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http://dx.doi.org/10.12941/jksiam.2013.17.279

ADAPTIVE GRID SIMULATION OF HYPERBOLIC EQUATIONS  

Li, Haojun (Department of Mathematical Sciences, Seoul National University)
Kang, Myungjoo (Department of Mathematical Sciences, Seoul National University)
Publication Information
Journal of the Korean Society for Industrial and Applied Mathematics / v.17, no.4, 2013 , pp. 279-294 More about this Journal
Abstract
We are interested in an adaptive grid method for hyperbolic equations. A multiresolution analysis, based on a biorthogonal family of interpolating scaling functions and lifted interpolating wavelets, is used to dynamically adapt grid points according to the physical field profile in each time step. Traditional finite-difference schemes with fixed stencils produce high oscillations around sharp discontinuities. In this paper, we hybridize high-resolution schemes, which are suitable for capturing singularities, and apply a finite-difference approach to the scaling functions at non-singular points. We use a total variation diminishing Runge-Kutta method for the time integration. The computational cost is proportional to the number of points present after compression. We provide several numerical examples to verify our approach.
Keywords
adaptive; multiresolution analysis; wavelet; hyperbolic conservation law;
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