elbow.set.dat (groups for post-processing, optional)](case_elbow.html#elbow_set_dat)
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* [elbow.fix.dat (boundary conditions data)](case_elbow.html#elbow_fix_dat)
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* [elbow.ker.dat](case_elbow.html#elbow_ker_dat)
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* [elbow.nsi.dat (incompressible Navier-Stokes solver parameters)](case_elbow.html#elbow_nsi_dat)
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* [elbow.post.alya.dat (alya2pos parameters)](case_elbow.html#elbow_post_alya_dat)
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* * *
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* * *
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# <a class="anchor" id="Steady_state_flow_2"></a>Steady state flow
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![image](uploads/ba9d7c69e8fd8c107569559d101d6776/image.png)
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<center>elbow case – 3D turbulent flow (Re=1e4) [(click for Turbulent Flow Development animation)](http://www.youtube.com/watch?feature=player_embedded&v=65YWYUH7zB8)</center>
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Simulation settings are specified to reach a steady state flow condition. The case is run with different Reynolds numbers, by changing the viscosity of the fluid, in order to analyze pressure drop variation. Total pipe length is roughly 6m.
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# <a class="anchor" id="Domain_boundaries_2"></a>Domain Boundaries
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* * *
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* * *
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Boundary numbers are as follow, outlet on the short straight. Inlet velocity is specified with a paraboloid surface function.
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![image](uploads/54403dd217af405828671cba2ed5e2da/image.png)
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<center>elbow case – domain boundaries</center>
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* * *
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* * *
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# <a class="anchor" id="Convergence_2"></a>Case convergence
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Time iteration is let to calculate automatically the time increment within each timestep and the maximum number of iterations is set to infinity (1e6), so that the simulation will finish when convergence criteria are reached. Next figure show two convergence plot (alya-all-nsi app) of the simulations with Re=150.
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![image](uploads/4c348a489ec56cba7f40864931e9fce1/image.png)
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<center>elbow case – numerical convergence</center>
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* * *
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* * *
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# <a class="anchor" id="Velocity_profiles_2"></a>Velocity field
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An animation of the resulting turbulent flow is found in this link: see elbow case animation. This is only a roughly approximate solution, since Re=1.0e4 is much beyond the limit of laminar flow and no turbulence model is used in the simulation. Next figure shows velocity results for Re=100:
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![image](uploads/1108db062f9faef759de3057ea12ab2b/image.png)
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<center>elbow case – velocity distribution (Re = 100)</center>
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* * *
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* * *
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# <a class="anchor" id="Pressure_drop"></a>Pressure drop
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In the following, pipe pressure drop results are compared to semi-empirical results calculated with classical engineering methods, such as Poiseuille and Darcy equations.
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![image](uploads/ddd0bb885f070b40945b343527a6639a/image.png)
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<center>elbow case – empirical data</center>
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The relation between flow pressure drop and Reynolds number is analyzed from the previous runs.
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Reynolds number is calculated as follows (taking ‘l’ as pipe diameter):
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```math
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\textnormal{Re} = \frac{(\rho \cdot {U} \cdot {l})}{\mu}
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```
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Theoretical pressure drop calculations have been performed using Poiseuille equation to account for pressure losses along pipe length, and an empirical formula to add minor fitting pressure loss:
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```math
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{\Delta p} = 8 \cdot \frac{{Q} \cdot \nu \cdot {l}}{\pi{R}^4} + \frac{1}{2}{k} \rho {U}^2}
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```
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being,
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* Q = mass rate
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* ν = dynamic viscosity
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* l = pipe axis lenght
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* k = elbow pressure loss coefficient (diagram)
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* ρ = density
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Next table and plot show the correlation between results calculated by Alya and the theoretical-empirical ones:
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<center>
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<table class="doxtable">
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<tbody>
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<tr>
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<td>mu</td>
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<td>2.000E-02</td>
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<td>1.000E-02</td>
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<td>6.667E-03</td>
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</tr>
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<tr>
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<td>Re</td>
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<td>5.000E+01</td>
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<td>1.000E+02</td>
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<td>1.500E+02</td>
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</tr>
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<tr>
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<td>Alya pressure drop</td>
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<td>2.0903</td>
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<td>1.0934</td>
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<td>0.7906</td>
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</tr>
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<tr>
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<td>Theoretical pressure drop</td>
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<td>2.0515</td>
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<td>1.0315</td>
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<td>0.6982</td>
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</tr>
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<tr>
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<td>error</td>
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<td>1.9%</td>
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<td>6.0%</td>
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<td>13.2%</td>
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</tr>
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</tbody>
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</table>
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</center>
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![image](uploads/62a37c3d2782b7b0fa63330040cd65db/image.png)
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<center>elbow case – pressure drop vs. Reynolds number</center>
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Pressure drop values from the different Alya runs are obtained from the file elbow-boundary.nsi.set, by reading inlet and outlet mean pressure values from the last time step results, corresponding in this case boundary sets 9 and 13 to inlet and outlet surfaces respectively.
