A simple construction of very high order non-oscillatory compact schemes on unstructured meshes

In [Abgrall R, Roe PL. High order fluctuation schemes on triangular meshes. J Sci Comput 2003;19(1–3):3–36] have been constructed very high order residual distribution schemes for scalar problems. They were using triangle unstructured meshes. However, the construction was quite involved and was not very flexible. Here, following [Abgrall R. Essentially non-oscillatory residual distribution schemes for hyperbolic problems. J Comput Phys 2006;214(2):773–808], we develop a systematic way of constructing very high order non-oscillatory schemes for such meshes. Applications to scalar and systems problems are given.