模型竞争机制下的算法层级粒子/连续多尺度耦合求解方法

Hypersonic flows in near space are typical multi-scale problems, and are accompanied by strong compression and expansion phenomena due to their properties of low density and high speed. As a result, the complicated local rarefied and non-equilibrium regions often appear in the flow field. Since the numerical simulation of these flows is a challenging work, the design process of hypersonic aircrafts in near space has a great deal of uncertainty. In this application, an Algorithm-level Hybrid Particle/Continuum method (AHPC) will be developed which uses the concept of model competition in multi-scale physics. In the AHPC, the integral solution of the model equations in gas-kinetic theory is used to quantify the weights of both particle method and continuum method, which are determined by the ratio of iteration time to mean collision time. The continuum method used in AHPC is the NS-type CFD method with a gas-kinetic boundary condition, and the DSMC method is adopted as the particle method. In order to couple the continuum and particle methods, the particles collide with others following the probability calculated from the weights. Once collision, their individual information disappears, and they merge into the macroscopic properties of gas flow. And at the new time step, they emerge from the macroscopic properties again through a sampling process. Given the AHPC method, the mechanism of non-equilibrium effect in hypersonic near-space flows will be studied in a numerical way, along with its influence on important flow parameters of the configuration of near space aircraft.

近空间高超声速流动因其高速和低密度特点，伴随着强烈的压缩和膨胀过程，具有显著的多尺度性质，并使流场呈现出复杂的局部稀薄非平衡流态，对数值预测提出挑战，并给相关飞行器设计工作带来大量不确定性。同时，近空间空气动力学的发展也急需在复杂多尺度流动机理上取得突破。申请借鉴多尺度问题中不同尺度模型间的竞争机制，以迭代时间与分子碰撞时间之比为参数，利用气体动理学模型方程对竞争机制中粒子模型和连续模型的权重分配进行准确量化，最终形成算法层级上的粒子/连续耦合方法（AHPC）。在耦合策略上，分子依概率发生碰撞后，随即失去个体信息并转入由连续求解器控制的宏观过程，在新的时间步中又依宏观量重新抽样生成。粒子求解器采用DSMC方法，连续求解器采用与气体动理学边界条件结合的NS方法。最后以AHPC方法为数值手段，定量研究局部稀薄流态中的非平衡流动机理、以及其对典型近空间高超声速外形关键流动参数的影响机制。

近空间高超声速流动因其高速和低密度的特点，具有显著的多尺度性质，其中强烈的压缩和膨胀过程，使流场呈现出复杂的局部稀薄非平衡流态。这一复杂多尺度问题对数值预测提出挑战，并给相关飞行器设计工作带来不确定性。同时，临近空间空气动力学的发展也急需在复杂多尺度流动机理上取得突破。本项目借鉴多尺度问题中不同尺度模型间的竞争机制，以迭代时间与分子碰撞时间之比为参数，利用气体动理学模型方程对竞争机制中粒子模型和连续模型的权重分配进行准确量化，最终形成简化统一波-粒子方法（SUWP）。本项目主要对SUWP方法的构建进行了研究，主要包括以下三个方面：1. 耦合方法的建模和计算，主要对粒子速度分布函数进行建模和抽样；2. 算法层级粒子-连续算法的研究，对SUWP方法的涨落进行抑制，并探索耦合方法可用的边界条件；3. 流动机理研究，包括对非平衡临近空间的高超声速流动进行模拟。初步研究证实了算法层级粒子-连续耦合方法的可行性以及其模拟非平衡临近空间流动的能力。