Abstract In “Solution Property Reconstruction for Finite Volume scheme: a BVD+MOOD framework”, Int. J. Numer. Methods Fluids, 2020, we have designed a novel solution property preserving reconstruction, so-called multi-stage BVD-MOOD scheme. The scheme is able to maintain a high accuracy in smooth profile, eliminate the oscillations in the vicinity of discontinuity, capture sharply discontinuity and preserve some physical properties like the positivity of density and pressure for the Euler equations of compressible gas dynamics. In this paper, we present an extension of this approach for the compressible Euler equations supplemented with source terms (e.g., gravity, chemical reaction). One of the main challenges when simulating these models is the occurrence of negative density or pressure during the time evolution, which leads to a blow-up of the computation. General compressible Euler equations with different type of source terms are considered as models for physical situations such as detonation waves. Then, we illustrate the performance of the proposed scheme via a numerical test suite including genuinely demanding numerical tests. We observe that the present scheme is able to preserve the physical properties of the numerical solution still ensuring robustness and accuracy when and where appropriate.

中文翻译：

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具有源项和爆震的可压缩欧拉方程的解保属性重构BVD+MOOD方案

摘要在“有限体积方案的解决方案属性重构：BVD+MOOD 框架”中，Int。J. 数字。在 Methods Fluids，2020 年，我们设计了一种新颖的解决方案属性保持重建，即所谓的多阶段 BVD-MOOD 方案。该方案能够在平滑剖面中保持高精度，消除不连续附近的振荡，捕捉不连续，并保留一些物理性质，如可压缩气体动力学欧拉方程的密度和压力的正性。在本文中，我们为补充源项（例如重力、化学反应）的可压缩欧拉方程提出了这种方法的扩展。模拟这些模型时的主要挑战之一是在时间演化过程中出现负密度或压力，这会导致计算爆炸。具有不同类型源项的一般可压缩欧拉方程被认为是爆震波等物理情况的模型。然后，我们通过一个数值测试套件来说明所提出方案的性能，其中包括真正要求严格的数值测试。我们观察到，本方案能够保留数值解的物理特性，并在适当的时候和地点确保鲁棒性和准确性。