Frobenius25
Aerospace
Hello to everybody, this is my first post here and I write since I'm having some problems in realizing a MATLAB code regarding a model for atmospheric circulation.
I have to consider the following set of two coupled diffusion equations:
du/dt=d/dz(K*du/dz)
dv/dt=d/dz(K*dv/dz)
where "u,v" are the variables we are studying (representing the wind speed and the potential temperature) and the diffusion coefficient is K=(l^2)*|du/dz|(1+b|Ri|)^n (with du/dz nonzero). In the previous definition "l"and "b" are constants and Ri is the Richardson number, given by
Ri=(g/a)*[(dv/dz)/(du/dz)^2] where "g" is the constant acceleration of gravity and "a" is a constant.
I am trying to realize a numerical discretization of this problem using second differences for what concern the spatial variable "z" and time-advancing schemes like esplicit or implicit Euler methods or Crank-Nicolson method. Can someone please help me realizing this MATLAB program?
Thank you very much!
I have to consider the following set of two coupled diffusion equations:
du/dt=d/dz(K*du/dz)
dv/dt=d/dz(K*dv/dz)
where "u,v" are the variables we are studying (representing the wind speed and the potential temperature) and the diffusion coefficient is K=(l^2)*|du/dz|(1+b|Ri|)^n (with du/dz nonzero). In the previous definition "l"and "b" are constants and Ri is the Richardson number, given by
Ri=(g/a)*[(dv/dz)/(du/dz)^2] where "g" is the constant acceleration of gravity and "a" is a constant.
I am trying to realize a numerical discretization of this problem using second differences for what concern the spatial variable "z" and time-advancing schemes like esplicit or implicit Euler methods or Crank-Nicolson method. Can someone please help me realizing this MATLAB program?
Thank you very much!
