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<p>We propose a fifth-order finite-difference bound- and positivity-preserving (BP-P) path-conservative central-upwind alternative weighted essentially non-oscillatory (PCCU-AWENO) scheme for the five-equation model of compressible two-component flows. The proposed scheme is capable of maintaining the equilibrium near moving material interfaces, ensuring that velocity and pressure remain continuous at these interfaces. In addition, the scheme is designed to preserve the bound of volume fraction and positivity of density and internal energy: these three properties are absolutely essential for robustness of the proposed scheme. To this end, we first prove the BP-P property of the first-order PCCU scheme under a sufficient CFL condition and then introduce high-order BP-P limiters. The performance of the introduced PCCU-AWENO scheme is demonstrated on several one- and two-dimensional challenging numerical examples.</p>

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Bound- and Positivity-Preserving Path-Conservative Central-Upwind AWENO Scheme for the Five-Equation Model of Compressible Two-Component Flows

  • 期刊论文

  • 发表日期：

    2025年7月29日

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  • Qingcheng Fu,
  • Yaguang Gu,
  • Alexander Kurganov,
  • Bao-Shan Wang

摘要

We propose a fifth-order finite-difference bound- and positivity-preserving (BP-P) path-conservative central-upwind alternative weighted essentially non-oscillatory (PCCU-AWENO) scheme for the five-equation model of compressible two-component flows. The proposed scheme is capable of maintaining the equilibrium near moving material interfaces, ensuring that velocity and pressure remain continuous at these interfaces. In addition, the scheme is designed to preserve the bound of volume fraction and positivity of density and internal energy: these three properties are absolutely essential for robustness of the proposed scheme. To this end, we first prove the BP-P property of the first-order PCCU scheme under a sufficient CFL condition and then introduce high-order BP-P limiters. The performance of the introduced PCCU-AWENO scheme is demonstrated on several one- and two-dimensional challenging numerical examples.