Distributed Approximating Functional Approach to Burgers’ Equation using Element Differential Quadrature Method|
Vagheefi, M.; Rahideh, H.; Golbahar, Haghighi & Manshad, A.K.
This paper presents a computationally efficient and an accurate methodology in differential
quadrature element method (EDQM) analysis of the nonlinear one-dimensional Burgers’ equation. Based on this
approach, the total spatial and temporal domain is divided into a set of sub-domain and in each sub-domain, the
DQ rule is employed to discretize the spatial and temporal domain derivatives. This equation is similar to, but
simpler than, the Navier-Stokes equation in fluid dynamics. To verify this advantage through some comparison
studies, an exact series solution are also obtained. In addition, the presented scheme has numerically stable
behavior. After demonstrating the convergence and accuracy of the method, the effects of velocity parameters on
the viscosity distribution are studied. It is found that element differential quadrature method provides highly
accurate an exact series solution for Burgers, equation, while a small number of grid points is needed.
Burgers, Equation, Differential quadrature method, Exact Series