tailieunhanh - Two approximation methods of spatial derivatives on unstructured triangular meshes and their application in computing two dimensional flows

The model is tested on rectangular grids triangulari2jed after the 8-neighbours strategy. In the context of t he semi-implicit time matching methods, the directional derivative technique is more accurate t han Green's theorem technique. The results from the t hird order Adams-Bashforth scheme are the most accurate, especially for discontinuous problems. In this case, there is a minor difference between two approximation techniques of spatial derivatives. | Vietnam Journal of Mechanics, VAST, Vol. 28, No. 4 (2006), pp. 230 - 240 ;. TWO APPROXIMATION METHODS OF SPAT IAL DERIVATIVES ON UNSTRUCTURED TRIANGULAR MESHES AND THEIR APPLICATION IN COMPUTING TWO DIM ENSIONAL FLOWS NGUYEN D ue LANG 1 ' TRAN GIA LICH 2 ' AND LE Duc 3 1 3 Falcuty of Natural Science, Thai Nguyen University 2 Institute of Mathematics National Center of Hydrological-Meteorological Forecast Abstract. Two approximation methods (the Green's t heorem technique and the directional derivative technique) of spatial derivatives have been proposed for finite differences on unstructured t riangular meshes. Both methods have the first order accuracy. A semi-implicit time matching methods beside the third order Adams-Bashforth method are used in integrating the water shallow equations written in both non-conservative and conservative forms. To remove spurious waves, a smooth procedure has been used. The model is tested on rectangular grids triangulari2jed after the 8-neighbours strategy. In t he context of t he semi-implicit time matching methods, the directional derivative technique is more accurate t han Green's theorem technique. The results from the t hird order Adams-Bashforth scheme are the most accurate, especially for discontinuous problems. In this case, there is a minor difference between two approximation techniques of spatial derivatives. 1. INTRODUCTION Models simulating flow in rivers, coastal areas, . . . are needed to resolve many natural phenomena in such domains. Because natural phenomena range from small scales to large scales, meshes used in models must vary and depend on problem geometries. That's why unstructured meshes are more appropriate than structured, uniform meshes in modeling flows [7] . The popular methods using unstructured meshes consist of finite volumes and finite elements. A cell, . a triangular, is a base element in such methods. The finite volume method is more preferable than the finite element method because