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WENO Scheme Defining Boundary Stencil

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Old   January 9, 2007, 12:01
Default WENO Scheme Defining Boundary Stencil
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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.
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Old   January 9, 2007, 19:43
Default Re: WENO Scheme Defining Boundary Stencil
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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.
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Old   January 10, 2007, 05:20
Default Re: WENO Scheme Defining Boundary Stencil
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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.

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Old   January 15, 2007, 01:08
Default Re: WENO Scheme Defining Boundary Stencil
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Thanks a lot for the replies.. It clears some of my fundamental concepts..!!!
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