Abstract
Using the possibilities of the new concept of Flux-Corrected Transport (FCT), our goal is to construct the flux limiters of this method for a nonconservative convection-diffusion equation. The proposed approach treats the classical FCT method as an approximate solution to the corresponding optimization problem. As in the classical FCT method, we consider a hybrid difference scheme whose fluxes are a linear combination of low- and high-order fluxes. The flux limiter is computed as an approximate solution to an optimization problem with a linear objective function. The constraints for this optimization problem are derived from inequalities that are valid for the low-order monotone scheme and apply to the hybrid scheme. The proposed approach applies to both explicit and implicit schemes and can be extended to multidimensional differential equations. Numerical results for different approximations of the convective fluxes are given. It is shown that numerical results with the flux limiters, which are exact and approximate solutions to the optimization problem, are in good agreement.
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Kivva, S. (2023). Flux Correction for Nonconservative Convection-Diffusion Equation. In: Shkarlet, S., et al. Mathematical Modeling and Simulation of Systems. MODS 2022. Lecture Notes in Networks and Systems, vol 667. Springer, Cham. https://doi.org/10.1007/978-3-031-30251-0_2
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