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