Recent Advancement of Computing Technology of a Method of Control Volume for Obtaining of the Approximate Analytical Solution One-dimensional Convection-diffusion Problems

The study aims to investigate the computing technology of a method of control volume for obtaining of
the approximate analytical solution one-dimensional convection-diffusion problems. Convectiondiffusion
problems arise frequently in many areas of applied sciences and engineering. They occur in
fields where mathematical modeling is important such as physics, engineering and particularly in fluid
dynamics and transport problems. The solution of problem convection-diffusion equation by way of
control volume method is considered. Approximate solution of problem is received. Three point
scheme of high resolution is constructed. Using MPG (method of moving grids), it is possible to
improve the quality of the difference scheme. An increase in the accuracy of various schemes of the
convective-diffusion problem using extrapolation of Richardson is given. Based on the developed
algorithm, numerical calculations were performed. The algorithm of deriving of a solution is based on
the control volume method. The analytical solution allows, also constructing the compact scheme.