In this article, we develop a fourth order finite difference method to solve the system of steady state Navier-Stokes equations and apply it to the benchmark problem known as the square cavity flow problem. The numerical results of 𝑢-velocity components and 𝑣-velocity components obtained at the center of the cavity are compared with the results obtained by the method developed by Greenspan and Casulli to solve the time dependent system of Navier-Stokes equations. The method described in this article is easy to implement and it has been shown to be more efficient and stable than the method by Greenspan and Casulli. Present method converges for a range of various viscosity coefficients for which the method of Greenspan and Casulli is not stable. We have included the contour plots of horizontal velocity (𝑢) components and vertical velocity (𝑣) components to facilitate the understanding of the steady state flow inside the cavity.
Siriwardana, Nihal J. and Pradhan, Saroj P.
A High Order Finite Difference Method to Solve the Steady State Navier-Stokes Equations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 16,
1, Article 19.
Available at: https://digitalcommons.pvamu.edu/aam/vol16/iss1/19