A low dissipation essentially non-oscillatory central scheme

Here we present a new, semidiscrete, central scheme for the numerical solution of one-dimensional systems of hyperbolic conservation laws. The method presented in this paper is an extension of the centrally weighted non-oscillatory schemes (Cweno) presented in [A. Kurganov, E. Tadmor, New high resolution central schemes for nonlinear conservation laws and convection–diffusion equations, J. Comp. Phys. 160 (2000) 241–282; A. Kurganov, D. Levy, A third-order semidiscrete central scheme for conservation laws and convection–diffusion equations, SIAM J. Sci. Comput. 22 (2000) 1461–1488; A. Kurganov, S. Noelle, G. Petrova, Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton–Jacobi equations, SIAM J. Sci. Comput. 23 (3) (2001) 707–740]. The method suggested in this manuscript is derived independently of the order of the scheme. The gain in this new method is a decreased dissipation especially for high Mach-number flows, which are frequently encountered, e.g., in astrophysical contexts or turbulent systems.