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This work proposed a new adaptive method which avails from the wavelets theory for transforming the local single resolution information into multiresolution information. This information became accessible and by deactivating or activating them, the spatial resolution adaptation was achieved. The adaptive technique was  combined with two standard numerical modelling schemes (i.e. finite volume and discontinuous Galerkin schemes) to produce two new adaptive schemes for modelling one dimensional shallow water flows so-called the Haar wavelets finite volume (HWFV) and multiwavelet discontinuous Galerkin (MWDG) schemes. Both adaptive schemes were tested using hydraulic test cases. The results demonstrated that the proposed adaptive technique could serve as the foundation on which to construct complete adaptive schemes for simulating the real problems of shallow water flow.

STUDY THE PERFORMANCE OF THE TWO WAVELET-BASED ADAPTATION SCHEMES FOR THE SHALLOW WATER FLOW MODELLING