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Summary: 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 L2$$ {\mathrm{L}}^2 $$‐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. [ABSTRACT FROM AUTHOR]