We present a numerical method for modelling and simulation of transport and dispersion of phosphogypsum in the Jorf Lasfar coastal zone located on the Atlantic Ocean at Morocco. The governing equations consist of the well-established barotropic ocean model including the barometric pressure, friction terms, Coriolis and wind stresses. To model transport and dispersion of phosphogypsum we consider an advection-diffusion equation with an anisotropic dispersion tensor and source terms. As a numerical solver, we propose a novel multilevel adaptive semi-Lagrangian finite element method. The proposed method combines the modified method of characteristics to deal with convection terms, the finite element discretization to handle complex geometries, a projection-based algorithm to solve the Stokes problem, and an adaptive -projection using quadrature rules to improve the efficiency and accuracy of the method. Numerical results are presented to demonstrate the high resolution of the proposed method and to confirm its capability to provide accurate and efficient simulations for transport and dispersion of phosphogypsum in the Jorf Lasfar coastal zone.

中文翻译：

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沿海地区磷石膏运输和分散的快速准确方法：在 Jorf Lasfar 中的应用

我们提出了一种数值方法，用于对位于摩洛哥大西洋的 Jorf Lasfar 沿海地区磷石膏的运输和扩散进行建模和模拟。控制方程由完善的正压海洋模型组成，包括气压、摩擦项、科里奥利力和风应力。为了模拟磷石膏的传输和分散，我们考虑具有各向异性分散张量和源项的平流扩散方程。作为数值求解器，我们提出了一种新颖的多级自适应半拉格朗日有限元方法。所提出的方法结合了处理对流项的特征修正方法、处理复杂几何形状的有限元离散化、解决斯托克斯问题的基于投影的算法以及求解斯托克斯问题的自适应算法。${\mathrm{L}}^2$-使用正交规则进行投影，以提高方法的效率和准确性。数值结果证明了该方法的高分辨率，并确认其为 Jorf Lasfar 沿海地区磷石膏的传输和扩散提供准确有效的模拟的能力。