Comparative Study of Arakawa Scheme and WENO Scheme for Solving Advection Equation. - Prokriti Biswas (Journal of Science, 2026)
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.