How do you implement a higher order finite difference schemes, like 5th or 7th order scheme, or a 6th order central scheme near boundaries? As in, near boundaries you don't have enough points to implement such schemes. What do you do in such cases?
Note that the boundary conditions are not periodic. There will be inflow, outflow and wall boundary conditions.
Thank you in advance:)
Central schemes: Use Summation-by-parts schemes that guarantee stability for linear/linearized problems with bcs.
If you want to use WENO, check out the work by Mark H. Carpenter and co-workers. They generalize the SBP framework to WENO both w.r.t. energy stability and entropy stability with bcs.
There's also the standard one-sided differencing stencils, and ghost point stencils as well.
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