| Distributed systems, such as dedicated networks of workstations, or non-dedicated inter-connection networks of computers, may be used to tackle mathematically intensive environmental research problems. The algorithms and methodologies underlying these research problems must be scalable on distributed systems. This research was concerned with developing such algorithms and methodologies for solving the advection-diffusion equation (ADE), which underlies almost all mechanistic models of aqueous environmental systems. The mass conservation law (which governs the distribution of mass in environmental systems) was taken in Cartesian coordinates, and then transformed into a natural coordinate system (NCS). The NCS was shown to simplify the ADE, and more importantly to suggest an elegant partitioning of the physical problem space into distinct and separate regions, which are computationally autonomous, at least for pure advection. An efficient algorithm for advective transport was developed and proven, by numerical analysis, to be unconditionally stable, conservative, and highly accurate. Because it has no stability limitation, this algorithm can dramatically reduce computational intensity. More significantly, in the context of parallel computation, this approach greatly reduces synchronizations and communications. Therefore, the algorithm is theoretically well-suited for distributed computations. In this research, the advection solver was coupled with a diffusion solver to produce a model for advection-diffusion transport. Key issues for parallel computations on both dedicated and non-dedicated distributed systems were analyzed and discussed.; Several numerical experiments were employed to demonstrate the error characteristics and usefulness of the model for both pure advection and advection-diffusion. Furthermore, the scalability of the algorithm on dedicated and non-dedicated distributed systems was evaluated. Both homogenous and heterogeneous systems were tested, along with static and self-scheduling job assignment algorithms. Finally, a hypothetical but realistic case study of fluvial transport has been presented to demonstrate the usefulness of the approach to a real-world scenario. |
