compact schemes

A collection of snippets that exemplify the proper implementation of conservative high-order compact-schemes.

This repository exemplifies the most clean and minimalistic way to program conservative compact schemes for solving systems of equations such as Navier-Stokes or Euler-Equations.

This short and extremely versatile implementation of conservative compact schemes is possible thanks to three ingredients:

1. A Taylor Table algorithm (see: Easy build compact schemes).
2. An ingenious spare technique to produce highly performing discrete finite-difference operations in higher-dimensions. (see: Easy build finite-difference operators).
3. The conservative boundary schemes by Brady and Livescu (2019).

Here we reproduce some of the invicid benchmark tests proposed by Brady and Livescu (2019).