In this work, we report the development of a spatially fourth order temporally second order compact scheme for incompressible Navier-Stokes (N-S) equations in time-varying domain. Sen [J. Comput. Phys. 251 (2013) 251-271] put forward an implicit compact finite difference scheme for the unsteady convection-diffusion equation. It is now further extended to simulate fluid flow problems on deformable surfaces using curvilinear moving grids. The formulation is conceptualized in conjunction with recent advances in numerical grid deformations techniques such as inverse distance weighting (IDW) interpolation and its hybrid implementation. Adequate emphasis is provided to approximate grid metrics up to the desired level of accuracy and freestream preserving property has been numerically examined. As we discretize the non-conservative form of the N-S equation, the importance of accurate satisfaction of geometric conservation law (GCL) is investigated. To the best of our knowledge, this is the first higher order compact method that can directly tackle non-conservative form of N-S equation in single and multi-block time dependent complex regions. Several numerical verification and validation studies are carried out to illustrate the flexibility of the approach to handle high-order approximations on evolving geometries.

翻译：在这项工作中,我们报告了在时间变化域内,为压抑性纳维埃-斯托克斯(N-S)方程式开发一个空间第四级时序第二级紧凑计划的情况。Sen[J.Compuut. Phys. 251(2013)(Fasy. 251(2013)(251-251-271))为不稳定的对流-扩散方程式提出了一个隐含的紧凑有限差异计划。现在,这个计划进一步扩大到模拟可变形表面的液流问题,使用曲线移动网格进行模拟。这一提法是结合数字电网变形变形技术(例如逆距离加权(IDW)的内插法及其混合实施的最新进展而构思的。充分强调将电网测量指标大约提高到预期的准确度和自由流保存财产的水平。随着我们将N-S方程式的非保守形式分解,正在调查精确满足几何计量保护法的重要性。据我们所知,这是第一个更高的顺序压缩方法,可以直接解决单级和多级间断式等方程式的非保守方程式形式。一些数字验证和跨级的复杂时程方法。