tailieunhanh - Báo cáo "Stability of spatial interpolation functions in finite element one‐dimensional kinematic wave rainfall‐runoff models "

This paper analyzes the stability of linear, lumped, quadratic, and cubic spatial interpolation functions in finite element one‐dimensional kinematic wave schemes for simulation of rainfall‐runoff processes. Galerkin’s residual method transforms the kinematic wave partial | VNU Journal of Science Earth Sciences 24 2008 57-65 Stability of spatial interpolation functions in finite element one-dimensional kinematic wave rainfall-runoff models Luong Tuan Anh Rolf Larsson 2 1 Research Center for Hydrology and Water Resources Institute of Hydro-meteorological and Environmental Sciences 2 Water Resources Engineering Department Lund University Box 118 S-221 00 Lund Sweden Received 27 May 2008 received in revised form 5 July 2008 Abstract. This paper analyzes the stability of linear lumped quadratic and cubic spatial interpolation functions in finite element one-dimensional kinematic wave schemes for simulation of rainfall-runoff processes. Galerkin s residual method transforms the kinematic wave partial differential equations into a system of ordinary differential equations. The stability of this system is analyzed using the definition of the norm of vectors and matrices. The stability index or singularity of the system is computed by the Singular Value Decomposition algorithm. The oscillation of the solution of the finite element one-dimensional kinematic wave schemes results both from the sources and from the multiplication operator of oscillation. The results of computation experiment and analysis show the advantage and disadvantage of different types of spatial interpolation functions when FEM is applied for rainfall- runoff modeling by kinematic wave equations. Keywords Rainfall-runoff Kinematic wave Spatial interpolation functions Singular value decomposition Stability index. 1. Introduction The need for tools which have capability of simulating influence of spatial distribution of rainfall and land use change on runoff processes initiated the development of hydrodynamic rainfall-runoff models 1 8 . One of the basic assumptions for such models regards the existence of a continuous layer of water moving over the whole surface of the catchments. Although observations show that such conditions are rare the assumption can Corresponding .