Hi,
Here is the problem:
I am solving these equations having a periodic boundary conditions in a square. At the top and bottom of the square the constant velocity v0 and pressure p0 is applied. It is a very classical problem in fluid mechanics to learn about dynamic viscosity. Something new that is added, is another PDE to minimize the shear with changing the density value throughout the domain.
I am using the General Form toolbox, using the quadratic interpolation for velocity field, and linear for pressure and density, also the average of density should remain constant which I added a pointwise constraint. For meshing I used boundary layers top and bottom which the laminar flow toolbox uses (as far as I understood). The viscosity is a function of density and pressure so it makes it more non-linear. Something else about the the pde for density is that, it is highly non-linear in the term lambda.
It would be great if someone could give me some hints on improving the convergence. the g2 and g3 are laminar flow equations and the g4 is
2pρf'〖 γ〗^2-λρ=∇.(pv)
where λ is constant and γ is a function of velocity field.
Here is the problem:
I am solving these equations having a periodic boundary conditions in a square. At the top and bottom of the square the constant velocity v0 and pressure p0 is applied. It is a very classical problem in fluid mechanics to learn about dynamic viscosity. Something new that is added, is another PDE to minimize the shear with changing the density value throughout the domain.
I am using the General Form toolbox, using the quadratic interpolation for velocity field, and linear for pressure and density, also the average of density should remain constant which I added a pointwise constraint. For meshing I used boundary layers top and bottom which the laminar flow toolbox uses (as far as I understood). The viscosity is a function of density and pressure so it makes it more non-linear. Something else about the the pde for density is that, it is highly non-linear in the term lambda.
It would be great if someone could give me some hints on improving the convergence. the g2 and g3 are laminar flow equations and the g4 is
2pρf'〖 γ〗^2-λρ=∇.(pv)
where λ is constant and γ is a function of velocity field.