On the Reduction of Numerical Dissipation in Central-Upwind Schemes (Communications in Computational Physics, 2007)
We study central-upwind schemes for systems of hyperbolic conservationlaws, recently introduced in [13]. Similarly to staggered non-oscillatory central schemes,these schemes are central Godunov-type projection-evolution methods that enjoy theadvantages of high resolution, simplicity, universality and robustness. At the sametime, the central-upwind framework allows one to decrease a relatively large amountof numerical dissipation present at the staggered central schemes. In this paper, wepresent a modification of the one-dimensional fully- and semi-discrete central-upwindschemes, in which the numerical dissipation is reduced even further. The goal isachieved by a more accurate projection of the evolved quantities onto the original grid.In the semi-discrete case, the reduction of dissipation procedure leads to a new, lessdissipative numerical flux. We also extend the new semi-discrete scheme to the two-dimensionalcase via the rigorous, genuinely multidimensional derivation. The newsemi-discrete schemes are tested on a number of numerical examples, where one canobserve an improved resolution, especially of the contact waves.