Burgers’ equation with high Reynolds number
نویسندگان
چکیده
Burgers’ equation, involving very high Reynolds numbers, is numerically solved by using a new approach based on the distributed approximating functional for representing spatial derivatives of the velocity field. For moderately large Reynolds numbers, this simple approach can provide very high accuracy while using a small number of grid points. In the case where the Reynolds number >10, the exact solution is not available and a discrepancy exists in the literature. Our results clarify the behavior of the solution under these conditions. © 1997 American Institute of Physics. @S1070-6631~97!02406-9#
منابع مشابه
Solution of two-dimensional time-fractional Burgers equation with high and low Reynolds numbers
Burgers’ equation frequently appears in the study of turbulence theory, as well as some other scientific fields. High and low Reynolds numbers play important roles in both modeling and numerical simulation. In this paper, we apply a numerical scheme to solve a two-dimensional time-fractional Burgers equation. The key feature of the proposed method is formed by combining the discontinuous Galerk...
متن کاملNumerical solution of the one dimensional non-linear Burgers equation using the Adomian decomposition method and the comparison between the modified Local Crank-Nicolson method and the VIM exact solution
The Burgers’ equation is a simplified form of the Navier-Stokes equations that very well represents their non-linear features. In this paper, numerical methods of the Adomian decomposition and the Modified Crank – Nicholson, used for solving the one-dimensional Burgers’ equation, have been compared. These numerical methods have also been compared with the analytical method. In contrast to...
متن کاملM ar 2 00 5 Three - Dimensional Stability of Burgers Vortices : the Low Reynolds Number
In this paper we establish rigorously that the family of Burgers vortices of the three-dimensional Navier-Stokes equation is stable for small Reynolds numbers. More precisely, we prove that any solution whose initial condition is a small perturbation of a Burgers vortex will converge toward another Burgers vortex as time goes to infinity, and we give an explicit formula for computing the change...
متن کاملThe solution of Burgers' equation for sinusoidal excitation at the upstream boundary
This paper generates an exact solution to Burgers' nonlinear diffusion equation on a convective stream with sinusoidal excitation applied at the upstream boundary, x = 0. The downstream boundary, effectively at x = 0% is assumed to always be far enough ahead of the convective front at x = Vst that no disturbance is felt there. The Hopf-Cole transformation is applied in achieving the analytical ...
متن کاملThree-Dimensional Stability of Burgers Vortices: the Low Reynolds Number Case
In this paper we establish rigorously that the family of Burgers vortices of the three-dimensional Navier-Stokes equation is stable for small Reynolds numbers. More precisely, we prove that any solution whose initial condition is a small perturbation of a Burgers vortex will converge toward another Burgers vortex as time goes to infinity, and we give an explicit formula for computing the change...
متن کامل