
[Sponsors] 
July 4, 2004, 16:43 
simple 3d simulation of atmosphere

#1 
Guest
Posts: n/a

Hello. I want to simulate the atmosphere on a global scale.
The equations I use are as follows: Horizontal wind equations: du/dt = udu/dx  v du/dy  wdu/dp +fv g dz/dx +Fx dv/dt = udv/dx  v dv/dy  wdv/dp fu g/dz/dy +Fy Equation of continuity(used to predict vertical motion) du/dx + dv/dy + dw/dp = 0 Temperature Forecast equation: dT/dt = u dT/dx  vdT/dy  w(dT/dp  RT/cp*p) + H/cp Hydrostatic: dz/dp = RT/pg the reference for these are http://meted.ucar.edu/nwp/pcu1/ic2/frameset.htm (select Model Type/Math.Basis for NWP and page 2) I use a box model with 100x100x20 boxes, where i store the quantities of p, u,v,w,T,rho, and so on. The model is initialized with the Logarithmic law p=p0(1az/T0)^(Mg/Ra), so i get pressure and also density as a function of height, and the temperature is made latitude dependent. The boundary conditions are periodical in the xdirection while in the y and z direction I use a layer which doesnt get updated, but is only initialized to some sensible value, so that the finite differences work in the boundary points also. I use finite differences to discretize the partial derivatives, i.e du/dx = (u2u1)/(x2x1), where u2 is the rightmost box and u1 the leftmost box, and x2x1 is the length of the boxes in x*2 > u1uu2 Then I go through each box and update the quantities of u,v,w,T. But here's the first problem, how should i update rho(density) and p(pressure)? Moreover, my model seems to blow up after only a few tens of iterations; the horizontal wind velocities of v and u seems to blow up and diverge after some time. I did convert from x,y,p, to x,y,z coordinate system using the hydrostatic equation and used layers of unequal spacing in vertical directions, to get more accuracy at lower altitudes. So my question is, are these equations enough to get something working or is there something missing? The model is hydrostatic, and the equation of continuity is used to predict only vertical motion, that is, if winds blows into a particular square from different directions, then the excess air starts moving upwards, since the model seems to assume incompressibility also. Does this model take into account the conservation of mass? Otherwise the wind equations looks pretty ok to me, they are a form of NavierStokes equation for incompressible flows, with some vertical motion included. PGM 

July 5, 2004, 02:11 
Re: simple 3d simulation of atmosphere

#2 
Guest
Posts: n/a

Have a look at http://www.gfdl.noaa.gov/~fms/, it may clarify some of your points.


Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Looking for simple, robust interface tracking algorithm  ThomasTC  Main CFD Forum  6  February 17, 2012 19:13 
blasius flow simulation using SIMPLE method  sizyef  Main CFD Forum  1  December 18, 2011 11:49 
(chtMultiRegionFoam) reducing gravity increase the simulation time !  openfoam1  OpenFOAM  7  March 10, 2010 10:41 
Simple icoFoam simulation gone wrong  rieuk  OpenFOAM Running, Solving & CFD  3  March 5, 2010 03:24 
Replacing mesh while running a simulation  akultane  CFX  1  November 15, 2009 14:46 