On the artificial compression method for second-order nonoscillatory central difference schemes for systems of conservation laws

The recently proposed high-order central difference schemes for conservation laws have a tendency of smearing linear discontinuities. In principle, Harten's artificial compression method (ACM) could be used to improve resolution. We analyze why this approach has not yet been used successfully and derive a more powerful version of the ACM based on a rigorous estimate of the total variation. We discuss the potential danger of overcompression and point out directions of future algorithmic development.