In this paper we introduce a new discretization of the incompressible Navier-Stokes equations. We use the Lamb identity for the advection term $(u \cdot \nabla)u$ and the general idea allows a lot of freedom in the treatment of the non-linear term. The main advantage of this scheme is that the divergence of the fluid velocity is pointwise zero at the discrete level. This exactness allows for exactly conserved quantities and pressure robustness. Discrete spaces consist of piecewise polynomials, they may be taken of arbitrary order and are already implemented in most libraries. Although the nonlinear term may be implemented as is, most proofs here are done for the linearized equation. The whole problem is expressed in the finite element exterior calculus framework. We also present numerical simulations, our codes are written with the FEniCS computing platform, version 2019.1.0.

翻译：在本文中,我们引入了不可压缩的 Navier- Stokes 方程式的新的分解。 我们使用 Lamb 身份来对等术语$( u\ cdot\ nabla) $( u), 并且一般想法允许大量自由处理非线性术语。 这个方案的主要优点是流体速度的差异在离散水平上是点偏零。 这个精确度允许精确保存数量和压力强度。 分解空间由片断的多元分子组成, 它们可以任意排列, 并且已经在大多数图书馆中执行。 虽然非线性术语可以按原样执行, 但这里的大多数证据是线性方程式。 整个问题表现在有限元素外部微积框架中 。 我们提出数字模拟, 我们的代码是用 FENICS 计算平台, 版本 2019.1.0 来写成 。