I’m solving a system of non-linear equations using finite element method. while giving the values of boundary condition I’m getting the error. How I’m getting that I don’t know.
In bcs you have typed u[x,y]=0 instead of ==0.
The first element of NeumannValue must be a value, not a predicate. Check your definitiopn of op, because it evaluates to False.
And I have given the Neumann value as zero for the top wall and y=1
op alreay contains the equation ==0, you do not need to write op=={0,0,0} again.
In your definition of op you have u[x,y] but also u alone. You must make the independent variables explicit everywhere. NeumannValue is used inside a differential equation, not free-standing.
how can I give that Neumann condition. I have searched in many things I got this only, kindly let me know how to define for that particular condition.
Sorry, I have no expertise on Neumann conditions. In the documentation I only see Neumann conditions for linear PDEs, but yours seems nonlinear.
It will be easier to help you if you include the actual code instead of a screenshot.
Pr = 0.71; Ra = 10^4;
Needs["NDSolve`FEM`"]
\[CapitalOmega] = ImplicitRegion[True, {{x, 0, 1}, {y, 0, 1}}];
op = {D[u[x, y], x]+D[v[x, y], y] \[Equal] 0, u[x, y]*D[u[x, y], x]+v[x, y]*D[u[x, y], y]+ D[P, x]-Pr*(D[u[x, y], x, x]+D[u[x, y], y, y]) \[Equal] 0, u[x, y]*D[v[x, y], x]+v[x, y]*D[v[x, y], y]+D[P, y] Pr*(D[v[x, y], x, x]+D[v[x, y], y, y])+Ra*Pr*\[Theta][x, y] \[Equal] 0, u[x, y]*D[\[Theta][x, y], x]+v[x, y]*D[\[Theta][x, y], y]-D[\[Theta][x, y], x, x]-D[\[Theta][x, y], y, y] \[Equal] 0}
bcs = {DirichletCondition[{u[x, y] \[Equal] 0, v[x, y] \[Equal] 0, \[Theta][x, y] \[Equal] 0}, x \[Equal] 0], DirichletCondition[{u[x, y] \[Equal] 0, v[x, y] \[Equal] 0, \[Theta][x, y] \[Equal] 1}, y \[Equal] 0], DirichletCondition[{u[x, y] \[Equal] 0, v[x, y] \[Equal] 0, \[Theta][x, y] \[Equal] 0}, x \[Equal] 1]}
NDSolveValue[{op, bcs}, {u, v, \[Theta], P}, {x, y} \[Element] \[CapitalOmega], Method -> {"FiniteElement"}]
What is D[P, x]?
P is a pressure term that is also function of x,y i haven’t mention that in explicit form
Now, do you get any idea about the Neumann boundary conditions. Till now I’m getting error.
I would write the region more simply as
\[CapitalOmega] = Rectangle[];
I get the error that op has four equations with only three unknown functions.
Sorry, I can’t help you with the Neumann condition.
Thank you for reply.