论文标题
Navier Stokes方程的双重自适应惩罚方法
A Doubly Adaptive Penalty Method for the Navier Stokes Equations
论文作者
论文摘要
我们开发，分析和测试自适应惩罚参数方法。当适应惩罚参数，$ε，$和速度时间导数的稳定性时，我们证明了速度无条件的稳定性，在惩罚参数更改的条件下，$ε（t_ {n+1}） - ε（t_n）$。分析和测试表明，适应$ε（t_ {n+1}）$，以响应$ \ nabla \ cdot u（t_n）$消除了选择$ε$的问题，并在速度上产生了良好的近似值。我们提供错误分析和数值测试以支持这些结果。我们还可以通过调整时间步长来补充自适应-yε$方法。罚款参数$ε$和时间步长独立调整。我们进一步比较了第一，第二和可变的订单时间步长算法。准确的压力恢复仍然是一个空旷的问题。
We develop, analyze and test adaptive penalty parameter methods. We prove unconditional stability for velocity when adapting the penalty parameter, $ε,$ and stability of the velocity time derivative under a condition on the change of the penalty parameter, $ε(t_{n+1})-ε(t_n)$. The analysis and tests show that adapting $ε(t_{n+1})$ in response to $\nabla\cdot u(t_n)$ removes the problem of picking $ε$ and yields good approximations for the velocity. We provide error analysis and numerical tests to support these results. We supplement the adaptive-$ε$ method by also adapting the time-step. The penalty parameter $ε$ and time-step are adapted independently. We further compare first, second and variable order time-step algorithms. Accurate recovery of pressure remains an open problem.
