engleski

Collocation method in solving saltwater intrusion problems

In this work we present an improved numerical solution of the saltwater intrusion problem. Presented numerical model solves the nonlinear couple equations by the collocation method named Fup Fragment Collocation Method (FFCM) and uses basis functions of type. Rvachev's basis functions - Rbf are infinitely derivable functions (B. Gotovac and Kozulic, 1999, 2000) classified between classical polynomials and spline functions, but in practice their application as basis functions is closer to splines. Thus, these functions can be treat as splines of infinite degree of the order that enables setting of the collocation points to the vertices of the basis fuctions. It enables also consistent, unique collocation method and application of the classical formulation and high approximation accuracy. The main property of this numerical method is universal vector space of basis functions that enables that solution with more collocation points (more basis functions) must be more accurately (it is not always the case, for instance, in the common finite element method). In that way we can improve our solution for any prescribed tolerance or degree of the accuracy. It can be using for creating "accurate" solution of the known saltwater intrusion problem as the Henry problem (H. Gotovac et al., 2003) and can be use as benchmark for other numerical codes.

numerical modeling; saltwater intrusion; collocation method; density dependent flow and transport

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