HIGH ORDER LOCALIZED ENO SCHEMES ON UNSTRUCTURED MESHES FOR CONSERVATION LAWS

We construct a localized finite volume method by applying ENO (essentially non-oscillatory) reconstruction to solve hyperbolic conservation laws following the partitions of the spectral volume methods. The main idea is as follows: Firstly, separate the calculating domain into intervals, named main-cells, then divide the intervals into subintervals, named sub-cells. Secondly, use ENO methodology to reconstruct conservative variables in the main-cells by using the cell averages of proper sub-cells. After that, use the TVD Runge-Kutta time discrete method to obtain fully discrete scheme. Several classic numerical tests show that this scheme has capabilities to capture discontinuities in high resolution and robustness.