We develop a semi-Lagrangian discretization of the time-dependent incompressible Navier-Stokes equations with free boundary conditions on arbitrary simplicial meshes. We recast the equations as a nonlinear transport problem for a momentum 1-form and discretize in space using methods from finite element exterior calculus. Numerical experiments show that the 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. We obtain second-order convergence and conservation of energy is achieved through a Lagrange multiplier.

中文翻译：

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不可压缩流的半拉格朗日有限元外微积分

我们在任意单纯网格上开发了具有自由边界条件的时变不可压缩纳维-斯托克斯方程的半拉格朗日离散化。我们将方程重新改写为动量 1 形式的非线性输运问题，并使用有限元外微积分方法在空间中进行离散化。数值实验表明，该格式的线性隐式全离散版本在消失粘度极限下具有良好的稳定性，适用于无粘不可压缩欧拉流。我们获得二阶收敛，并且通过拉格朗日乘子实现能量守恒。