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 rampy January 9, 2007 12:01

WENO Scheme Defining Boundary Stencil

My research area requires me to implement a 5th order explicit Weighted Essentially Non-Oscillating scheme for a simple Linear Advection equation (du/dt+du/dx=0) . Since its a 5th order scheme, each node is dependent on 5 neighboring stencils. I have questions on how does one address the problem of defining boundary stencils without losing the order of accuracy or defining them at least using 4th order accuracy.

 Sya January 9, 2007 19:43

Re: WENO Scheme Defining Boundary Stencil

I simply created ghost cells outside the domain since I knew what the distribution of the scalar was outside the domain. Otherwise use the available stencils and go to 4th order. I would be very surprised if the difference between 4th and 5th WENO was worth considering.

 saygin January 10, 2007 05:20

Re: WENO Scheme Defining Boundary Stencil

Hi rampy,

I also used ghost cell approach. For a 5th order reconstruction it means 3 ghost cells at each end. It is not a problem for rectangular domain. However, for a highly skewed curvilinear domain it is becoming a problem. For example, a flow around airfoil cross section, which I implemented for the thesis, especially for the leading edge and the trailing edge (if you are using a conforming boundary implementation, imagine the beginning of a C-cut boundary, where all three cell layers has to be aligned with the 3 cell layer of the other part). Or a multiblock grid, you have to make conforming meshes for these 3 interacting cell layers. In order to overcome these difficulties, order reduction is a choice, like reducing the order to 3rd order then to MUSCL.

But you say you are using advection equation, I guess you are on a simple rectangular domain or it is a 1D implementation, so you don't need to avoid to use 3 ghost cells, there is no need for an order reduction in that case.

 Rampy January 15, 2007 01:08

Re: WENO Scheme Defining Boundary Stencil

Thanks a lot for the replies.. It clears some of my fundamental concepts..!!!

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