I use PDE( coefficient) to solve a problem, here is the simplified model:
It's a 2D problem. I want to solve wave equation in fluid. There is a square area (water in it), and an imaginary, smaller square frame( water in the frame is called area B,outside is called area A), and they have the same center. The boundary of the frame has two parts:
1) p(A)=p(B)-------p stands for the sound pressure
2) v(A)=v(B)-------the continuation of normal particle velocity
Now comes the question. Since the wave equation is in the form of sound pressure p, the the boundary (1) is easy. But for boundary(2), as the time derivative of v is proportional to the gradient of p, how to implement the boundary about v? The general form of boundary no matter Neuman or Dirichlet has no relationship with time.
Any help or comment is helpful. Thanks~
It's a 2D problem. I want to solve wave equation in fluid. There is a square area (water in it), and an imaginary, smaller square frame( water in the frame is called area B,outside is called area A), and they have the same center. The boundary of the frame has two parts:
1) p(A)=p(B)-------p stands for the sound pressure
2) v(A)=v(B)-------the continuation of normal particle velocity
Now comes the question. Since the wave equation is in the form of sound pressure p, the the boundary (1) is easy. But for boundary(2), as the time derivative of v is proportional to the gradient of p, how to implement the boundary about v? The general form of boundary no matter Neuman or Dirichlet has no relationship with time.
Any help or comment is helpful. Thanks~