长腔体内混合流体Rayleigh-Bénard对流的高精度数值模拟

The study focusing on the dynamics behaviors of the binary fluid mixtures Rayleigh-Bénard convection system, such as the spatio-temporal evolution, bifurcation, turbulence, etc., as well as their stability, is an important research topic in the nonlinear science. Numerical simulation is an important means to carry out the research on this issue. Since the existing research on this aspect usually uses the first order or second order accurate scheme, that leads to a large dissipation error and dispersion error, and usually produces inaccurate computational results. In order to get accurate solutions, it usually requires fine grid mesh, however, this would result in large computational cost. Therefore, this application, firstly, dedicates to study the high order numerical simulation methods for solving this problem, to develop the high order compact difference schemes. And then, to use them to study the dynamics behaviors and the stability of the binary fluid mixtures Rayleigh-Bénard convection system in a long rectangular enclosure under asymmetric and non-periodic boundary conditions, and to analyze the effects of the physical parameters, dimensionless parameters, boundary conditions and changes of the size of the fluid field to the structures of the flow fields for the binary fluid mixtures. To find out the conditions for the occurance of temporal-spatio defects and the ways to supress these defects. The purpose of this study is to reveal the spatio-temporal structure of the traveling wave phenomena and the formation mechanism of the dynamics behaviors in the binary fluid mixtures convection. On the whole, this research can help us achieve accurate simulation of the binary mixture process under the complex conditions and boundary conditions, profoundly reveal the dynamics behaviors of the binary fluid mixtures convection system, and understand the formation mechanism of the turbulence.

对双流体混合Raleigh-Bénard对流系统的时空演化、分叉、湍流等动力学行为及其稳定性的研究是非线性科学的重要研究课题。数值模拟是对此类问题开展研究的重要手段。鉴于目前此方面研究所采用的数值方法主要是低精度格式，存在较大的耗散和色散误差，从而导致计算结果不精确，本申请致力于这一问题的高精度数值模拟方法的研究。发展高精度紧致差分格式，并将之用于研究长腔体内非周期非对称边界条件下双流体混合Rayleigh-Bénard对流系统的动力学特性及其稳定性，分析物性参数、无量纲参数、边界条件、流场尺寸变化对双流体混合流场结构的影响，对流结构的多重稳定性现象，以及对流系统出现时空缺陷所具备的条件，及消除和抑制缺陷的方法和途径。通过本项目研究，可以实现对复杂工况和边界条件下流体混合过程的精准模拟，深刻揭示双流体混合对流运动中行波现象的时空结构及其动力学行为的形成机理，也有助于深入理解湍流形成的机理。

对双流体混合Raleigh-Bénard对流系统的时空演化、分叉等动力学行为的研究是非线性科学的重要研究课题。鉴于目前此方面研究所采用的数值方法主要是低精度格式，存在较大的耗散和色散误差，从而导致计算结果不精确，本申请致力于这一问题的高精度数值模拟方法的研究。构造了一致高精度紧致差分格式，并给出了构造原则，这一格式解决了以往边界格式精度低从而导致降低整体算法精度且导致数值不稳定的问题，并将之用于研究驱动方腔内的Hopf分岔问题并给出Hopf分岔临界雷诺数存在的区间及分析了更高雷诺数下驱动方腔内的系统由稳态向失稳状态转变的过程。也有助于深入理解湍流形成的机理。及应用此算法研究长腔体内非周期非对称边界条件下双流体混Rayleigh-Bénard对流系统的动力学特性及其稳定性。