I'm trying so solve 1D fluid equations (modeling a plasma):
d/dx(n*v)=Sp
d/dx(m*n*v^2+n*T)=Sm
d/dx(5/2*n*T*v+1/2*m*n*v^3+q)=Sq
q=kappa*T^(5/2)*dT/dx
Where d/dx is the derivative with respect to the spatial coordinate. The variables (n, v, T, and q) are all dependent variables. As is, these are too unstable to solve by plugging them into the General Form PDE and going with the defaults (with appropriate boundary conditions).
I am profficient at using COMSOL, but not at all skilled at using weak forms or doing my own stabilization. So I've taken the monkey-see monkey-do technique of copying the implementation of streamline diffusion in the COMSOL shock tube model (www.comsol.com/showroom/documentation/model/100/). Doing this, I can successfully solve either the isothermal (T constant) or the n & v constant cases. But putting them together, I cannot get a solution.
Has anyone any experience doing something similar or suggestions? I see either two ways forward: 1. Shoe-horning this problem into one of COMSOL's Fluid Flow models. This would allow me to use the stabilization built into the model. 2. Sticking with the General Form PDE and finding a way to get this stable and solvable.
d/dx(n*v)=Sp
d/dx(m*n*v^2+n*T)=Sm
d/dx(5/2*n*T*v+1/2*m*n*v^3+q)=Sq
q=kappa*T^(5/2)*dT/dx
Where d/dx is the derivative with respect to the spatial coordinate. The variables (n, v, T, and q) are all dependent variables. As is, these are too unstable to solve by plugging them into the General Form PDE and going with the defaults (with appropriate boundary conditions).
I am profficient at using COMSOL, but not at all skilled at using weak forms or doing my own stabilization. So I've taken the monkey-see monkey-do technique of copying the implementation of streamline diffusion in the COMSOL shock tube model (www.comsol.com/showroom/documentation/model/100/). Doing this, I can successfully solve either the isothermal (T constant) or the n & v constant cases. But putting them together, I cannot get a solution.
Has anyone any experience doing something similar or suggestions? I see either two ways forward: 1. Shoe-horning this problem into one of COMSOL's Fluid Flow models. This would allow me to use the stabilization built into the model. 2. Sticking with the General Form PDE and finding a way to get this stable and solvable.