Comparative Study of Arakawa Scheme and WENO Scheme for Solving Advection Equation.

Abstract

In this paper, we investigate the impact of Arakawa and WENO advection schemes in numerical ocean modelling. Numerical simulation s in ocean models rely on non-oscillatory advection scheme, which minimizes numerical dissipation and dispersion problems. We study the Arakawa scheme and WENO-5 scheme in the 2-D advection problem. The Arakawa scheme preserves important physical phenomena and the WENO-5 scheme emphasizes high resolution and non-oscillatory solutions, so we study both numerical methods. Our key focus is to observe the oscillatory behavior of the numerical solutions, examine the total variation diminishing (TVD ) property and assess numerical dissipation and dispersion of these schemes . We observe that the Arakawa scheme shows an oscillatory solution with slight dissipation, yet preserves energy well. The WENO-5 scheme produces a non-oscillatory numerical solution and minimizes numerical dissipation in 2-D advection equations. The WENO-5 scheme performs better than Arakawa 2-D advection scheme and the WENO-5 reconstruction minimizes numerical dissipation.