Conservation properties of a new unstructured staggered scheme

In Wenneker et al. [Computation of compressible flows on unstructured staggered grids. In: Onate E, Bugeda G, Suarez B, editors. Proceedings European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000, Barcelona, 11-14 September 2000, Barcelona, 2000. CIMNE. http://ta.twi.tudelft.nl/users/wesseling/pub.html] an unstructured staggered scheme for the two-dimensional (2D) Euler equations is discussed. Such a scheme cannot be in classic conservation form for momentum. The aim of the present paper is to formulate a generalized conservation form for momentum on unstructured staggered grids, and to demonstrate by numerical experiments that the scheme satisfies the Rankine-Hugoniot conditions. Numerical results for 1D Riemann problems on 2D unstructured grids confirm that the scheme converges to the entropy solution. In addition, transonic flow around an airfoil is computed. (C) 2002 Elsevier Science Ltd. All rights reserved.