Non-oscillatory third order fluctuation splitting schemes for steady scalar conservation laws

This paper addresses the issue of constructing non-oscillatory, higher than second order, fluctuation splitting methods on unstructured triangular meshes. It highlights the reasons why existing approaches fail and proposes a procedure which can be applied to any high order fluctuation splitting scheme to impose positivity on it. Its success is demonstrated through application to a series of linear and nonlinear scalar problems, using a pseudo-time-stepping technique to reach steady state solutions on two-dimensional unstructured meshes.