Modeling Pollutant Dispersion over Irregular Terrain with Second Moments and Cubic Splines

摘要

Under ideal conditions, dispersion can be reasonably predicted with analytical methods, such as Gaussian puff/plume theory. However, analytical methods are typically inflexible under variable wind conditions, particularly in cases where dispersion occurs over irregular surfaces. A specific need exists for more detailed study into the effect of surface irregularities on dispersion. The requirement is to establish an accurate and efficient numerical solution algorithm for three-dimensional mesoscale atmospheric transport and diffusion over irregular terrain. Herein, a three-dimensional method-of-moments technique is employed to calculate pollutant advection. The method is based on the calculation of moment distributions of a concentration within a cell (volume). By summing moments over the solution domain, and using a Lagrangian advection scheme, concentration can be transported without generation of numerical dispersion error. Because the method maintains subgrid scale resolution, problems involving steep gradients can be calculated without significant computational damping. Three-dimensional diffusion is solved by the method of cubic splines. The cubic spline method is based on continuous-curvature cubic spline relations used as interpolation functions for first and second derivative terms. After solution of the diffusion terms, the first and second moments are recalculated to ensure continuity with the advection terms. To reduce computer programming complexity, the procedure of fractional steps is used to calculate the three-dimensional solutions. A coordinate transformation is employed to transform the terrain-lid variability into regular intervals in the computational domain. Simple tests are conducted to determine the accuracy of the numerical methods. The effect of topography on a continuous emission is examined under ideal conditions and the results compared with values obtained from an analytical Gaussian plume relation. (ERA citation 04:031385)