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Regularizing discontinuities based on filtering using dirac delta kernels

Wissink, B.W. (2016) Regularizing discontinuities based on filtering using dirac delta kernels.

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Abstract:In this report the regularization of discontinuous initial conditions of the one-dimensional Advection Equation will be studied. The discrete initial conditions will be interpolated using polynomial interpolation. This polynomial interpolation is convoluted with a high order regularized Dirac-delta function. The equation will be solved using a spectral collocation method. The convolution with the polynomial-based Dirac-delta function is written in a matrix-vector multiplication for convenient implementation. It is shown that this method yields stable results and higher order convergence away from the regularization zone for different discontinuous initial conditions. The influence of the variables of the regularized delta function is studied and explained. Furthermore, the results are compared with the theoretical filter error. It is shown that the solution converges according to the theoretical filter error in the case of filtered boundary conditions and sufficiently wide regularization zones.
Item Type:Internship Report (Master)
Clients:
San Diego State University, United States
Faculty:ET: Engineering Technology
Subject:52 mechanical engineering
Programme:Mechanical Engineering MSc (60439)
Link to this item:http://purl.utwente.nl/essays/71933
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