Decoupled flux limiting high order finite difference methods for hyperbolic conservation laws

Document Type

Article

Publication Date

12-15-2026

Abstract

The parametrized bound preserving flux limiters for high order methods solving scalar conservation laws were generalized from the flux corrected transport approach to a conservative high order finite difference method to preserve upper and lower bounds on the numerical solution while maintaining the high order accuracy. The main advantage is its conceptually simple derivation and its general application to high order difference and finite volume or discontinuous Galerkin methods for bound preserving with little CFL constraints. However, such an advantage is accompanied by the inconvenience that the limiting parameters are coupled together in a group of inequalities, which makes its application to multidimensional problems and systems complicated. In this paper, we propose a novel decoupled flux limiting method in the high order finite difference framework so that each limiting parameter is isolated to its own interface. Meanwhile, we prove that such practice preserves both global bounds and high order accuracy with mild CFL constraints. Numerical evidence from simulation of scalar problems indicates clear success in preserving global maximum and minimum, while maintaining the designed order of accuracy. The simplicity for implementation and the convenience for generalization of the decoupled flux limiting are fully demonstrated when applied to preserve positive density and pressure for high order finite difference methods computing the solution to the compressible Euler problems with marginal computational cost.

Publication Title

Journal of Computational Physics

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