The Convection-Diffusion Equation is a partial differential equation that is used to study the effect of convective and diffusive processes on incompressible fluids. Among other things, it can be used to analyze various types of batteries, including battery setups where the chemical solutions that power the battery are in motion. Between these battery types, one that is commonly used is the Rot...

A simple Taylor-series analysis is made of the finite-difference formulations of the convection terms of convection-diffusion equations. A limitation is derived on grid Peclet number and grid size for a formulation to produce the expected numerical results. To verify the theory, the systematic numerical computations were carried out of a simple one-dimensional convection-diffusion equation. The...

The convection-diffusion equation is a fundamental that exists widely. consists of two processes: diffusion and convection. can also be called drift-diffusion equaintion. convection – mainly characterizes natural phenomenon in which physical particles, energy are transferred system. well-known linear transport one kind equation. describe the scalar field such as material feature, chemical react...

We use the finite element method to solve a convection-diffusion equation when convection is dominating, a problem which describes the behavior of the concentration of a solute in a blood vessel. A new technique for computing the discrete problem is used.

In the paper, we consider the large time behavior of solutions to the convection-diffusion equation ut−∆u+∇·f(u) = 0 in IRn× [0,∞), where f(u) ∼ uq as u → 0. Under the assumption that q ≥ 1 + 1/(n + β) and the initial condition u0 satisfies: u0 ∈ L1(IRn), ∫ IRn u0(x) dx = 0, and ‖eu0‖L1(IRn) ≤ Ct−β/2 for fixed β ∈ (0, 1), all t > 0, and a constant C, we show that the L1-norm of the solution to ...

Petroleum reservoir engineering requires solutions to the transient diffusion and convection-diffusion equations. Traditionally these calculations are carried out using finite difference methods. Prior workers have used perturbation-based boundary element methods for single phase flow in heterogeneous media. The current work applies the Dual Reciprocity Boundary Element Method (DRBEM) and the G...

This work investigates how we can extend the invariant subspace method to $$(2+1)$$ -dimensional time-fractional non-linear PDEs. More precisely, systematic study has been provided for constructing various dimensions of subspaces generalized convection–reaction–diffusion wave equation along with initial conditions first time. Additionally, special types above-mentioned are discussed through thi...

We consider a time-dependent and a steady linear convection-diffusion equation. These equations are approximately solved by a combined finite element – finite volume method: the diffusion term is discretized by Crouzeix-Raviart piecewise linear finite elements on a triangular grid, and the convection term by upwind barycentric finite volumes. In the unsteady case, the implicit Euler method is u...

We design several implicit asymptotic-preserving schemes for the linear semiconductor Boltzmann equation with a diffusive scaling, which lead asymptotically to the implicit discretizations of the drift-diffusion equation. The constructions are based on a stiff relaxation step and a stiff convection step obtained by splitting the system equal to the model equation. The one space dimensional sche...