Numerical Solution of two dimensional coupled viscous Burgers Equation using the Modified Cubic B Spline Differential Quadrature Method

TL;DR

This paper presents a modified cubic B spline differential quadrature method for efficiently solving the two-dimensional coupled viscous Burgers equation, demonstrating high accuracy and reliability through numerical examples.

Contribution

The paper introduces a novel modified cubic B spline differential quadrature method for solving coupled Burgers equations, reducing them to ODEs and applying a high-order Runge Kutta scheme.

Findings

The method achieves high accuracy compared to exact solutions.

Numerical results confirm the efficiency and reliability of the proposed scheme.

The approach outperforms existing methods in solving coupled Burgers equations.

Abstract

In this paper, a numerical solution of the two dimensional nonlinear coupled viscous Burgers equation is discussed with the appropriate initial and boundary conditions using the modified cubic B spline differential quadrature method. In this method, the weighting coefficients are computed using the modified cubic B spline as a basis function in the differential quadrature method. Thus, the coupled Burgers equations are reduced into a system of ordinary differential equations (ODEs). An optimal five stage and fourth order strong stability preserving Runge Kutta scheme is applied to solve the resulting system of ODEs. The accuracy of the scheme is illustrated via two numerical examples. Computed results are compared with the exact solutions and other results available in the literature. Numerical results show that the MCB DQM is efficient and reliable scheme for solving the two dimensional coupled Burgers equation.