论文标题
压力泊松方程式的高阶方法与电界条件的Navier-Stokes方程式
High-order Methods for a Pressure Poisson Equation Reformulation of the Navier-Stokes Equations with Electric Boundary Conditions
论文作者
论文摘要
不可压缩的Navier-Stokes方程（NSE）的压力泊松方程（PPE）重新构造，用泊松方程代替了压力和适当选择边界条件的不可压缩性约束。这仅适用于速度场的时间进化方程，压力梯度充当非局部操作员。因此，原则上，基于PPE重新制定的数值方法在实现高级方面没有局限性。在本文中，研究了NSE的高阶方法可以从具有电气边界条件（EBC）的特定PPE重新印度获得。为此，使用隐式解释（IMEX）时间步长以将压力从速度更新中解脱出来，同时避免了抛物线时间段限制。并在空间中使用混合有限元素，以捕获EBC施加的结构。通过数值示例，可以证明该方法可以在时空和时间上产生至少三阶的准确性。
Pressure Poisson equation (PPE) reformulations of the incompressible Navier-Stokes equations (NSE) replace the incompressibility constraint by a Poisson equation for the pressure and a suitable choice of boundary conditions. This yields a time-evolution equation for the velocity field only, with the pressure gradient acting as a nonlocal operator. Thus, numerical methods based on PPE reformulations, in principle, have no limitations in achieving high order. In this paper, it is studied to what extent high-order methods for the NSE can be obtained from a specific PPE reformulation with electric boundary conditions (EBC). To that end, implicit-explicit (IMEX) time-stepping is used to decouple the pressure solve from the velocity update, while avoiding a parabolic time-step restriction; and mixed finite elements are used in space, to capture the structure imposed by the EBC. Via numerical examples, it is demonstrated that the methodology can yield at least third order accuracy in space and time.
