Weighted essentially non-oscillatory schemes for the interpolation of mean values on unstructured grids

In this paper the weighted ENO (essentially non-oscillatory) scheme developed for the one-dimensional case by Liu, Osher, and Chan is applied to the case of unstructured triangular grids in two space dimensions. Ideas from Jiang and Shu, especially their new way of smoothness measuring, are considered. As a starting point for the unstructured case we use an ENO scheme like the one introduced by Abgrall. Beside the application of the weighted ENO ideas the whole reconstruction algorithm is analyzed and described in derail. Here we also concentrate on technical problems and their solution. Finally, some applications are given to demonstrate the accuracy and robustness of the resulting new method. The whole reconstruction algorithm described here can be applied to any kind of data on triangular unstructured grids, although it is used in the framework of compressible How computation in this paper only, (C) 1998 Academic Press.