Accuracy and efficiency improvements of the navier stokes equation using modified splitting method

Abstract

Solution to Navier-Stokes equation using Splitting Method is tailored to promote accuracy and efficiency of the original flow algorithm. Two-dimensional unsteady lid-driven cavity flow based on basic Splitting algorithm on Cartesian Coordinates is compared with two advanced codes, Splitting on Stretched Coordinates and Splitting with Spectral Approach. In both Cartesian and stretched Splitting methods, the linear terms in Navier-Stokes equations are solved by Crank-Nicholson method while the non-linear terms are solved by second order Adams-Bashforth method while the spectral method approximates the fluid as linear combination of non-zero continuous Chebyshev Polynomials function over solution domain. Spectral method immensely improves the accuracy of solver with a drawback of large computational cost while Splitting in Stretched coordinates is superior in efficiency but less accuracy progression. The graphical correlations between accuracy, efficiency and grid resolutions suggest the use of Splitting-Stretched method for comparable accuracy and intensive flow profile with least time consumption.