O metodo de Galerkin descontinuo com difusividade implicita e h-adaptabilidade baseada em tecnicas Wavelet

AUTOR(ES)
DATA DE PUBLICAÇÃO

2002

RESUMO

In this work an inovative technique is presented for the numerical approximation of conservation laws on unstructured meshes. The numerical scheme uses a discontinuous piecewise polynomial approximation with hadaptivity. The self-adaptive h-refinement strategy uses a regularity assessment of the solution based on wavelet techniques. This strategy determines the sub-domains or regions where the solution is smooth and where elements can be coarsened and/or regions of singularity where the elements are refined. Numerical oscillations within the discontinuous element are controlled by adding a difusive term. The wavelet analysis is also used to determine the magnitude of the diffusive term. The resulting scheme is based both on the Runga-Kutta Discontinuous Galerkin method [16] and the streamline diffusion method [33] : when the order of interpolation within the elements is zero it is a cell centered finite volume method, and for interpolation order p _ 1 , it is an h-adaptive discontinuous Galerkin method, using Euler time-stepping. Internal oscillations are entirely controlled by the added streamline diffusion operator. An optimal relationship between the time step (in terms of the CFL condition) and the size of the diffusion coeficient is analysed for numerical precision. When the diffusive term ??? , the presented scheme reduces to the finite volume method. The scheme is implemented using the object oriented programming philosophy based on the environment described in [21]. Within this context, a library of classes was developed which implements piecewise polynomial discontinuous approximations and which analyses the regularity of the approximate solution using the wavelet technique

ASSUNTO(S)

galerkin metodos de analise numerica lei da conservação (fisica) wavelets (matematica)

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