We investigate numerical algorithms for use in air pollution models. The emphasis lies on time integration aspects in connection with advection, vertical turbulent diffusion and stiff chemical transformations. The time integration scheme considered is a 2nd-order implicit-explicit BDF scheme which handles advection explicitly and vertical turbulent diffusion and chemistry implicitly and coupled. The investigation is divided into three parts. In the first part we propose a Gauss-Seidel technique for the implicit solution of the chemistry and vertical turbulent diffusion. For a hypothetical 1D model, based on a 66-species EMEP photochemical ozone chemistry scheme, this technique is shown to be significantly more efficient than the usual approach of using modified Newton with a linear band solver. For the stiff chemistry the Gauss-Seidel iteration is effectively explicit. For the diffusion the implicitness is retained, which gives rise to tridiagonal linear systems. In the second part we discuss stability and consistency properties of the implicit-explicit BDF scheme, assuming the 3rd-order upwind biased finite-difference discretization of the advection operator. In the third part we apply the implicit-explicit scheme to a hypothetical 3D model based on the same photochemical ozone chemistry. Here we employ vectorization over the horizontal grid. Grid-vectorization is of large practical interest as it leads to significantly higher efficiency on a vector computer. Dependent of the process at hand, parallelization is obtained either over the horizontal or over the vertical grid.

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Department of Numerical Mathematics [NM]
Discretization of evoluation problems

Verwer, J.G, Blom, J.G, & Hundsdorfer, W. (1995). An implicit-explicit approach for atmospheric transport-chemistry problems. Department of Numerical Mathematics [NM]. CWI.