# ADAPTIVE GRID SIMULATION OF HYPERBOLIC EQUATIONS

• Li, Haojun (Department of Mathematical Sciences, Seoul National University) ;
• Kang, Myungjoo (Department of Mathematical Sciences, Seoul National University)
• Accepted : 2013.10.23
• Published : 2013.12.25

#### 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.

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