Two-dimensional Burgers Cellular Automaton
نویسندگان
چکیده
In this paper, a two-dimensional cellular automaton(CA) associated with a two-dimensional Burgers equation is presented. The 2D Burgers equation is an integrable generalization of the well-known Burgers equation, and is transformed into a 2D diffusion equation by the Cole-Hopf transformation. The CA is derived from the 2D Burgers equation by using the ultradiscrete method, which can transform dependent variables into discrete ones. Some exact solutions of the CA, such as shock wave solutions, are studied in detail.
منابع مشابه
Comparison of The LBM With the Modified Local Crank-Nicolson Method Solution of Transient Two-Dimensional Non-Linear Burgers Equation
Burgers equation is a simplified form of the Navier-Stokes equation that represents the non-linear features of it. In this paper, the transient two-dimensional non-linear Burgers equation is solved using the Lattice Boltzmann Method (LBM). The results are compared with the Modified Local Crank-Nicolson method (MLCN) and exact solutions. The LBM has been emerged as a new numerical method for sol...
متن کاملHomotopy analysis and Homotopy Pad$acute{e}$ methods for two-dimensional coupled Burgers\' equations
In this paper, analytic solutions of two-dimensional coupled Burgers' equations are obtained by the Homotopy analysis and the Homotopy Pad$acute{e}$ methods. The obtained approximation by using Homotopy method contains an auxiliary parameter which is a simple way to control and adjust the convergence region and rate of solution series. The approximation solutions by $[m,m]$ Homotopy Pad$acute{e...
متن کاملA stochastic cellular automaton model for traffic flow with multiple metastable states
A new stochastic cellular automaton (CA) model of traffic flow, which includes slow-to-start effects and a driver’s perspective, is proposed by extending the Burgers CA and the Nagel-Schreckenberg CA model. The flowdensity relation of this model shows multiple metastable branches near the transition density from free to congested traffic, which form a wide scattering area in the fundamental dia...
متن کاملSolving a system of 2D Burgers' equations using Semi-Lagrangian finite difference schemes
In this paper, we aim to generalize semi-Lagrangian finite difference schemes for a system of two-dimensional (2D) Burgers' equations. Our scheme is not limited by the Courant-Friedrichs-Lewy (CFL) condition and therefore we can apply larger step size for the time variable. Proposed schemes can be implemented in parallel very well and in fact, it is a local one-dimensional (LOD) scheme which o...
متن کاملA Cellular Automaton for Burgers' Equation
A bstract. We study the app roximation of solut ions to the Burgers' equation , an + c!.-(n _n 2) = v a 2 n ilt ilx 2 ilx' (1) by spatially avera ging a prob abilistic cellular automaton motivated by random walks on a line. The auto maton consists of moving "particles" on Q. one-dimensional periodic lattice with spe ed one and in a random direction subject to the exclusion principle that at mos...
متن کامل