A mimetic discretization of Westervelt's equation
<|reference_start|>A mimetic discretization of Westervelt's equation: A broad class of nonlinear acoustic wave models possess a Hamiltonian structure in their dissipation-free limit and a gradient flow structure for their dissipative dynamics. This structure may be exploited to design numerical methods which preserve the Hamiltonian structure in the dissipation-free limit, and which achieve the correct dissipation rate in the spatially-discrete dissipative dynamics. Moreover, by using spatial discretizations which preserve the de Rham cohomology, the non-evolving involution constraint for the vorticity may be exactly satisfied for all of time. Numerical examples are given using a mimetic finite difference spatial discretization.<|reference_end|>
@article{barham2024a,
    title={A mimetic discretization of Westervelt's equation},
    author={William Barham and Philip J. Morrison},
    journal={arXiv preprint arXiv:2407.14718},
    year={2024},
    archivePrefix={arXiv},
    eprint={2407.14718},
    primaryClass={math.NA cs.NA math-ph math.MP}
}