Unconditionally stable schemes for non-stationary convection-diffusion equations

TL;DR

This paper develops unconditionally stable numerical schemes for non-stationary convection-diffusion equations, including convection-diffusion-reaction forms, using new variables and operator splitting techniques.

Contribution

It introduces novel unconditionally stable schemes for convection-diffusion equations based on new variables and splitting methods, advancing numerical stability analysis.

Findings

Successfully constructed unconditionally stable schemes for convection-diffusion equations.

Extended schemes to convection-diffusion-reaction equations with operator splitting.

Demonstrated stability without restrictions on time step size.

Abstract

Convection-diffusion problem are the base for continuum mechanics. The main features of these problems are associated with an indefinite operator the problem. In this work we construct unconditionally stable scheme for non-stationary convection-diffusion equations, which are based on use of new variables. Also, we consider these equations in the form of convection-diffusion-reaction and construct unconditionally stable schemes when explicit-implicit approximations are used with splitting of the reaction operator.