https://ntrs.nasa.gov/api/citations/20010075154/downloads/20010075154.pdf

Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations

A Semi-implicit Numerical Scheme for Reacting Flow

An Analysis of Operator Splitting Techniques in the Stiff Case

http://web.pdx.edu/~daescu/papers/JCP2005.pdf

Adjoint sensitivity analysis of regional air quality models

Splitting methods for partial differential equations with rough solutions : analysis and MATLAB programs

Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling

The shallow water equations in spherical geometry provide a prototype for developing and testing numerical algorithms for atmospheric circulation models. In a previous paper we have studied a spatial discretization of these equations based on an Osher-type finite-volume method on stereographic and latitude-longitude grids. The current paper is a companion devoted to time integration. Our main aim is to discuss and demonstrate a third-order, A-stable, Runge-Kutta-Rosenbrock method. To reduce the costs related to the linear algebra operations, this linearly implicit method is combined with approximate matrix factorization. Its efficiency is demonstrated by comparison with a classical third-order explicit Runge-Kutta method. For that purpose we use a known test set from literature. The comparison shows that the Rosenbrock method is by far superior.

Time integration of the shallow water equations in spherical geometry

Spatial discretization of the Shallow water equations in spherical geometry using Osher's scheme

The shallow water equations in spherical geometry provide a first prototype for developing and testing numerical algorithms for atmospheric circulation models Since the seventies these models are often solved with spectral methods Increasing demands on grid resolution combined with massive parallelism and local grid refinement seem to offer significantly better perspectives for gridpoint methods In this paper we study the use of Osher's finite-volume scheme for the spatial discretization of the shallow water equations on the rotating sphere This high-order finite volume scheme of upwind type is well suited to solve a hyperbolic system of equations Special attention is paid to the pole problem To that end Osher's scheme is applied on the common (reduced) latitude-longitude grid and on a stereographic grid The latter is most appropriate in the polar region as in stereographic coordinates the pole singularity does not exist The latitude-longitude grid is preferred on lower latitudes Therefore, across the sphere we apply Osher's scheme on a combined grid connecting the two grids at high latitude We will show that this provides an attractive spatial discretization for explicit integration methods, as it can greatly reduce the time step limitation incurred by the pole singularity when using a latitude-longitude grid only When time step limitation plays no significant role, the standard (reduced) latitude-longitude grid is advocated provided that the grid is kept sufficiently fine in the polar region to resolve flow over the poles

D. Lanser

Papers

Analysis of operator splitting for advection-diffusion-reaction problems from air pollution modelling

Time integration of the shallow water equations in spherical geometry

Time integration of the shallow water equations in spherical geometry

Spatial discretization of the Shallow water equations in spherical geometry using Osher's scheme

Spatial discretization of the shallow water equations in spherical geometryusing Osher's scheme