- #1
uqjzhang
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I am a noob so please let me know if here isn't the right place to post this.
Recently I am trying to solve hyperbolic equation m*dU/dt=k*d^2U/dx^2+q using Crank-Nicholson and finite element method. The final form of the solution is to compute the increment of the unknown at each time step through: (M/dt+0.5*K)dU=-KU(t)+q, U(t+dt)=U(t)+dU
The problem I am solving is quite simple: for a 1D bar x∈[0,1], initial U(x,t0)=U0=1, m=k=1. Boundary conditions are: U(1,t)=U0=1 (right end fixed); q(0.5,t)=-0.01 (point sink at center of the bar).
I read papers about time step control about this kind of problem. Obviously the time step can not be too small or it will cause oscillation around the sink location. But when I choose large time steps, I get this. (in this case, dt=3000s)
http://www.freeimagehosting.net/uploads/b541c099d4.jpg
I don't understand one thing here is: why the dU for these 4 time steps are so uneven? dU at odd time steps (e.g. 1,3) are much larger than even time steps (e.g. 2,4). If I increase the time step size, problem gets more severe.
If you have ideas about how this happens or how to eliminate this, I will be appreciated if you can share some light with me.
Recently I am trying to solve hyperbolic equation m*dU/dt=k*d^2U/dx^2+q using Crank-Nicholson and finite element method. The final form of the solution is to compute the increment of the unknown at each time step through: (M/dt+0.5*K)dU=-KU(t)+q, U(t+dt)=U(t)+dU
The problem I am solving is quite simple: for a 1D bar x∈[0,1], initial U(x,t0)=U0=1, m=k=1. Boundary conditions are: U(1,t)=U0=1 (right end fixed); q(0.5,t)=-0.01 (point sink at center of the bar).
I read papers about time step control about this kind of problem. Obviously the time step can not be too small or it will cause oscillation around the sink location. But when I choose large time steps, I get this. (in this case, dt=3000s)
http://www.freeimagehosting.net/uploads/b541c099d4.jpg
I don't understand one thing here is: why the dU for these 4 time steps are so uneven? dU at odd time steps (e.g. 1,3) are much larger than even time steps (e.g. 2,4). If I increase the time step size, problem gets more severe.
If you have ideas about how this happens or how to eliminate this, I will be appreciated if you can share some light with me.