On some explicit local time stepping finite volume schemes for CFD

In this paper, two local time stepping schemes of order two and three in time are proposed. By construction, they are not mass conservative but a correction stage is added to make them conservative. These schemes are compared with some local time stepping schemes existing in the literature (schemes of Constantinescu and Sandu). The comparisons are carried out on various test cases. They prove that our schemes are efficient and our third order local time stepping has a higher time accuracy than the schemes based on the strategy of Constantinescu and Sandu. Our third order local time stepping scheme is used to perform an industrial-like test case: a 3D Large-Eddy Simulation over an airfoil.