Central-upwind (CU) schemes are Riemann-problem-solver-free finite-volume methods widely applied to a variety of hyperbolic systems of PDEs. Exact solutions of these systems typically satisfy certain bounds, and it is highly desirable or even crucial for the numerical schemes to preserve these bounds. In this paper, we develop and analyze bound-preserving (BP) CU schemes for general hyperbolic systems of conservation laws. Unlike many other Godunov-type methods, CU schemes cannot, in general, be recast as convex combinations of first-order BP schemes. Consequently, standard BP analysis techniques are invalidated. We address these challenges by establishing a novel framework for analyzing the BP property of CU schemes. To this end, we discover that the CU schemes can be decomposed as a convex combination of several intermediate solution states. Thanks to this key finding, the goal of designing BPCU schemes is simplified to the enforcement of four more accessible BP conditions, each of which can be achieved with the help of a minor modification of the CU schemes. We employ the proposed approach to construct provably BPCU schemes for the Euler equations of gas dynamics. The robustness and effectiveness of the BPCU schemes are validated by several demanding numerical examples, including high-speed jet problems, flow past a forward-facing step, and a shock diffraction problem.

翻译：中心迎风格式（CU格式）是一类无需黎曼问题求解器的有限体积方法，广泛应用于各类双曲型偏微分方程组。此类系统的精确解通常满足特定界限，数值格式能否保持这些界限至关重要。本文针对一般双曲守恒律系统，研究并构建了保界（BP）中心迎风格式。与许多其他Godunov型方法不同，CU格式一般无法重构为一阶BP格式的凸组合，因此标准BP分析技术不再适用。为克服这一挑战，我们建立了一个分析CU格式保界性的新框架。为此，我们发现CU格式可分解为若干中间解状态的凸组合。基于这一关键发现，设计BPCU格式的目标简化为满足四个更易实现的BP条件，每个条件均可通过CU格式的微调实现。我们采用所提方法构建了气体动力学欧拉方程的可证BPCU格式。通过多个高要求数值算例（包括高速射流问题、前向台阶绕流及激波衍射问题）验证了BPCU格式的鲁棒性与有效性。