Herbin, Raphaéle (ed.) et al., Finite volumes for complex applications III. Problems and perspectives. Papers from the 3rd symposium of finite volumes for complex applications, Porquerolles, France, June 24–28, 2002. London: Hermes Penton Science (ISBN 1-9039-9634-1/pbk). 793-800 (2002).

Summary: We present several improvements for the Jiang-Nessyahu-Tadmor second-order, nonoscillatory, central difference scheme on two-dimensional, staggered, Cartesian grids for systems of conservation laws [cf.

*G. S. Jiang* and

*E. Tadmor*, SIAM J. Sci. Comput. 19, No. 6, 1892–1917 (1998;

Zbl 0914.65095);

*H. Nessyahuh* and

*E. Tadmor*, J. Comput. Phys. 87, No. 2, 408–463 (1990;

Zbl 0697.65068)]. They concern the flux quadrature to reduce grid orientation effects, a more powerful version of

*A. Harten’s* artificial compression method [ibid. 49, 357–393 (1983;

Zbl 0565.65050)] to improve the resolution of linear discontinuities, some experiments and analysis of instabilities in 2D as well as an adaptive staggered scheme on structured Cartesian grids.