Development of a GPGPU accelerated tool to simulate advection-reaction-diffusion phenomena in 2D

Abstract

Computational models are powerful tools to the study of environmental systems, playing a fundamental role in several fields of research (hydrological sciences, biomathematics, atmospheric sciences, geosciences, among others). Most of these models require high computational capacity, especially when one considers high spatial resolution and the application to large areas. In this context, the exponential increase in computational power brought by General Purpose Graphics Processing Units (GPGPU) has drawn the attention of scientists and engineers to the development of low cost and high performance parallel implementations of environmental models. In this research, we apply GPGPU computing for the development of a model that describes the physical processes of advection, reaction and diffusion. This presentation is held in the form of three self-contained articles. In the first one, we present a GPGPU implementation for the solution of the 2D groundwater flow equation in unconfined aquifers for heterogenous and anisotropic media. We implement a finite difference solution scheme based on the Crank- Nicolson method and show that the GPGPU accelerated solution implemented using CUDA C/C++ (Compute Unified Device Architecture) greatly outperforms the corresponding serial solution implemented in C/C++. The results show that accelerated GPGPU implementation is capable of delivering up to 56 times acceleration in the solution process using an ordinary office computer. In the second article, we study the application of a diffusive-logistic growth (DLG) model to the problem of forest growth and regeneration. The study focuses on vegetation belonging to preservation areas, such as riparian buffer zones. The study was developed in two stages: (i) a methodology based on Artificial Neural Network Ensembles (ANNE) was applied to evaluate the width of riparian buffer required to filter 90% of the residual nitrogen; (ii) the DLG model was calibrated and validated to generate a prognostic of forest regeneration in riparian protection bands considering the minimum widths indicated by the ANNE. The solution was implemented in GPGPU and it was applied to simulate the forest regeneration process for forty years on the riparian protection bands along the Ligeiro river, in Brazil. The results from calibration and validation showed that the DLG model provides fairly accurate results for the modelling of forest regeneration. In the third manuscript, we present a GPGPU implementation of the solution of the advection-reaction-diffusion equation in 2D. The implementation is designed to be general and flexible to allow the modeling of a wide range of processes, including those with heterogeneity and anisotropy. We show that simulations performed in GPGPU allow the use of mesh grids containing more than 20 million points, corresponding to an area of 18,000 km² in a standard Landsat image resolution.