Abstract
We present a family of central‐upwind schemes on general triangular grids for solving two‐dimensional systems of conservation laws. The new schemes enjoy the main advantages of the Godunov‐type central schemes—simplicity, universality, and robustness and can be applied to problems with complicated geometries. The “triangular” central‐upwind schemes are based on the use of the directional local speeds of propagation and are a generalization of the central‐upwind schemes on rectangular grids, recently introduced in Kurganov et al. [SIAM J Sci Comput 23 (2001), 707–740]. We test a second‐order version of the proposed scheme on various examples. The main purpose of the numerical experiments is to demonstrate the potential of our method. The more universal “triangular” central‐upwind schemes provide the same high accuracy and resolution as the original, “rectangular” ones, and at the same time, they can be used to solve hyperbolic systems of conservation laws on complicated domains, where the implementation of triangular or mixed grids is advantageous. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005