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* * *
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* * *
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# <a class="anchor" id="Input_files_2"></a>Input files
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* * *
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## <a class="anchor" id="elbow_dat"></a>elbow.dat (case global parameters)
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```
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$----------------------------------------------------------—
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RUN_DATA
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ALYA: elbow $ case name
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END_RUN_DATA
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$----------------------------------------------------------—
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PROBLEM_DATA
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TIME_COUPLING: Global, From_critical $ global time step is prescribed
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TIME_INTERVAL= 0.0, 1.0e6 $ integration time domain from t=0 to t=10s
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NUMBER_OF_STEPS= 1e5 $ infinite time steps
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MAXIMUM_NUMBER_GLOBAL= 1 $ only used when coupling modules
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NASTIN_MODULE: On $ nastin module (Incompressible Navier-Stokes) is used
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END_NASTIN_MODULE
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PARALL_SERVICE: On
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END_PARALL_SERVICE
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END_PROBLEM_DATA
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$----------------------------------------------------------—
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```
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* * *
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|
```
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## <a class="anchor" id="elbow_dom_dat"></a>elbow.dom.dat (domain input data)
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$----------------------------------------------------------—
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DIMENSIONS
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NODAL_POINTS= 5682 $ number of nodes
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ELEMENTS= 26410 $ number of elements
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SPACE_DIMENSIONS= 3 $ 3D mesh
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TYPES_OF_ELEMENTS= 30 $ 4 node tetrahedral elements
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BOUNDARIES= 4046 $ number of boundary edges
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END_DIMENSIONS
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$----------------------------------------------------------—
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STRATEGY
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INTEGRATION_RULE: Open $ open rule is the default
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DOMAIN_INTEGRATION_POINTS: 0 $ 0 = automatic, depending on each element type
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END_STRATEGY
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$----------------------------------------------------------—
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GEOMETRY
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GROUPS=100 $ number of groups (for deflation based solvers)
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INCLUDE elbow.geo.dat $ include geometry file (nodes, elements & boundaries)
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END_GEOMETRY
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$----------------------------------------------------------—
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SETS
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INCLUDE elbow.set.dat $ include set file (groups for post-processing)
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END_SETS
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$----------------------------------------------------------—
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BOUNDARY_CONDITIONS, EXTRAPOLATE $ edge BC’s extrapolate to nodes
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|
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INCLUDE elbow.fix.dat $ include boundary conditions file
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END_BOUNDARY_CONDITIONS
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$----------------------------------------------------------—
|
|
|
```
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* * *
|
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|
|
## <a class="anchor" id="elbow_geo_dat"></a>elbow.geo.dat (mesh information)
|
|
|
```
|
|
|
$----------------------------------------------------------—
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NODES_PER_ELEMENT
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1 4 $ element number, # nodes
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2 4
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3 4
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:
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:
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26409 4
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26410 4
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END_NODES_PER_ELEMENT
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$----------------------------------------------------------—
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ELEMENTS (element connectivity list)
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1 5585 5586 5518 5562 $ element number, node number 1, node number 2, ...
