Numerical Solution of two dimensional coupled viscous Burgers Equation using the Modified Cubic B Spline Differential Quadrature Method
This work offers an efficient numerical scheme for solving coupled Burgers equations, which are important in fluid dynamics and nonlinear wave propagation.
The paper presents a numerical solution for the two-dimensional coupled viscous Burgers equation using a modified cubic B-spline differential quadrature method, achieving high accuracy as demonstrated by comparison with exact solutions and literature results.
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.