Numerical solution of unsteady Navier-Stokes equations on curvilinear meshes

Authors:
Abdullah Shah;Li Yuan;Shamsul Islam
Affiliations:
Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad 44000, Pakistan;LSEC and Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics & Systems Science, Chinese Academy of Sciences, Beijing 100190, PR China;Department of Mathematics, COMSATS Institute of Information Technology, Park Road, Islamabad 44000, Pakistan
Venue:
Computers & Mathematics with Applications
Year:
2012

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Abstract

The objective of the present work is to extend our FDS-based third-order upwind compact schemes by Shah et al. (2009) [8] to numerical solutions of the unsteady incompressible Navier-Stokes equations in curvilinear coordinates, which will save much computing time and memory allocation by clustering grids in regions of high velocity gradients. The dual-time stepping approach is used for obtaining a divergence-free flow field at each physical time step. We have focused on addressing the crucial issue of implementing upwind compact schemes for the convective terms and a central compact scheme for the viscous terms on curvilinear structured grids. The method is evaluated in solving several two-dimensional unsteady benchmark flow problems.