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2 5660 5630 5629 5613
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3 5676 5662 5647 5666
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:
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:
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26409 1638 1433 1313 1315
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26410 1491 1638 1313 1315
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END_ELEMENTS
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$----------------------------------------------------------—
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COORDINATES
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1 1.638713e+00 -2.971132e+00 2.893691e-02 $ node number, coord X, coord Y , coord Z
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2 1.533333e+00 -2.971132e+00 2.886751e-02
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3 1.873338e+00 -2.971128e+00 2.852064e-01
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:
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:
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5681 1.045415e+00 0.000000e+00 0.000000e+00
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5682 1.000000e+00 0.000000e+00 0.000000e+00
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END_COORDINATES
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$----------------------------------------------------------—
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BOUNDARIES, ELEMENT
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1 5681 5676 5682 9402 $ boundary element #, node #s, element # boundary belongs to
|
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|
2 5666 5676 5681 9399
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3 5666 5638 5660 9763
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:
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:
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|
4045 54 71 12 24996
|
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|
4046 12 67 54 26111
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END_BOUNDARIES MATERIALS, NUMBER=0, DEFAULT=1 $ vall elements have material 1 END_MATERIALS CHARACTERISTICS END_CHARACTERISTICS
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$----------------------------------------------------------—
|
|
|
```
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* * *
|
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|
|
## <a class="anchor" id="elbow_set_dat"></a>elbow.set.dat (groups for post-processing, optional)
|
|
|
```
|
|
|
$----------------------------------------------------------—
|
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ELEMENTS
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|
|
1 1 $ element number, set number
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|
|
2 1
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3 1
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:
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:
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:
|
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|
26409 1
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|
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26410 1
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END_ELEMENTS
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$----------------------------------------------------------—
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BOUNDARIES (boundary sets definition)
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1 2 $ boundary element number, boundary set number
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|
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2 2
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3 2
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:
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:
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:
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|
4045 13
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|
4046 13
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END_BOUNDARIES
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$----------------------------------------------------------—
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NODES (node sets definition)
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0
