可压缩多介质界面不稳定性及湍流混合的高分辨率算法研究

The study of compressible multi-material interface instability and turbulence mixing problem with complicated equation of state has important scientific significance and application value for weapon physics and inertial confinement fusion, and et. al.. However, the extreme flow conditions of such flows and the later large deformation of turbulence mixing bring great challenges to the existing physical model and numerical methods.. The projec will perform two things. (1) Based on the five-equation model of pressure equilibruim hypothesis, the effects of heat transfer/physical viscosity on volume fraction will be discused, and a full governing euqations will be established which can describe multi-material interface problem and its final turbulence mixing. (2) A physical-compatable ROE solver, which is suitable for the complicated Mie-Gruneisen type euqations of state, will be established. Combined with the early study on high-order scheme, a full high-resolution and low-dissipation numerical method for such physical model is expected to be accomplished.. Through this project, a solid foundation will be laid down for perfoming direct numerical simulation of multi-material turbulence mixing problem with complicated equation of state in the future.

开展对具有复杂状态方程的可压缩多介质界面不稳定性及其湍流混合问题的研究对武器物理和惯性约束核聚变等研究有着重要的科学意义和应用价值。 但这种流动的极端流场条件以及后期的大变形湍流混合特点给现有的物理模型和数值方法均带来极大的挑战。. 本项目计划开展:（1）基于等速度等压力平衡假设的五方程模型，探讨热传导/物理粘性对体积分数影响及其数值建模，从而建立适用于多介质界面问题以及湍流混合问题的统一的控制方程；（2）针对复杂的 Mie-Gruneisen 类型的状态方程，研究一种物理兼容的 ROE 求解器。结合前期对高精度格式的研究，形成一套简单实用且稳定性好的高分辨率和高置信度算法。. 力争通过此次系统性研究，为今后开展具有复杂状态方程的多介质湍流混合问题的高精度直接数值模拟工作奠定扎实的建模和数值算法基础。

针对具有复杂状态方程的可压缩多介质界面不稳定性及其湍流混合问题的数值模拟困难，发展低耗散无振荡高效数值算法，研究了物理粘性的影响，做出一些有创新性的研究工作。..重点研究：.1.设计了适用于可压缩多介质界面不稳定性及其湍流混合问题的低耗散无振荡高效离散算法；.2.研究了不同物理粘性对多介质界面不稳定性问题中气泡速度和涡量演化的规律研究。..通过此次系统性研究，为今后开展具有复杂状态方程的多介质湍流混合问题的高精度直接数值模拟工作奠定扎实的建模和数值算法基础。