Central schemes and contact discontinuities

We introduce a family of new second-order Godunov-type central schemes for one-dimensional systems of conservation laws. They are a less dissipative generalization of the central-upwind schemes, proposed in [A. Kurganov et al., submitted to SIAM J. Sci. Comput.], whose construction is based on the maximal one-sided local speeds of propagation. We also present a recipe, which helps to improve the resolution of contact waves. This is achieved by using the partial characteristic decomposition, suggested by Nessyahu and Tadmor [J. Comput. Phys. 87 (1990) 408-463], which is efficiently applied in the context of the new schemes. The method is tested on the one-dimensional Euler equations, subject to different initial data, and the results are compared to the numerical solutions, computed by other second-order central schemes. The numerical experiments clearly illustrate the advantages of the proposed technique