CLOSED FORM SOLUTIONS FOR WATER POLLUTION PROBLEMS - II

Abstract

IN THE LAST DECADES, THE INTEREST IN STUDYING POLLUTANT DISPERSION IN WATER BODIES HAS INCREASED AS A CONSEQUENCE OF THE ENVIRONMENTAL PROBLEMS CAUSED BY THE INDUSTRIAL AND TECHNOLOGICAL DEVELOPMENT. THIS WORK PROPOSES A NEW ANALYTICAL METHOD FOR SOLVING THE TWODIMENSIONAL ADVECTION-DIFFUSION EQUATION DESCRIBING THE DISPERSION OF BACTERIA AND CHEMICALS IN LAKES AND RIVERS. THE METHOD IS BASED ON AN ITERATIVE SCHEME THAT PROVIDES A SEQUENCE OF EXACT SOLUTIONS WITH AN INCREASING NUMBER OF ARBITRARY FUNCTIONS AND PARAMETERS, THEREBY AVOIDING THE A PRIORI KNOWLEDGE OF ANY OF THE LIE SYMMETRIES ADMITTED BY THE EQUATION. THE ARBITRARY COMPONENTS ARE ULTIMATELY SPECIFIED BY THE APPLICATION OF APPROPRIATE BOUNDARY CONDITIONS TO THE PROBLEM. A SIMULATION WAS MADE OF THE POLLUTANT PROPAGATION PROBLEM IN THE GUAíBA LAKE IN THE OUTSKIRTS OF PORTO ALEGRE, BRAZIL, FOR DEPARTAMENTO MUNICIPAL DE AGUAS E ESGOTOS (DMAE), THE COUNTY'S WATER TREATMENT AND SEWAGE DISPOSAL AUTHORITY, AND THE RESULTS WERE COMPARED WITH AVAILABLE EXPERIMENTAL DATA. THE MAIN ADVANTAGES OF THE METHOD RELY ON THE LOW PROCESSING TIME AND ON THE ANALYTICAL CHARACTER OF THE SOLUTIONS OBTAINED.