受无约束压力泊松方程（UPPE）公式[Liu, Liu, & Pego 2007 Comm. Pure Appl. Math., 60 pp. 1443]的启发，我们此前提出了GePUP公式[Zhang 2016 J. Sci. Comput., 67 pp. 1134]，用于在无滑移区域上数值求解不可压缩Navier-Stokes方程（INSE）。本文提出GePUP-E和GePUP-ES，它们是GePUP的变体，具备以下特性：(a) 采用电边界条件，无需显式施加无穿透条件；(b) 与无滑移INSE等价；(c) 初始非螺线管速度的散度呈指数衰减；(d) 动能单调递减。与UPPE不同，GePUP-E和GePUP-ES公式为强形式，是为线法框架下的有限体积/有限差分方法设计的。此外，我们开发了能保持特性(c)和(d)的半离散算法，以及速度在时间和空间上均达到四阶精度的全离散算法。这些算法以黑盒方式使用代数稳定时间积分器，每个时间步仅需求解一系列线性方程。数值测试结果验证了我们的分析。
英文摘要：
Inspired by the unconstrained PPE (UPPE) formulation [Liu, Liu, & Pego 2007 Comm. Pure Appl. Math., 60 pp. 1443], we previously proposed the GePUP formulation [Zhang 2016 J. Sci. Comput., 67 pp. 1134] for numerically solving the incompressible Navier-Stokes equations (INSE) on no-slip domains. In this paper, we propose GePUP-E and GePUP-ES, variants of GePUP that feature (a) electric boundary conditions with no explicit enforcement of the no-penetration condition, (b) equivalence to the no-slip INSE, (c) exponential decay of the divergence of an initially non-solenoidal velocity, and (d) monotonic decrease of the kinetic energy. Different from UPPE, the GePUP-E and GePUP-ES formulations are of strong forms and are designed for finite volume/difference methods under the framework of method of lines. Furthermore, we develop semi-discrete algorithms that preserve (c) and (d) and fully discrete algorithms that are fourth-order accurate for velocity both in time and in space. These algorithms employ algebraically stable time integrators in a black-box manner and only consist of solving a sequence of linear equations in each time step. Results of numerical tests confirm our analysis.
A Nitsche method for incompressible fluids with general dynamic boundary conditions
Charles University（查理大学）；Universität Konstanz（康斯坦茨大学）；Institute of Science and Technology Austria (ISTA)（奥地利科学技术研究所）；Technische Universität Darmstadt（达姆施塔特工业大学）
H(curl)-based approximation of the Stokes problem with slip boundary conditions
Faculty of Mathematics, University of Duisburg-Essen（杜伊斯堡-埃森大学数学学院）；SAM, ETH Zürich（苏黎世联邦理工学院应用数学系）；Department of Mathematics, University of Vienna（维也纳大学数学系）
An efficient method for the incompressible Navier-Stokes equations on irregular domains with no-slip boundary conditions, high order up to the boundary
Stability and error analysis of IMEX-BDFk finite element schemes for the incompressible Navier-Stokes system
Beijing Jiaotong University（北京交通大学）；Academy of Mathematics and Systems Science, Chinese Academy of Sciences（中国科学院数学与系统科学研究院）；University of Chinese Academy of Sciences（中国科学院大学）
