Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Eine Plattform für die Wissenschaft: Bauingenieurwesen, Architektur und Urbanistik
Explicit Methods using Various Spatial Discretizations
Abstract Stability and accuracy properties of finite element schemes for the shallow water equations have been investigated earlier (Gray and Lynch, 1977) for different time marching schemes. This chapter concentrates on two time marching procedures, the primitive equation leapfrog approximation and the wave equation formulation, in conjunction with various spatial discretizations. Consistent and lumped, linear and quadratic isoparametric Lagrangian finite elements as well as second and fourth order finite differences are studied on a uniform mesh with constant bathymetry in Section 5.2. It is shown that quadratic Lagrangian finite elements require the use of a smaller time step than linear elements to remain stable (Kinnmark and Gray, 1984c). This effect is more severe for the leapfrog method than for the wave equation formulation. For the two-dimensional cases considered, in Section 5.5, with equal node spacing, constant bathymetry and the Coriolis force neglected, the stability constraint is identical in form to the one-dimensional case with the square of the Courant number replaced by the sums of squares of the Courant number in x- and y-directions.
Explicit Methods using Various Spatial Discretizations
Abstract Stability and accuracy properties of finite element schemes for the shallow water equations have been investigated earlier (Gray and Lynch, 1977) for different time marching schemes. This chapter concentrates on two time marching procedures, the primitive equation leapfrog approximation and the wave equation formulation, in conjunction with various spatial discretizations. Consistent and lumped, linear and quadratic isoparametric Lagrangian finite elements as well as second and fourth order finite differences are studied on a uniform mesh with constant bathymetry in Section 5.2. It is shown that quadratic Lagrangian finite elements require the use of a smaller time step than linear elements to remain stable (Kinnmark and Gray, 1984c). This effect is more severe for the leapfrog method than for the wave equation formulation. For the two-dimensional cases considered, in Section 5.5, with equal node spacing, constant bathymetry and the Coriolis force neglected, the stability constraint is identical in form to the one-dimensional case with the square of the Courant number replaced by the sums of squares of the Courant number in x- and y-directions.
Explicit Methods using Various Spatial Discretizations
Kinnmark, Ingemar (Autor:in)
01.01.1986
28 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
Evaluation of spatial discretizations of the shallow water equations
| British Library Conference Proceedings | 2000
Discrete spectrum analyses for various mixed discretizations of the Stokes eigenproblem
| British Library Online Contents | 2012
| British Library Online Contents | 2009
High-order TVB discretizations in time using Richardson's extrapolation
| British Library Online Contents | 2010
Two Finite-Element Discretizations for Gradient Elasticity
| Online Contents | 2009