标题： 一种质量、能量、涡量和旋度守恒的（MEEVC）仿微谱元离散化方法用于二维不可压缩纳维-斯托克斯方程 显示英文标题

标题： A mass, energy, enstrophy and vorticity conserving (MEEVC) mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations

摘要： 在本工作中，我们提出了一种用于二维不可压缩纳维-斯托克斯方程的仿射谱元离散化方法，在耗散消失的极限情况下，该方法在非结构化网格上精确保持质量、动能、涡量和总旋度。 实现这些的关键要素是： (i) 旋转形式的速度-涡量公式，(ii) 一组能够精确满足速度场散度为零性质的函数空间，以及(iii) 一个保守的时间积分器。 同时给出了离散精确守恒性质的证明以及在高度不规则网格上的数值测试案例。 显示英文摘要

摘要： In this work we present a mimetic spectral element discretization for the 2D incompressible Navier-Stokes equations that in the limit of vanishing dissipation exactly preserves mass, kinetic energy, enstrophy and total vorticity on unstructured grids. The essential ingredients to achieve this are: (i) a velocity-vorticity formulation in rotational form, (ii) a sequence of function spaces capable of exactly satisfying the divergence free nature of the velocity field, and (iii) a conserving time integrator. Proofs for the exact discrete conservation properties are presented together with numerical test cases on highly irregular grids.