A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonline...

A number of nonlinear phenomena in many branches of sciences such as physical [6], chemical, economical [20] and biological processes [15,14] are described by the interplay of reaction and diffusion or by the interaction between convection and diffusion. One of the well-known partial differential equations (PDEs) which governs a wide variety of them is Burgers equation, which provides the simpl...

Based on the exponent transform to eliminate the “convection item” in the equation and the fourth-order compact difference formulas for the first and second derivatives, two chasses of new implicit difference schemes are proposed for solving the one-dimensional convection-diffusion equation. The methods are of order O ( τ2 + h4 ) and O ( τ4 + h4 ) respectively. The former is proved to be uncond...

The numerical solution of convection-diffusion transport problems arises in many important applications in science and engineering. These problems occur in many applications such as in the transport of air and ground water pollutants, oil reservoir flow, in the modeling of semiconductors, and so forth. This paper describes several finite difference schemes for solving the one-dimensional convec...

The Optimized Order 2 (OO2) method is a non-overlapping domain decomposition method with differential interface conditions of order 2 along the interfaces which approximate the exact artificial boundary conditions [13, 9]. The convergence of Schwarz type methods with these interface conditions is proved in [12]. There already exists applications of the OO2 method to convection-diffusion equatio...

We present an approach for the efficient parallel solution of convection diffusion equations. Based on iterative nested dissection techniques [1] we extended these existing iterative algorithms to a solver based on nested dissection with incomplete elimination of the unknowns. Our elimination strategy is derived from physical properties of the convection diffusion equation, but is independent o...

A new modified diffusi on coefficient (MDC) technique for solv ing conve ction diffusion equation is proposed. The Galerkin finite-element discretization process is applied on the modified equation rather than the original one. For a class of one-dimensional convec-tion–diffusion equations, we derive the modi fied diffusion coefficient analytically as a function of the equation coefficients and...