Discrete mechanics makes it possible to formulate any problem of fluid mechanics or fluid-structure interaction in terms of velocity and potentials of acceleration; the equation system consists of a single-vector equation and potential updates. The scalar potential of the acceleration represents the pressure stress, and the vector potential is related to the rotational shear stress. The formulation of the equation of motion can be expressed in the form of a splitting which leads to an exact projection method; the application of the divergence operator to the discrete motion equation exhibits, without any approximation, a Poisson equation with constant coefficients on the scalar potential whatever the variations in the physical properties of the media. The a posteriori calculation of the pressure is done explicitly by introducing at this stage the local density. Two first examples show the interest of the formulation presented on classical solutions of Navier–Stokes equations; similar to other results obtained with this formulation, the convergence is of order two in space and time for all the quantities, velocity and potentials. This formulation is then applied to a two-phase flow driven by surface tension and partial wettability. The last case corresponds to a fluid–structure interaction problem for which an analytical solution exists.

中文翻译：

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关于流体力学和流体-结构相互作用的原始公式，在速度-加速度势中具有恒定的分段特性

离散力学可以根据速度和加速度势来表述任何流体力学或流固耦合问题；方程系统由单向量方程和潜在更新组成。加速度的标量势代表压力应力，矢量势与旋转剪应力有关。运动方程的公式可以用分裂的形式表达，这导致了精确的投影方法；散度算子在离散运动方程中的应用展示了一个泊松方程，在没有任何近似的情况下，无论介质的物理性质如何变化，标量势的系数都是恒定的。压力的后验计算是通过在这个阶段引入局部密度来明确完成的。前两个例子显示了 Navier-Stokes 方程经典解的公式的重要性；与使用该公式获得的其他结果类似，对于所有数量、速度和势能，在空间和时间上的收敛性都是二阶的。然后将该配方应用于由表面张力和部分润湿性驱动的两相流。最后一种情况对应于存在解析解的流固耦合问题。速度和潜力。然后将该配方应用于由表面张力和部分润湿性驱动的两相流。最后一种情况对应于存在解析解的流固耦合问题。速度和潜力。然后将该配方应用于由表面张力和部分润湿性驱动的两相流。最后一种情况对应于存在解析解的流固耦合问题。