Mijo Vranješ

An improved collocation method for solving the Henry problem

The original Henry problem is characterized with severe (albeit unphysical) sea boundary condition difficult to handle with numerical methods. In this paper, we present an improved numerical solution of the Henry problem. Presented numerical model solves the steady-state dimensionless equations by the collocation method named Fup Fragment Collocation Method (FFCM) and uses R(bf) basis functions of Fup(2) (x, y) type. This method enables application of the classical formulation and high approximation accuracy as proven in comparison with published solutions. Particular difficulty in solving the original Henry problem is in the accurate representation of the seepage face due to the fixed sea concentration at the sea boundary. The results of the original Henry problem formulation and problem with modified boundary conditions indicate the accuracy and robustness of the FFCM in describing the discharge area of the considered problem.