Use of Galerkin methods in numerical weather prediction
Williams, Roger Terry
MetadataShow full item record
In this report the Galerkin method is presented and the spectral and finite element methods are shown to be special cases of the general method. The spectral and finite methods are applied to a simple linear equation and compared. The spectral method is then applied to the non-linear baratropic vorticity equation in Cartesian coordinates and in spherical coordinates. The transform technique is presented which allows efficient treatment of the nonlinear terms in the spectral method. This method is also applied to the shallow water equations. The finite element method with linear basis functions is applied to the linear advection equation and compared to second and fourth order finite difference approximations. The nonlinear barotropic vorticity is also developed in finite elements.
NPS Report NumberNPS63-78-006
Showing items related by title, author, creator and subject.
Verification of a non-hydrostatic dynamical core using the horizontal spectral element method and vertical finite difference method: 2-D aspects Giraldo, F.X.; Choi, S.-J.; Kim, J.; Shin, S. (Copernicus Publications, 2014);The non-hydrostatic (NH) compressible Euler equations for dry atmosphere were solved in a simplified two-dimensional (2-D) slice framework employing a spectral element method (SEM) for the horizontal discretization and ...
Giraldo, F.X. (2001);The spectral element method for the two-dimensional shallow water equations on the sphere is presented. The equations are written in conservation form and the domains are discretized using quadrilateral elements obtained ...
Finite volume element (FVE) discretization and multilevel solution of the axisymmetric heat equation Litaker, Eric T. (Monterey, California. Naval Postgraduate School, 1994-12);The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum ...