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：我们将含自由边界条件的时变不可压缩纳维-斯托克斯方程重新表述为动量1形式的非线性输运问题，并据此开发了基于网格的半拉格朗日离散格式。该格式的线性隐式全离散版本在粘性消失极限下具有优异的稳定性，且适用于无粘不可压缩欧拉流动。能量和螺旋度分别得到守恒。