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

Abstract

In this paper, we investigate the impact of various advection schemes in numerical ocean modelling. Numerical simulation in ocean models rely on the 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. Our key focus is to observe the oscillatory behavior of the numerical solutions, TVD property and numerical dissipation and dispersion 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 other advection schemes and the WENO-5 reconstruction minimizes numerical dissipation.