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END_NODES
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$----------------------------------------------------------—
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|
```
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* * *
|
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|
|
|
## <a class="anchor" id="elbow_fix_dat"></a>elbow.fix.dat (boundary conditions data)
|
|
|
```
|
|
|
$----------------------------------------------------------—
|
|
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|
|
ON_BOUNDARIES
|
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|
|
|
|
1 4 $ boundary element number, boundary set number
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|
|
2 4
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|
|
3 4
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|
|
:
|
|
|
:
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|
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:
|
|
|
4045 1
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|
|
4046 1
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END_ON_BOUNDARIES
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|
$----------------------------------------------------------—
|
|
|
```
|
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|
* * *
|
|
|
|
|
|
## <a class="anchor" id="elbow_ker_dat"></a>elbow.ker.dat
|
|
|
```
|
|
|
$---------------------------------------------------------—
|
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|
|
|
|
PHYSICAL_PROBLEM
|
|
|
|
|
|
PROPERTIES $ fluid physical properties (water)
|
|
|
DENSITY: CONSTANT, PARAMETERS = 1.0 $ mass density
|
|
|
VISCOSITY: CONSTANT, PARAMETERS = 0.0005 $ dynamic viscosity (μ)
|
|
|
END_PROPERTIES
|
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|
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|
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|
|
END_PHYSICAL_PROBLEM
|
|
|
|
|
|
$---------------------------------------------------------—
|
|
|
|
|
|
NUMERICAL_TREATMENT
|
|
|
|
|
|
MESH
|
|
|
DIVISION=1 $ 2 automatic mesh subdivisions
|
|
|
END_MESH
|
|
|
ELSEST $ element search strategy
|
|
|
STRATEGY: BIN BIN divide mesh into boxes to find elements that host
|
|
|
witness points (suited for structured meshes)
|
|
|
NUMBER: 20, 20, 20
|
|
|
DATAF: LINKED_LIST
|
|
|
END_ELSEST
|
|
|
SPACE_&_TIME_FUNCTIONS
|
|
|
FUNCTION=INFLOW
|
|
|
-4*y**2-4*z**2+12*y-8 $ paraboloid surface function (Umax=1)
|
|
|
END_FUNCTION
|
|
|
END_SPACE_&_TIME_FUNCTIONS
|
|
|
|
|
|
|
|
|
END_NUMERICAL_TREATMENT
|
|
|
|
|
|
$---------------------------------------------------------—
|
|
|
|
|
|
OUTPUT_&_POST_PROCESS
|
|
|
|
|
|
ON_LAST_MESH
|
|
|
STEPS=10 $ post-process every ‘STEPS’ time steps
|
|
|
|
|
|
|
|
|
END_OUTPUT_&_POST_PROCESS
|
|
|
|
|
|
$---------------------------------------------------------—
|
|
|
```
|
|
|
* * *
|
|
|
|
|
|
## <a class="anchor" id="elbow_nsi_dat"></a>elbow.nsi.dat (incompressible Navier-Stokes solver parameters)
|
|
|
```
|
|
|
$---------------------------------------------------------—
|
|
|
|
|
|
PHYSICAL_PROBLEM
|
|
|
|
|
|
PROBLEM_DEFINITION
|
|
|
TEMPORAL_DERIVATIVES: On $ transient problem
|
|
|
CONVECTIVE_TERM: On $ off for Stokes flow (negligible for high viscosity fluids)
|
|
|
VISCOUS_TERM: LAPLACIAN $ suitable for constant viscosity fluid assumption
|
|
|
END_PROBLEM_DEFINITION
|
|
|
|
|
|
|
|
|
END_PHYSICAL_PROBLEM
|
|
|
|
|
|
$---------------------------------------------------------—
|
|
|
|
|
|
NUMERICAL_TREATMENT
|
|
|
|
|
|
ELEMENT_LENGTH: Minimum $ element length for Alya to calculate critical time step
|
|
|
STABILIZATION: ASGS $ numerical stabilization method
|
|
|
TIME_INTEGRATION: Trapezoidal, ORDER: 1, EULER=20 $ time integration scheme
|
|
|
SAFETY_FACTOR: 100.0 $ multiply global time step: Alya calculates critical time step
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|
as required by explicit solvers, which is suited for transient
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|
|
analysis but makes stationary solutions converge very slowly
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STEADY_STATE_TOLER: 1.0e-10 $ convergence tolerance for steady state
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MAXIMUM_NUMBER_OF_IT: 1 $ max number of inner NS iterations
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CONVERGENCE_TOLERANCE: 1.0e-3 $ convergence tolerance for inner NS loop (useless in this case)
