Low Density Simulation
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Hello,
I am doing a simulation which has an inlet and outlet as velocity boundary condition of 1e-06 m/s. I want to have the geometry under variable pressure which is 10 millibar,100 millibar and 1 bar. The fluid I am using is air. So basically, my physical density which I got in this case were 0.0071,0.1123,1.1639 kg/m3 respectively.
Initially, as per the book “The lattice Boltzmann Method: Principle and Practice by Timm Krüger (Chapter 7), it is recommended to keep the lattice density to be 1. I used this principle in my simulation, so that my physical density and density factor becomes same to make my lattice density 1. However, after the simulation I observed in Paraview that the pressure in all the three cases is showing the same. I dont see any difference in my pressure values.
After that, I tried to make density factor 1 and made sure that my physical and lattice density remains same in this case. However, my simulation diverges at low density values.
I am defining the density in the prepare lattice
sLattice.iniEquilibrium( bulkIndicator1, rhoF, uF );
sLattice.defineRhoU( bulkIndicator1, rhoF, uF );sLattice.iniEquilibrium( bulkIndicator2, rhoF, uTop );
sLattice.defineRhoU( bulkIndicator2, rhoF, uTop );where bulkindicator1 are my wall region and fluid region. (2,1) with uF being zero.
and bulkindicator 2 are my inlet and outlet region with utop being my velocity of 1e-06 in z direction.What would be the density you recommend which I should consider while defining lattice density(rhoF). I would really appreciate any help in this case.
Thanking you in anticipation,
Sahil
Dear Sahil,
generally, it is a good idea to set the initial lattice density to unity, as described in the book you referred to. You will find this very approach in most of our examples. Your usage of the OpenLB methodology seems to be correct.
The density derived from the first moment of the distribution function, however, will change during your simulation. In order to end up with a pressure difference in a force free flow you need to have some proper boundary conditions applied to your walls. It might be a good idea to start with a common setup of velocity inflow, pressure outflow and no-slip wall condition first and see whether the expected pressure drop can be observed, both reflected by the console output and the VTK writout. You can then adapt this to a double velocity condition setup and see, whether your issues still persist.Best,
Nicolas
Dear Sahil,
the relation between density and pressure you mentioned is correct and holds in this context for the LBM considering the respective equation of state. A proper derivation can be found in many LBM related literature (e.g https://www.springer.com/de/book/9783319446479).
Setting a specific characteristic physical pressure, however, is not solely an LBM related issue. As the compressible/slightly-compressible Navier-Stokes equation does not include the absolute pressure, but only the pressure gradient, changing the default value does not have any effect on the fluid flow solution (despite, obviously the resulting absolute pressure). As this is a matter of general fluid dynamics, you might want to have a look at respective literature for further insights.Best,
Nicolas
correction: “compressible” should of course be “incompressible”…
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