Lattice Boltzmann model for two-dimensional unsteady Burgers’ equation

A Multilevel Finite Difference Scheme for One-Dimensional Burgers Equation Derived from the Lattice Boltzmann Method

An explicit finite difference scheme for one-dimensional Burgers equation is derived from the lattice Boltzmannmethod. The system of the lattice Boltzmann equations for the distribution of the fictitious particles is rewritten as a three-level finite difference equation. The scheme is monotonic and satisfies maximum value principle; therefore, the stability is proved. Numerical solutions have b...

Optimizing lattice Boltzmann simulations for unsteady flows

We present detailed analysis of a lattice Boltzmann approach to model time-dependent Newtonian flows. The aim of this study is to find optimized simulation parameters for a desired accuracy with minimal computational time. Simulation parameters for fixed Reynolds and Womersley numbers are studied. We investigate influences from the Mach number and different boundary conditions on the accuracy a...

Alternative and Explicit Derivation of the Lattice Boltzmann Equation for the Unsteady Incompressible Navier-Stokes Equation

Quantum lattice-gas model for the Burgers equation

A quantum algorithm is presented for modeling the time evolution of a continuous field governed by the nonlinear Burgers equation in one spatial dimension. It is a microscopic-scale algorithm for a type-II quantum computer, a large lattice of small quantum computers interconnected in nearest neighbor fashion by classical communication channels. A formula for quantum state preparation is present...

Infinite-dimensional symmetries of a two-dimensional generalized Burgers equation

The conditions for a generalized Burgers equation which a priori involves nine arbitrary functions of one, or two variables to allow an infinite dimensional symmetry algebra are determined. Though this algebra can involve up to two arbitrary functions of time, it does not allow a Virasoro algebra. This result confirms that variable coefficient generalizations of a non-integrable equation should...