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Subject: search.filters.subject.Finite Difference Method

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    A two-dimensional mathematical model for long-term contaminated groundwater pollution measurement around a land fill
    (2020-01-01)
    Limthanakul, Jirapud
    ;
    Pochai, Nopparat
    A source of contaminated groundwater is governed by the disposal of waste material on a land fill. There are many people in rural areas where the primary source of drinking water is well water. This well water may be contaminated with groundwater from landfills. In this research, a two-dimensional mathematical model for long-term contaminated groundwater pollution measurement around a land fill is proposed. The model is governed by a combination of two models. The first model is a transient two-dimensional groundwater flow model that provides the hydraulic head of the groundwater. The second model is a transient two-dimensional advection-diffusion equation that provides the groundwater pollutant concentration. The proposed explicit finite difference techniques are used to approximate the hydraulic head and the groundwater pollutant concentration. The simulations can be used to indicate when each simulated zone becomes a hazardous zone or a protection zone.
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    Numerical treatment of a two-dimensional vertically-averaged groundwater flow model using alternating direction explicit methods
    (2020-01-01)
    Yena, Supawan
    ;
    Pochai, Nopparat
    Leachate from a landfill can flow down and contaminate groundwater. Mathematical models are often used to describe groundwater flow, which can help designers to identify an appropriate location for a landfill area. We focused on simulation of hydraulic head of groundwater under landfill construction in a rural area. We used a partial differential equation model called two-dimensional vertically-averaged groundwater flow model to explain groundwater volume, in particular, to explain the hydraulic head of the groundwater which strongly affected the groundwater quality. We applied two alternating direction explicit methods to the groundwater flow model under general boundary conditions and rates of change of boundary conditions to obtain an approximate hydraulic head of groundwater. An alternating direction explicit method for all types of boundaries is used to find approximate solutions. The traditional alternative direction explicit method was modified to form our modified alternative direction explicit method. The results of all method are closed. The traditional alternative direction explicit method and the modified alternative direction explicit method led to more accurate solutions than forward time centered space in heterogeneous aquifer, two methods ensured that a stable solution of all interior points can be obtained by using a fine grid spacing.
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    A mathematical model of horizontal averaged groundwater pollution measurement with several substances due to chemical reaction
    (2020-01-01)
    Limthanakul, Jirapud
    ;
    Pochai, Nopparat
    Chloride is a well-known chemical compound that is very useful in industry and agricultural. Chloride can be transformed to hypochlorite, chlorite, chlorate and perchlorate, chloride and their substances are not dangerous if they are used in the optimal level. Groundwater containing contamination chloride and their substances impacts human health, for ex-ample, drinking water contaminated chloride exceed 250 mg/L can cause heart problems and lead to high blood pressure. To avoid this problem, we used mathematical models to explain groundwater contamination with chloride and their substances. Transient groundwater flow model provides the hydraulic head of groundwater. In this model we will get the level of ground-water, next, we need to find its velocity and direction by using the result in first model put into second model. Groundwater velocity model provides x-and z-direction vector in ground-water, after computation we will plugin the result into the last model to approximate the chloride concentration in ground-water. Groundwater contamination dispersion model provides chloride, hypochlorite, chlorite, chlorate and perchlorate con-centration. The proposed explicit finite difference techniques are used to approximate the model solution. Explicit method was used to solved hydraulic head model. Forward space de-scribed groundwater velocity model. Forward time and central space used to predict transient groundwater contaminated mod-els. The simulations can be used to indicate when each simu-lated zone becomes a hazardous zone or a protection zone.