Hi,
I am trying to use Chebyshev pseudospectral method to simulate 3D wave propagation problems. The solver works but is very unstable. I applied mapping functions to make the boundary mesh grid larger but still instability is very apparent.
I read staggered grid tends is helpful in improving the stability of a finite difference solver. I am wondering if that can applied to pseudospectral method. How can it be used in Chebyshev method, in particular?
Any suggestions will be appreciated. Thanks.
Bo
Dear ,
You may first simulate your algorithm in 2D case. From which you can get a clue that why the algorithm become unstable. I think that then it would be easy to generalize the algoritham.
I am not sure wheter you use the Chebsheve method to discritize the spatial domain and a marching method to slove the wave equation. If so, the stability connect closely with the stepsize in time domian. One resolution is decreasing the stepsize, the other is use implicit marching scheme.
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