A Hybrid Numerical Model for Simulating Atmospheric Dispersion

A hybrid numerical model for simulating atmospheric contaminant dispersion is developed. The hybrid numerical scheme employs an hp-adaptive finite element method coupled with a Lagrangian particle transport technique to solve the governing equations for atmospheric flow and species transport. A random walk/stochastic approach is used to generate Lagrangian particles that define the contaminant dispersion traces. A coarse mesh using low order shape functions is initially generated. Both the mesh and shape function order are subsequently refined and enriched in those regions where high computational error exist. Compared with fine mesh and high order numerical solutions, the hybrid scheme produces highly accurate solutions with reduced computational cost. A general probability distribution is used in the particle transport module for the random component of motion due to turbulent diffusion. Results depicting contaminant transport and dispersion in the atmosphere are presented. The computational efficiency of the hybrid numerical model is also discussed. INTRODUCTION Contaminant dispersion is a serious environmental problem [1]. Analytical solutions for the equations used to describe the advection and diffusion of contaminants in the atmosphere are intractable for most real-world situations. Consequently, researchers have had to rely upon numerical simulations for many years [2]-[5]. Regardless of which numerical methods researchers may use, the goal has been essentially to achieve fast and accurate predictions of wind fields and contaminant dispersion traces. The finite element method (FEM), with its ability to easily deal with irregular geometries while employing the use of general-purpose algorithms, is one of the most popular numerical tools for solving contaminant dispersion problems. Adaptive FEM is especially attractive for it can obtain highly accurate results beginning with a coarse mesh and low order shape functions. In this study, an hp-adaptive FEM is employed to efficiently construct highly accurate 3-D wind fields; a Lagrangian Particle Transport (LPT) technique is coupled to the FEM model. The LPT scheme uses a large number of particles to approximate advection and diffusion instead of solving the transport equation for species concentration directly. A brief discussion of the principles describing the two major numerical schemes is presented. Simulation test cases are given for contaminant dispersion released into the atmosphere and enveloping a series of buildings. The simulation is further enhanced as the contaminant enters a window within a building complex and disperses within a set of interior offices. The hybrid numerical model appears well suited for solving contaminant dispersion related environmental problems. The model can be effective for use in emergency response and homeland security situations. NOMENCLATURE B Body force C Gradient operator D Domain D ∂ Domain boundary Fv Load vector for velocity Fθ Load vector for temperature Cm F Load vector for mass concentration h Characteristic of element length