论文标题
在流体力学和流体结构相互作用中具有恒定分段特性的原始配方在加速度的速度电势中
On primitive formulation in fluid mechanics and fluid-structure interaction with constant piecewise properties in velocity-potentials of acceleration
论文作者
论文摘要
离散的力学使得在速度和加速电位中制定流体力学或流体结构相互作用的任何问题；方程系统由单个向量方程和电势更新组成。加速度的标量电势代表压力应力，矢量电位与旋转剪切应力有关。运动方程的表述可以以分裂的形式表达，从而导致精确的投影方法。分散操作员在离散运动方程式中的应用显示，无论介质的物理特性的变化，标量势上都具有恒定系数的泊松方程。通过在此阶段引入局部密度来明确进行压力的A后验计算。两个第一个示例表明，在Navier-Stokes方程的经典解决方案上提出的配方的兴趣。类似地，与使用该公式获得的其他结果相似，收敛性在所有数量，速度和电势的时空和时间上都是阶的。然后将该公式应用于由表面张力和部分润湿性驱动的两相流。最后一个情况对应于分析解决方案的流体结构相互作用问题。
Discrete mechanics makes it possible to formulate any problem of fluid mechanics or fluid-structure interaction in velocity and potentials of acceleration; the equation system consists of a single vector equation and potentials 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 of the physical properties of the media. The a posteriori calculation of the pressure is made 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; similarly as 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.
