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.

翻译：一类广泛的非线性声波模型在其无耗散极限下具有哈密顿结构，而其耗散动力学则呈现梯度流结构。该结构可用于设计数值方法，使其在无耗散极限下保持哈密顿结构，并在空间离散的耗散动力学中实现正确的耗散率。此外，通过采用保持德拉姆上同调的空间离散格式，涡量的非演化对合约束可对所有时间精确满足。文中采用拟态有限差分空间离散方法给出了数值算例。