Search Results - subject:"Burgers equation"

On the application of the Cole–Hopf transformation to hyperbolic equations based on second-sound models

Jordan, P.M. - In: Mathematics and Computers in Simulation (MATCOM) 81 (2010) 1, pp. 18-25

We point out and examine two nonlinear, hyperbolic equations, both of which arise in kinematic-wave theory, that can be solved exactly using a conditional application of the Cole–Hopf transformation. Both of these equations are based on flux relations that were originally proposed as models of...

Persistent link: https://www.econbiz.de/10010749631

Traveling-wave solutions for a discrete Burgers equation with nonlinear diffusion

Mickens, Ronald E. - In: Mathematics and Computers in Simulation (MATCOM) 80 (2009) 4, pp. 855-859

We construct a nonstandard finite difference (NSFD) scheme for a Burgers type partial differential equation (PDE) for which the diffusion coefficient has a linear dependence on the dependent variable. After a study of this PDE's traveling-wave solutions, we examine the corresponding properties...

Persistent link: https://www.econbiz.de/10010870582

Statistical moments of the solution of the random Burgers–Riemann problem

Cunha, M. Cristina C.; Dorini, Fábio A. - In: Mathematics and Computers in Simulation (MATCOM) 79 (2009) 5, pp. 1440-1451

We solve Burgers’ equation with random Riemann initial conditions. The closed solution allows simple expressions for …

Persistent link: https://www.econbiz.de/10011051129

Ballistic aggregation for one-sided Brownian initial velocity

Valageas, Patrick - In: Physica A: Statistical Mechanics and its Applications 388 (2009) 7, pp. 1031-1045

We study the one-dimensional ballistic aggregation process in the continuum limit for one-sided Brownian initial velocity (i.e. particles merge when they collide and move freely between collisions, and in the continuum limit the initial velocity on the right side is a Brownian motion that...

Persistent link: https://www.econbiz.de/10011064418

Lattice Boltzmann method for one and two-dimensional Burgers equation

Zhang, Jianying; Yan, Guangwu - In: Physica A: Statistical Mechanics and its Applications 387 (2008) 19, pp. 4771-4786

In this paper, a new method, higher-order moment lattice Boltzmann method for one and two-dimensional Burgers’ equation …, we provide a fine numerical result of a one-dimensional Burgers’ equation. Numerical examples show the method can be used … to simulate one and two-dimensional Burgers’ equation. …

Persistent link: https://www.econbiz.de/10010874612

Exact solutions for a forced Burgers equation with a linear external force

Zola, R.S.; Dias, J.C.; Lenzi, E.K.; Evangelista, L.R.; … - In: Physica A: Statistical Mechanics and its Applications 387 (2008) 12, pp. 2690-2696

We investigate the solutions of the Burgers equation ∂tu(x,t)=D∂x2u(x,t)−∂x[F(x,t)u(x,t)]−κu(x,t)∂xu(x,t)+Φ(x,t), where …

Persistent link: https://www.econbiz.de/10011064206

Density waves in the continuum analog of the full velocity difference model

Ou, Zhong-Hui - In: Physica A: Statistical Mechanics and its Applications 387 (2008) 8, pp. 1799-1806

A continuum version of the car-following full velocity difference model (FVDM) is developed using a series expansion of the headway in terms of the density. This continuum model obeys the equivalent stability criterion as its discrete counterpart, and the Burgers and Korteweg-de Vries equations...

Persistent link: https://www.econbiz.de/10010589614

Critical mass of bacterial populations and critical temperature of self-gravitating Brownian particles in two dimensions

Chavanis, Pierre-Henri - In: Physica A: Statistical Mechanics and its Applications 384 (2007) 2, pp. 392-412

Smoluchowski–Poisson system. We also consider the case of one-dimensional systems and develop the connection with the Burgers … equation. Finally, we discuss the evolution of the system as a function of M or T in bounded and unbounded domains in …

Persistent link: https://www.econbiz.de/10011060669

Expansion, compression and triangular shockwaves in traffic flow above critical point

Onouchi, Tunetoshi; Nagatani, Takashi - In: Physica A: Statistical Mechanics and its Applications 373 (2007) C, pp. 713-720

described by the Burgers equation. …

Persistent link: https://www.econbiz.de/10010590854

Toda lattice mass transport in Lagrangian mechanics and in a two-dimensional system

Horii, Zene - In: Physica A: Statistical Mechanics and its Applications 361 (2006) 2, pp. 511-533

, the Burgers equation in two dimensions is formulated. These results contribute to an understanding of the broken isotropy …

Persistent link: https://www.econbiz.de/10010590635