Effects of Mesh Number and the Time-step-based Parameter on the Accuracy of Couette Solution

Abstract

Couette flow, a flow between two parallel plates with one plate in motion and the other stationary, has been extensively studied and applied in vaCouette flow, a flow between two parallel plates with one plate in motion and the other stationary, has been extensively studied and applied in various engineering and scientific fields. However, optimizing the accuracy of numerical solutions for such a flow is always a challenge. In this study, we focus on a quasi-1-dimensional Couette flow to investigate the impact of mesh number and the time-step-based parameter on the accuracy of the numerical solution. The Crank-Nicolson finite difference method is employed to solve the corresponding equation. The results suggest that the error linked to the unsteady Couette solution increases as the number of intervals rises. However, increasing the time-step-based parameter, has the potential to reduce the error, although it may lead to a simultaneous increase in the likelihood of oscillation. The findings can be leveraged in real applications to enhance the accuracy, efficiency, and reliability of computational simulations for improving the quality of the results, making informed decisions, and advancing the state of the art in respective fields.rious engineering and scientific fields. However, optimizing the accuracy of numerical solutions for such a flow is always a challenge. In this study, we focus on a quasi-1-dimensional Couette flow to investigate the impact of mesh number and the time-step-based parameter on the accuracy of the numerical solution. The Crank-Nicolson finite difference method is employed to solve the corresponding equation. The results suggest that the error linked to the unsteady Couette solution increases as the number of intervals rises. However, increasing the time-step-based parameter, has the potential to reduce the error, although it may lead to a simultaneous increase in the likelihood of oscillation. The findings can be leveraged in real applications to enhance the accuracy, efficiency, and reliability of computational simulations for improving the quality of the results, making informed decisions, and advancing the state of the art in respective fields.