We introduce a mimetic dual-field discretization which conserves mass, kinetic energy and helicity for three-dimensional incompressible Navier-Stokes equations. The discretization makes use of a conservative dual-field mixed weak formulation where two evolution equations of velocity are employed and dual representations of the solution are sought for each variable. A temporal discretization, which staggers the evolution equations and handles the nonlinearity such that the resulting discrete algebraic systems are linear and decoupled, is constructed. The spatial discretization is mimetic in the sense that the finite dimensional function spaces form a discrete de Rham complex. Conservation of mass, kinetic energy and helicity in the absence of dissipative terms is proven at the discrete level. Proper dissipation rates of kinetic energy and helicity in the viscous case is also proven. Numerical tests supporting the method are provided.
翻译:我们引入了一种模子双场分解,为三维压缩的纳维-斯托克斯方程式保护质量、动能和热能和热度。这种分解使用一种保守的双场混合弱化配方,采用两种速度进化方程,并寻求对每种变量的解决方案进行双重表述。一种时间分解,将进化方程式叠叠叠起来,处理非线性,使由此产生的离散代数系统为线性并脱钩。空间分解是模拟的,即有限维功能空间形成一个离散的雷姆复合体。在离散的状态下保护质量、动能和高能。在离散的状态下保护质量、动能和高能,在离散的状态下,在离散状态下得到证明。在粘结的动能和高能中的适当消散率也得到证明。提供了支持这种方法的数值测试。