Abstract Compressible multi-material flows are characterized by complex flow structures with a broad range of length scales and discontinuities associated with material interfaces and shock waves. High order and high resolution numerical methods are required to capture material interface as sharply as possible and to increase the resolution of complex structures along the material interface. This paper will present the application of the high resolution finite volume (FV) method based on the minimized dispersion and controllable dissipation (MDCD) reconstruction to compressible multi-material flows. The MDCD scheme with independent dispersion and dissipation provides a flexible mechanism to control the numerical dissipation. The adjustment of dissipation of the MDCD reconstruction will not affect the consistency, which is required for interface-diffusion capturing methods to prevent spurious oscillations. Several one- and two dimensional multi-material numerical simulations have indicated that the high resolution FV method based on MDCD reconstruction can capture material interfaces free of spurious oscillations and provide better resolved small-scale features than other numerical schemes on the same grid resolution.

中文翻译：

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可压缩多材料流的一致高分辨率界面捕获有限体积方法

摘要 可压缩多材料流动的特点是复杂的流动结构，具有广泛的长度尺度和与材料界面和冲击波相关的不连续性。需要高阶和高分辨率的数值方法来尽可能清晰地捕捉材料界面并提高沿材料界面的复杂结构的分辨率。本文将介绍基于最小弥散和可控耗散 (MDCD) 重建的高分辨率有限体积 (FV) 方法在可压缩多材料流中的应用。具有独立色散和耗散的 MDCD 方案提供了一种灵活的机制来控制数值耗散。调整MDCD重建的耗散不会影响一致性，这是界面扩散捕获方法所必需的，以防止虚假振荡。几个一维和二维多材料数值模拟表明，基于 MDCD 重建的高分辨率 FV 方法可以捕获没有虚假振荡的材料界面，并在相同的网格分辨率下提供比其他数值方案更好的解析小尺度特征。