加速度守恒的统一离散方法
Unified discrete approach of acceleration conservation
摘要：
离散力学是用来目前流体力学，流体结构相互作用，电磁学和光学物理在一个连贯的理论和数值方法。加速度被认为是一个绝对量，被写为两项之和，即一个无旋分量和一个无发散分量，对应于一个正式的Hodge-Helmholtz分解。这个离散运动方程的变量只是加速度的标量势和矢量势，而不管物理场是什么。这些，像物理性质一样，只表示为两个基本单位的函数，即长度和时间。与该运动方程相关的数值方法基于离散算子、梯度、发散、应用于原始几何拓扑的速度分量的原始和对偶旋度。在每个域中进行的模拟产生的一些解决方案使得有可能找到从Navier-Stokes、Navier-Lam{é}和麦克斯韦方程组获得的结果，并显示所提出的统一方法的一致性。
英文摘要：
Discrete mechanics is used to present fluid mechanics, fluid-structure interactions, electromagnetism and optical physics in a coherent theoretical and numerical approach. Acceleration considered as an absolute quantity is written as a sum of two terms, i.e. an irrotational and a divergence-free component corresponding to a formal Hodge-Helmholtz decomposition. The variables of this equation of discrete motion are only the scalar and vector potential of the acceleration, whatever the physical field. These, like the physical properties, are only expressed as a function of two fundamental units, namely a length and a time. The numerical methodology associated with this equation of motion is based on discrete operators, gradient, divergence, primal and dual curl applied to the velocity components of the primal geometric topology. Some solutions resulting from simulations carried out in each domain make it possible to find the results obtained from the Navier-Stokes, Navier-Lam{é} and Maxwell equations and to show the coherence of the proposed unified approach.
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