An implicit numerical scheme for solution of incompressible Navier-Stokes equations on curvilinear grids
Bull. Korean Math. Soc. 2018 Vol. 55, No. 3, 881-898
https://doi.org/10.4134/BKMS.b170357
Published online May 31, 2018
Hassan Fayyaz, Abdullah Shah
COMSATS Institute of Information Technology, COMSATS Institute of Information Technology
Abstract : This article deals with implementation of a high-order finite difference scheme for numerical solution of the incompressible Navier-Stokes equations on curvilinear grids. The numerical scheme is based on pseudo-compressibility approach. A fifth-order upwind compact scheme is used to approximate the inviscid fluxes while the discretization of metric and viscous terms is accomplished using sixth-order central compact scheme. An implicit Euler method is used for discretization of the pseudo-time derivative to obtain the steady-state solution. The resulting block tridiagonal matrix system is solved by approximate factorization based alternating direction implicit scheme (AF-ADI) which consists of an alternate sweep in each direction for every pseudo-time step. The convergence and efficiency of the method are evaluated by solving some 2D benchmark problems. Finally, computed results are compared with numerical results in the literature and a good agreement is observed.
Keywords : incompressible Navier-Stokes equations, curvilinear coordinate, artificial compressibility method, alternate direction implicit method
MSC numbers : 65N06, 76D05, 65D25
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