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arXiv · 2602.12580

Adaptive mesh methods for hyperbolic conservation laws with bound-preserving flux limiters

Yaguang Gu·Guanghui Hu·Tao Tang
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Abstract

In this paper, we develop bound-preserving (BP) finite-volume schemes for hyperbolic conservation laws on adaptive moving meshes. For scalar conservative laws, we rewrite the conventional high-order discretization as a convex combination of first-order counterparts on each sub-cell, which is mathematically equivalent to introducing a bound-preserving flux limiter. Such a limiter is inexpensive to evaluate, with a feature that the corresponding BP CFL conditions depend solely on the first-order sub-cell schemes. A mild CFL restriction is derived under which high-order spatial accuracy is retained. The proposed BP schemes are extend to two nonlinear systems, namely, the Euler equations and the five-equation transport model of two-medium flows. Numerical results demonstrate that the present schemes possess high resolution and strong robustness properties.

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Yaguang Gu, Guanghui Hu, Tao Tang. 2026-02-13. Adaptive mesh methods for hyperbolic conservation laws with bound-preserving flux limiters. https://arxiv.org/abs/2602.12580

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