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solvers:density [2013/01/05 22:41]
gag [General Description] |
solvers:density [2014/01/31 08:16]
ltavard [Examples] |
| This page explains how to use the general AdvectionReactionSolver from the Elmer distribution to get the density evolution in case of a compressible material (snow/firn) under a given velocity field computed from the [[solvers:porous|Porous Solver]]. The AdvectionReactionSolver solves the general equation | This page explains how to use the general AdvectionReactionSolver from the Elmer distribution to get the density evolution in case of a compressible material (snow/firn) under a given velocity field computed from the [[solvers:porous|Porous Solver]]. The AdvectionReactionSolver solves the general equation |
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| <m>{{\partial A}/{\partial t}} + u {{\partial A}/{\partial x}}+v{{\partial A}/{\partial y}}</m> | <m>{{\partial A}/{\partial t}} + div (A u) + gamma A=sigma</m> |
| <m>+w{{\partial A}/{\partial z}}+gamma A=sigma</m> | |
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| In the particular case of the mass conservation equation, one has <m>gamma = 0</m> and <m>sigma = 0</m> (the trace of the strain-rate tensor appears directly when integrating by part this equation and should not be specified trough <m>gamma</m>). Solving for the true density (kg/m^3) or the relative density is equivalent (but limit values and Dirichlet boundary conditions have to be set accordingly). | where <m>u</m> is the velocity vector. In the particular case of the mass conservation equation, one has therefore <m>gamma = 0</m> and <m>sigma = 0</m>. Solving for the true density (kg/m^3) or the relative density is equivalent (but limit values and Dirichlet boundary conditions have to be set accordingly). |
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| | Note 1: equation (4.1) in the Elmer Model Manual for the AdvectionReaction sover is not correct. The previous equation is the one implemented. |
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| | Note 2: Have a look to this [[http://elmerfem.org/forum/viewtopic.php?f=7&t=3066&p=9570#p9570|post]] on the Elmer Forum regarding the initialisation of both the DG primary and exported variables of the AdvectionReaction solver (see the example at the end of this page). |
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| </code> | </code> |
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| ===== Example ===== | ===== Examples ===== |
| {{:solvers:test_density.tar.gz|Download}} a 1D example build from an analytical solution. In that case, the velocity and density are inversely proportional (u(z) = K/D(z)). | A 1D example build from an analytical solution can be found in ''[ELMER_TRUNK]/elmerice/Tests/Density''. In that case, the velocity and density are inversely proportional (u(z) = K/D(z)). |
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| | A 3D example coupling the [[solvers:porous|Porous Solver]] and the calculation of the density field can be found in ''[ELMER_TRUNK]/elmerice/Tests/Test_DGsolver''. |
