A vertex centered high order MUSCL scheme applying to linearised Euler acoustics

Overview & Synopsis

This report proposes a linearised Euler discretisation that will be compatibl- e with some existing state of art in numerical methods for compressible flows on unstructured triangulations. The important property is the use of a stabilisation terms involving sixth-order derivatives. The main idea is to realize this programme by developing a scheme that enjoys superconvergence, i.e. a high convergence order when it is applied to a cartesian triangulation. We present a test case validating the theoretical order of accuracy and the so-called Tam test case, allowing some comparisons with two other typical numerical schemes for acoustics.