Flux correction for nonconservative convection-diffusion equation

TL;DR

This paper develops a flux limiter for a nonconservative convection-diffusion equation using a hybrid scheme and optimization-based flux correction, improving numerical accuracy while maintaining stability.

Contribution

It introduces a novel flux limiter based on an optimization problem for nonconservative convection-diffusion equations, combining monotone and high-order schemes.

Findings

Flux limiters show good agreement with numerical results.

The method effectively balances accuracy and stability.

Exact and approximate solutions to the optimization problem perform well.

Abstract

Our goal is to develop a flux limiter of the Flux-Corrected Transport method for a nonconservative convection-diffusion equation. For this, we consider a hybrid difference scheme that is a linear combination of a monotone scheme and a scheme of high-order accuracy. The flux limiter is computed as an approximate solution of a corresponding optimization problem with a linear objective function. The constraints for this optimization problem are derived from inequalities that are valid for the monotone scheme and apply to the hybrid scheme. Our numerical results with the flux limiters, which are exact and approximate solutions to the optimization problem, are in good agreement.