标题： 不可压缩流体和磁流体的压力测定 显示英文标题

标题： Pressure determinations for incompressible fluids and magnetofluids

摘要： 对于不可压缩流动的压力确定，存在一些未解决的模糊之处，无论是纳维-斯托克斯方程还是磁流体动力学方程都是如此。 对于具有均匀密度和标准牛顿粘性项的流体，对运动方程取散度会得到一个用于求解压力的泊松方程。 但泊松方程需要边界条件。 在矩形周期性边界条件下，以这种方式确定的压力是明确的。 但在存在“无滑移”刚性壁的情况下，运动方程可以用来推断压力P的狄利克雷和诺伊曼边界条件，因此会导致过度确定的问题。 这种情况偶尔被认识到是一个问题，通常在处理壁限制剪切流的数值方法中会内置某种相对随意的动力学方案来处理它，通常是一种似乎能令人满意地“工作”的方案。 在这里，我们考虑一类在无滑移壁处消失的管状速度场，它们具有所有空间导数，但足够简单以至于可以给出压力P的显式解析解。 分别满足两个边界条件会产生两种压力，“诺伊曼压力”和“狄利克雷压力”，即使在任何动力学实施之前，在初始时刻它们也非平凡地不同。 我们比较这两种压力，并发现它们在壁附近导致不同的体积力。 这表明需要重新考虑无滑移边界条件，在这种情况下，无滑移壁处切向速度的消失被替换为运动方程中的局部壁摩擦项。 显示英文摘要

摘要： Certain unresolved ambiguities surround pressure determinations for incompressible flows, both Navier-Stokes and magnetohydrodynamic. For uniform-density fluids with standard Newtonian viscous terms, taking the divergence of the equation of motion leaves a Poisson equation for the pressure to be solved. But Poisson equations require boundary conditions. For the case of rectangular periodic boundary conditions, pressures determined in this way are unambiguous. But in the presence of "no-slip" rigid walls, the equation of motion can be used to infer both Dirichlet and Neumann boundary conditions on the pressure P, and thus amounts to an over-determination. This has occasionally been recognized as a problem, and numerical treatments of wall-bounded shear flows usually have built in some relatively ad hoc dynamical recipe for dealing with it, often one which appears to "work" satisfactorily. Here we consider a class of solenoidal velocity fields which vanish at no-slip walls, have all spatial derivatives, but are simple enough that explicit analytical solutions for P can be given. Satisfying the two boundary conditions separately gives two pressures, a "Neumann pressure" and a "Dirichlet pressure" which differ non-trivially at the initial instant, even before any dynamics are implemented. We compare the two pressures, and find that in particular, they lead to different volume forces near the walls. This suggests a reconsideration of no-slip boundary conditions, in which the vanishing of the tangential velocity at a no-slip wall is replaced by a local wall-friction term in the equation of motion.