Fourth-order central compact scheme for the numerical solution of incompressible Navier–Stokes equations

ABSTRACT

This paper provides an implicit central compact scheme for the numerical solution of incompressible Navier–Stokes equations. The solution procedure is based on the artificial compressibility method that transforms the governing equations into a hyperbolic-parabolic form. A fourth-order central compact scheme with a sixth-order numerical filtering is used for the discretization of convective terms and fourth-order central compact scheme for the viscous terms. Dual-time stepping approach is applied to time discretization with backward Euler difference scheme to the pseudo-time derivative, and three point second-order backward difference scheme to the physical time derivative. An approximate factorization-based alternating direction implicit scheme is used to solve the resulting block tridiagonal system of equations. The accuracy and efficiency of the proposed numerical method is verified by simulating several two-dimensional steady and unsteady benchmark problems.

KEYWORDS:

• Incompressible Navier–Stokes equations
• artificial compressibility method
• central compact scheme
• numerical filtering
• dual-time stepping

AMSS CLASSIFICATIONS:

• 35Q35
• 35Q30
• 93B40
• 80M20
• 15A30

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Abdullah Shah http://orcid.org/0000-0002-0337-1216