Global multiquadric collocation method for groundwater contaminant source identification

In this paper, a radial basis collocation method (RBCM) based on the global space-time multiquadric (GST-MQ) is developed to solve the inverse problem of groundwater contaminant source identification. This deterministic method directly induces the problem to a single-step solution of a system of linear algebraic equations in the entire space-time domain. The least-square-based radial basis collocation method (LS-RBCM) is introduced to overcome the ill-posedness of the linear system. To increase confidence in the GST-MQ solutions, the sensitivity analysis with respect to calculation parameters, observation data and model uncertainty is investigated. The performance of the application examples of contaminant source identification in one- and two-dimensional porous media demonstrates that the proposed method poses the meshfree advantage and direct identification of contaminant source with efficient methodology. The GST-MQ method provides a robust tool for estimating spatial plume distribution as well as the release history of groundwater contaminant source from concentration measurements.

► We develop a meshfree method for groundwater contaminant source identification. ► The method is based on the global space-time multiquadric. ► The method solves the inverse problem in the same numerical procedure as a direct one. ► The contaminant sources are efficiently identified in 1D and 2D porous media examples.