A stable gradient reconstruction for the MUSCL schemes applied to systems of conservation laws

The numerical simulations of compressible flows need more and more accuracy. Several approaches can be used to increase the order of the scheme. One of the most popular has been introduced by [11]: the so-called MUSCL scheme. In the present work, we focus our attention on the robustness of this method. We propose a relevant CFL restriction and a new gradient reconstruction strategy to enforce stability of the method. The novelty stays in the fact that non conservation argument is involved in the gradient reconstruction. Numerical results are performed using this new variant of the MUSCL scheme.