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Access type: UnknownSubject: search.filters.subject.finite difference method

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    An Unconditionally Stable Explicit Finite Difference Method for a Non-Dimensional Mathematical Model of Shoreline Evolution with a Twin Groins Structure
    (2024-02-01)
    Manilam, Surasak
    ;
    Pochai, Nopparat
    The development of a more effective model and the prediction of trends in shorelines were the two goals of this study. For simulations of shoreline evolution utilizing the straight twin groin structure, we used two mathematical models. A one-dimensional evolution model makes up the initial model. The first model is transformed into a non-dimensional evolution model in the second model. We propose a method for transforming one-dimensional models into non-dimensional models, that involves creating initial and boundary conditions for each model. The forward time centered space (FTCS) technique and the Saulyev finite difference technique were applied to approximately represent shoreline evolution each year. Their simulation results demonstrate that when the engineering structure was built on the nearby shorelines, shoreline evolution accelerated annually. As the Saulyev finite difference technique is not restricted by the stability conditions, it produces better simulations.
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    A Numerical Groundwater Quality Assessment Model Using the Cubic Spline Method
    (2024-01-01)
    Klankaew, Pantira
    ;
    Pochai, Nopparat
    Human activities on the surface, including municipal garbage disposal, pesticide usage, and fertilizer use, can contaminate groundwater. Long-term groundwater quality investigations near landfill sites necessitate the use of mathematical models. Research on the environmental impacts of projects, including landfills, depends on the long-term expansion of groundwater quality. Analyzing the quality of groundwater employed an advection-diffusion equation (ADE) in one dimension to describe the quantity of pollution in the groundwater. In this research, numerical simulations for a one-dimensional mathematical model for a long-term contaminated groundwater pollution measurement around landfills are proposed. The finite difference and the natural cubic spline techniques are approximated by the model solution. In a given scenario, the approximate solutions are compared with the exact solutions. The proposed finite difference analysis provides close-to-exact and properly accurate solutions. Numerous varieties of soil physics can be used for the suggested numerical simulation. The simulations can be used to assess the quality of groundwater that becomes contaminated in the future. It is demonstrated that the cubic spline method yields acceptable approximations. It is an alternate finite difference technique.