Mathematica Asked on November 3, 2020
So I am trying to get a good representation of the 2d heat equation with mathematica but it does not seem to work correctly:
heqn = D[u[t,x,y], t] -Laplacian[u[t,x,y], {x,y}]
shape = Rectangle[{0,0},{10,10}]
ic = u[0,x,y] == x+y
bc = NeumannValue[0, True]
sol = NDSolveValue[{heqn == bc, ic}, u, {t, 0, 300}, {x,y}[Element]shape]
Manipulate[Plot3D[sol[t,x,y], {x, 0,10},{y,0,10},ColorFunction->Function[{x,y,z},Hue[z]]], {t,0,300}]
Initial Condition :
The expected result is equilibrium after some time but instead the heat is just transferring over and causing really weird things to happen in the plot:
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