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arXiv · 2210.16349

Numerical analysis of a time-stepping method for the Westervelt equation with time-fractional damping

Katherine Baker·Lehel Banjai·Mariya Ptashnyk
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Abstract

We develop a numerical method for the Westervelt equation, an important equation in nonlinear acoustics, in the form where the attenuation is represented by a class of non-local in time operators. A semi-discretisation in time based on the trapezoidal rule and A-stable convolution quadrature is stated and analysed. Existence and regularity analysis of the continuous equations informs the stability and error analysis of the semi-discrete system. The error analysis includes the consideration of the singularity at $t = 0$ which is addressed by the use of a correction in the numerical scheme. Extensive numerical experiments confirm the theory.

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Katherine Baker, Lehel Banjai, Mariya Ptashnyk. 2022-10-28. Numerical analysis of a time-stepping method for the Westervelt equation with time-fractional damping. https://arxiv.org/abs/2210.16349

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