A New Approach to Solving Two-Dimensional Unsteady Incompressible Navier-Stokes Equations  

作　　者：Zinah Abdulkadhim Hasan Abdul-Sattar J. Al-Saif Zinah Abdulkadhim Hasan;Abdul-Sattar J. Al-Saif(Department of Mathematics, College of Education for Pure Science, University of Basrah, Basra, Iraq)

机构地区：[1]Department of Mathematics, College of Education for Pure Science, University of Basrah, Basra, Iraq

出　　处：《Journal of Applied Mathematics and Physics》2022年第10期3218-3239,共22页应用数学与应用物理（英文）

摘　　要：This paper proposes a new approach that combines the reduced differential transform method (RDTM), a resummation method based on the Yang transform, and a Padé approximant to the kinetically reduced local Navier-Stokes equation to find approximate solutions to the problem of lid-driven square cavity flow. The new approach, called PYRDM, considerably improves the convergence rate of the truncated series solution of RDTM and also is based on a simple process that yields highly precise estimates. The numerical results achieved by this method are compared to earlier studies’ results. Our results indicate that this method is more efficient and precise in generating analytic solutions. Furthermore, it provides highly precise solutions with good convergence that is simple to apply for great Reynolds and low Mach numbers. Moreover, the new solution’ graphs demonstrate the new approach’s validity, usefulness, and necessity.This paper proposes a new approach that combines the reduced differential transform method (RDTM), a resummation method based on the Yang transform, and a Padé approximant to the kinetically reduced local Navier-Stokes equation to find approximate solutions to the problem of lid-driven square cavity flow. The new approach, called PYRDM, considerably improves the convergence rate of the truncated series solution of RDTM and also is based on a simple process that yields highly precise estimates. The numerical results achieved by this method are compared to earlier studies’ results. Our results indicate that this method is more efficient and precise in generating analytic solutions. Furthermore, it provides highly precise solutions with good convergence that is simple to apply for great Reynolds and low Mach numbers. Moreover, the new solution’ graphs demonstrate the new approach’s validity, usefulness, and necessity.

关 键 词：Navier-Stokes Equations RDTM Yang Transform Padé Approximation Accuracy Convergence Analysis 

分 类 号：O17[理学—数学]