论文标题
不可压缩的Navier-Stokes方程的嵌入式变量步骤IMEX方案
An embedded variable step IMEX scheme for the incompressible Navier-Stokes equations
论文作者
论文摘要
本报告提供了一系列的隐式解释（IMEX）变量时间段算法，用于不可压缩的Navier-Stokes方程（NSE）。随着新计算机体系结构的出现，对这种类型的低内存求解器的需求日益增长。时间适应性的增加可提高准确性，并大大提高算法的效率。我们证明了嵌入的第一阶阶IMEX对的能量稳定性。对于这对的一阶成员，我们证明了可变步骤的稳定性，并分析收敛性。我们认为，这是不可压缩NSE的可变步骤IMEX方案的第一个证明。然后，我们使用这些方法来定义和测试一个可变的步骤imex方案。我们的工作为IMEX NSE方案贡献了几个第一个，包括对两步，可变步骤方法的能量论证和误差分析以及IMEX多步法方法的嵌入式误差估计。
This report presents a series of implicit-explicit (IMEX) variable timestep algorithms for the incompressible Navier-Stokes equations (NSE). With the advent of new computer architectures there has been growing demand for low memory solvers of this type. The addition of time adaptivity improves the accuracy and greatly enhances the efficiency of the algorithm. We prove energy stability of an embedded first-second order IMEX pair. For the first order member of the pair, we prove stability for variable stepsizes, and analyze convergence. We believe this to be the first proof of this type for a variable step IMEX scheme for the incompressible NSE. We then define and test a variable stepsize, variable order IMEX scheme using these methods. Our work contributes several firsts for IMEX NSE schemes, including an energy argument and error analysis of a two-step, variable stepsize method, and embedded error estimation for an IMEX multi-step method.
