2021/12/08 by Robert Altmann, Altmann, Robert · 1 citation
Earth and Planetary Sciences · Engineering · #Meteorological Phenomena and Simulations #Lattice Boltzmann Simulation Studies #Computational Fluid Dynamics and Aerodynamics
paper · pdf · doi:10.48550/arxiv.2112.04321
This paper introduces novel bulk-surface splitting schemes of first and second order for the wave equation with kinetic and acoustic boundary conditions of semi-linear type. For kinetic boundary conditions, we propose a reinterpretation of the system equations as a coupled system. This means that the bulk and surface dynamics are modeled separately and connected through a coupling constraint. This allows the implementation of splitting schemes, which show first-order convergence in numerical experiments. On the other hand, acoustic boundary conditions naturally separate bulk and surface dynamics. Here, Lie and Strang splitting schemes reach first- and second-order convergence, respectively, as we reveal numerically.