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.

翻译：我们的目标是为非保守的对流-扩散方程式开发通量调整运输方法的通量限制。 为此, 我们考虑混合差分法, 这是一种单质和高分级精度的线性组合。 通量限制法是用线性目标函数来计算相应的优化问题的近似解决办法。 优化问题的制约因素来自适用于单质和混合法的不平等。 我们对通量限制法的数值结果非常一致, 它们是优化问题的确切和近似解决办法。