Solute Transport Models And Inversion Algorithm For Multi-Parameters Identification

This dissertation deals with the use of the optimal perturbation algorithm for the simultaneous inversion of the dispersion coefficient and the source term in solute transport model. We are mainly devoted to the choice of regularization parameter, and several factors affecting the algorithm's realization are discussed. Numerical simulations are presented showing that the inversion algorithm is not only efficient to multi-parameters identification in two-dimensional solute transport model, but also to the one-dimensional fractional-order solute transport model.The main contents of this dissertation are given as follows:In chapter1, background and significance of this dissertation are introduced, and the main researching works and structure of this dissertation are discussed.In chapter2, the models of integer order and fractional order solute transportation are introduced which include the high dimension advection-dispersion equation and the fractional advection-dispersion equation. The forward problem is solved by finite difference scheme, and numerical simulations are also presented.Chapter3deals with an inverse problem for determining a time-dependent reaction coefficient in one-dimensional advection-dispersion equation. Based on the ordinary optimal perturbation algorithm and homotopy regularization algorithm, we set up a new method to the choice of the regularization parameter utilizing a transfer function in artificial neural network.In chapter4, we consider with an inverse problem for determining the dispersion coefficient and the source term simultaneously in two-dimensional solute transport model by the optimal perturbation algorithm. Several factors affecting the algorithm's realization are discussed which are approximation space, additional data, numerical differential steps, initial iterations and noisy data. Numerical simulations are presented showing that the inversion algorithm is efficient to the inverse problem discussed here.In chapter5, an inverse problem is studied for determining the fractional order and the source term or diffusion coefficient simultaneously in one-dimensional space fractional order and time fractional order diffusion model by the optimal perturbation algorithm. We focus on the change of the fractional order affecting the inversion algorithm's realization and the numerical stability.In chapter6, a summary of the thesis is given, and some related problems which could be considered for the future work are discussed.