README.md

# PSAAP3 WENO

Standalone Fortran WENO code with Loopy transformations.

## Notes

* The WENO scheme is taken from [1]
* Boundary conditions are not really handled correctly at all
* For now, the Fortran code will not compile -- the main focus is expressing
    the mathematics
* A declaration of "real" is not intended to suggest single precision
* This implementation does not include the severe shock correction proposed
    by [1]
* Current assumption for metrics is that metrics(i,j) = (\xi_i)_(x_j)
* Some matrix/vector operations are assumed:
  * Multiplication (matmul)
  * Sum of all elements (sum)
* It's not immediately obvious, but there might be some wasted work in the
    frozen generalized flux computation
* Roe eigensystem and pointwise eigenvalue computation currently
    unimplemented -- this is where the equation of state will come in

## References

[1] Nonomura, T., Terakado, D., Abe, Y., & Fujii, K. (2015).
*A new technique for freestream preservation of finite-difference WENO on curvilinear grid.*
Computers and Fluids, 107, 242–255.

## Fortran dialect wishlist

- Automatic line continuation in parentheses
- Array-valued expressions
- In-place operators
- Slicing that automatically picks an increment of -1 when appropriate
  - (e.g. 2:0 instead of 2:0:-1)