We develop a mesh-based semi-Lagrangian discretization of the time-dependent incompressible Navier-Stokes equations with free boundary conditions recast as a non-linear transport problem for a momentum 1-form. A linearly implicit fully discrete version of the scheme enjoys excellent stability properties in the vanishing viscosity limit and is applicable to inviscid incompressible Euler flows. Conservation of energy and helicity are enforced separately.

翻译：我们开发了一个基于网状的半拉格朗格式半分解法,将基于时间的不压缩纳维埃-斯托克斯方程式与自由边界条件相分离,将自由边界条件作为非线性运输问题重新定位为动力1形。 线性、完全离散的系统版本在消失的粘度限制中具有极强的稳定特性,并适用于不可窥视的不压缩脉冲流。 能源和热度的保护是单独实施的。