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A One-Dimensional Discrete Boltzmann Method for Multidimensional Compressible Flows
arXiv:2603.01546v2 Announce Type: replace Abstract: A simple and efficient one-dimensional discrete Boltzmann method is developed for compressible flows with tunable specific heat ratios by incorporating extra degrees of freedom. To guarantee Galilean invariance in numerical simulations, a discrete velocity set is constructed with high spatial symmetry. Furthermore, an operator-splitting scheme is proposed to extend the one-dimensional kinetic formulation to simulations of one-, two-, and...
A high-order regularization of the non-linear shallow water equations with weakly singular shock waves and its approximation by finite volume methods
arXiv:2606.01200v1 Announce Type: cross Abstract: Considered herein is a high-order regularization of the nonlinear shallow water equations within the framework of water wave theory. The regularized system is Galilean invariant and its solutions maintain an energy level that closely matches that of the nonlinear shallow water equations.
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