跨流域高超声速绕流Boltzmann模型方程并行算法

通过对Boltzmann方程碰撞积分进行模型化处理,提出了统一描述各流域复杂高超声速流动输运现象的气体分子速度分布函数控制方程,使用离散速度坐标法对分布函数方程所依赖的速度空间离散降维,构造出直接求解分子速度分布函数的气体动理论耦合迭代数值格式,研制了复杂飞行器高超声速绕流气动热力学计算模型。基于对气体动理论数值计算方法内在并行性、变量依赖关系、数据通信与并行可扩展性的分析研究,使用区域分解并行化方法提出了新型的气体动理论数值算法并行方案;研究了数据的并行分布与并行执行特征,开展了大规模的并行化程序设计,构造了可稳定运行于成千上万CPU的高性能并行算法,用以模拟各流域复杂飞行器的高超声速绕流问题。以稀薄流到连续流环境下不同Knudsen数、不同马赫数的可重复使用类球锥卫星体及翼身组合复杂飞行器等气动力、热绕流问题为研究对象展开大规模并行计算,并进行算法验证,所得计算结果与理论分析、直接模拟蒙特卡罗方法(DSMC)的模拟值及有关实验数据吻合较好,揭示了飞行器跨流域高超声速下的复杂流动机理与变化规律,提供了一条能够可靠模拟高超声速飞行器跨流域气动力及热问题的统一的算法应用研究途径。

A massively parallel algorithm for hypersonic covering various flow regimes to solve Boltzmann model equation

The unified equation on the molecular velocity distribution function is presented for describing complex hypersonic flow transport phenomena covering various flow regimes by the computable model of Boltzmann collision integral. The discrete velocity ordinate method is used to discretize and reduce velocity space dimensionality of the velocity distribution function, and the gas-kinetic numerical schemes of coupling iteration are constructed directly to solve the molecular velocity distribution function. The computing models of hypersonic aerothermodynamics for the complex vehicles are developed by the evolution and updating based on the molecular velocity distribution function. The new parallel strategy of the gas-kinetic numerical algorithm is established by using the parallelizing technique of domain decomposition with the analysis from variable dependency relations, data communication and parallel expansibility. The data parallel distribution and parallel implementation are researched, the large-scale parallel program design is carried out and then the high-performance parallel algorithm has been established to simulate the hypersonic flow problems around complex vehicles covering various flow regimes, which can run stably in the tens of thousands of CPU or more scale. The hypersonic aerothermodynamics problems from high rarefied transition to continuum flow regimes around three-dimensional sphere-cone satellite body and complex wing-body combination shape with various Knudsen numbers, different Mach numbers, and diverse flying of angles have been computed and verified in high-performance computer with massive scale parallel. The computed results are found in high resolution of the flow fields and good agreement with the related reference experimental data, direct simulation Monte Carlo (DSMC) and theoretical predictions, and the hypersonic complex flow mechanism and changing laws are revealed. It is probably practical that the applying research approaches of the gas-kinetic unified algorithm can be provided to simulate complex hypersonic flow problems covering the whole of flow regimes.