Novel 3D coupled convection–diffusion model algorithm

Abstract

The potential of a partial differential equations model is to anticipate its computational behavior. The simulation of a transient 3D coupled convection–diffusion system using a numerical model is described. The main objective of this article is to offer effective limited contrast compact finite difference techniques for use with nonlinear coupled partial differential systems that mimic overseeing differential frameworks. The three-dimensional compact finite difference formulation serves as the model’s foundation. An analytical model has been used to validate finite difference techniques that are numerically compact. By examining the consistency and union of the arrangement, which may be seen from figures and information tables, we can evaluate the model and the suggested numerical schemes. The schemes are unconditionally stable and accurate up to two orders in time and six orders in space, according to the results of the stability and accuracy tests. The implicit method used in the algorithm’s design was examined for stability criteria. Because mesh-independent solutions for non-linear differential systems are expensive, block tridiagonal matrix structures, measured in terms of L2 and L∞ norms, which are inherent characteristics of schemes and have excellent agreement with the investigation arrangement, are created.