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ALGORITHM: SCHUR $ NS solution algorithm (uncouples p & V)
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SOLVER: ORTHOMIN, CONTINUITY_PRESERVING $ default is MOMENTUM_PRESERVING
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PRECONDITION: DT
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END_ALGORITHM
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MOMENTUM $ velocity solver
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ALGEBRAIC_SOLVER
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|
SOLVER: GMRES, KRYLOV=10 $ solver suited for asymmetric matrix
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|
CONVERGENCE: ITERA=1000, TOLER=1.0e-12, ADAPTIVE, RATIO=0.01 $ max iter #, convergence criteria
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|
ADAPTIVE, RATIO=0.01 means that the loop will end also if the difference of the norm of convergence value changes less than 1% in two consecutive iterations
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OUTPUT: CONVERGENCE $ solver convergence file (.cso) is generated
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|
PRECONDITIONER: DIAGONAL $ matrix preconditioner type
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|
END_ALGEBRAIC_SOLVER
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|
END_MOMENTUM
|
|
|
CONTINUITY $ pressure solver
|
|
|
ALGEBRAIC_SOLVER
|
|
|
SOLVER: DEFLATED_CG, COARSE: SPARSE $ CG solvers are suited for symmetric matrix
|
|
|
CONVERGENCE: ITERA=1000, TOLER=1.0e-12, ADAPTIVE, RATIO=0.01 $ max iter #, convergence criteria
|
|
|
ADAPTIVE, RATIO=0.01 means that the loop will end also if the difference of the norm of convergence value changes less than 1% in two consecutive iterations
|
|
|
OUTPUT: CONVERGENCE $ solver convergence file (.cso) is generated
|
|
|
PRECONDITIONER: DIAGONAL $ matrix preconditioner type
|
|
|
END_ALGEBRAIC_SOLVER
|
|
|
END_CONTINUITY
|
|
|
|
|
|
|
|
|
END_NUMERICAL_TREATMENT
|
|
|
|
|
|
$---------------------------------------------------------—
|
|
|
|
|
|
OUTPUT_&_POST_PROCESS
|
|
|
|
|
|
START_POSTPROCES_AT STEP = 0 $ initial step to post process
|
|
|
POSTPROCESS VELOCITY STEPS = 10 $ post process velocity every 10 steps (priority ker.dat)
|
|
|
POSTPROCESS PRESSURE STEPS = 10 $ post process pressure every 10 steps (priority ker.dat)
|
|
|
POSTPROCESS MEAN_PRESSURE, STEPS = 1
|
|
|
BOUNDARY_SET
|
|
|
FORCE
|
|
|
TORQUE, CENTER=0,0,0
|
|
|
MASS
|
|
|
MEAN_PRESSURE
|
|
|
END_BOUNDARY_SET
|
|
|
|
|
|
|
|
|
END_OUTPUT_&_POST_PROCESS
|
|
|
|
|
|
$---------------------------------------------------------—
|
|
|
|
|
|
BOUNDARY_CONDITIONS
|
|
|
|
|
|
PARAMETERS
|
|
|
VARIATION: NON_CONSTANT $ there will be parameters specifyed by function
|
|
|
INITIAL: COARSE $ domain velocity initialization
|
|
|
END_PARAMETERS
|
|
|
CODES, NODES $ Boundary Conditions
|
|
|
1 000 0.000000 0.000000 0.000000 $ outlet
|
|
|
2 111 1.000000 0.000000 0.000000, SPACE_TIME_FUNCTION=INFLOW $ inlet
|
|
|
3 111 0.000000 0.000000 0.000000 $ wall
|
|
|
4 001 0.000000 0.000000 0.000000 $ symmetry
|
|
|
1 & 3 111 0.000000 0.000000 0.000000 $ edges...
|
|
|
1 & 4 001 0.000000 0.000000 0.000000
|
|
|
2 & 3 111 0.000000 0.000000 0.000000
|
|
|
2 & 4 111 1.000000 0.000000 0.000000, SPACE_TIME_FUNCTION=INFLOW $ inlet
|
|
|
3 & 4 111 0.000000 0.000000 0.000000
|
|
|
1 & 3 & 4 111 0.000000 0.000000 0.000000 $ $ vertex...
|
|
|
2 & 3 & 4 111 0.000000 0.000000 0.000000
|
|
|
END_CODES $ inlet(note that BC’s apply to boundaries, not to boundary sets)
|
|
|
|
|
|
|
|
|
END_BOUNDARY_CONDITIONS
|
|
|
|
|
|
$---------------------------------------------------------—
|
|
|
```
|
|
|
* * *
|
|
|
|
|
|
## <a class="anchor" id="elbow_post_alya_dat"></a>elbow.post.alya.dat (alya2pos parameters)
|
|
|
```
|
|
|
$----------------------------------------------------------------—
|
|
|
|
|
|
DATA
|
|
|
|
|
|
FORMAT: visit $ also valid for ParaView
|
|
|
MARK_ELEMENTS: type $ to create automatic layers in post process according to some criterion
|
|
|
ELIMINATE_BOUNDARY_NODES: yes $ for parallel runs, to avoid node duplicity between subdomain
|
|
|
BOUNDARY: ON $ to post process boundary mesh
|
|
|
SUBDOMAINS, ALL $ subdomains (parallel partitions) to post process
|
|
|
END_SUBDOMAINS
|
|
|
|
|
|
|
|
|
END_DATA
|
|
|
|
|
|
$----------------------------------------------------------------—
|
|
|
```
|
|
|
* * * |