Differences
This shows you the differences between two versions of the page.
Both sides previous revision
Previous revision
Next revision
|
Previous revision
|
solvers:density [2013/01/05 22:38] gag [Example] |
solvers:density [2014/01/31 08:16] (current) 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 |
| |
<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> | |
| |
| |
In the particular case of the mass conservation equation, one has <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). | 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). |
| |
| Note 1: equation (4.1) in the Elmer Model Manual for the AdvectionReaction sover is not correct. The previous equation is the one implemented. |
| |
| 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). |
| |
| |
</code> | </code> |
| |
===== 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 (<m>u(z) = K / D(z)</m>). | 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)). |
| |
| A 3D example coupling the [[solvers:porous|Porous Solver]] and the calculation of the density field can be found in ''[ELMER_TRUNK]/elmerice/Tests/DGsolver''. |