Peridynamic calculation scheme of a one-dimensional passive convection-diffusion equation

Abstract

To examine the convection-diffusion problem in-depth, we take the one-dimensional (1D) passive convection-diffusion equation as the research object and propose a general calculation scheme for the solution. The calculation formulation for the convergence time step of the convection term is derived, and the upwind scheme is used to verify the 1D passive convection equation. The results prove that peridynamics can be used to solve the convection equation. Moreover, when the safety factor ζ and horizon factor m satisfy 1/ζ=2m, the error in solving the convection equation is minimal. Through the introduction of the dimensionless number Pe, the dominant situation in convective diffusion can be evaluated, and the time step that satisfies convection and diffusion is obtained. The feasibility and numerical accuracy of peridynamics in solving the 1D passive convection-diffusion equation can be proved through the comparison of theoretical and calculated values.