Progress on acceleration algorithm of the computation for chemical reactions in turbulent combustion simulation
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摘要: 为研究湍流燃烧数值模拟中化学反应机理计算的加速方法，讨论了动态自适应化学（Dynamic Adaptive Chemistry，DAC）方法和Krylov子空间近似的指数格式的应用情况。在湍流火焰大涡模拟中，使用DAC简化可以加速化学反应计算。然而，在并行燃烧数值模拟中，处理器核心的负载极度不平衡，加速效果有限。而Krylov子空间近似的指数格式的加速效果可以作用于每个处理器核心，更有利于整体计算效率的提高。在同等精度下，相比于隐式格式耦合DAC和MTS加速方法，Krylov子空间近似的指数积分格式对化学反应计算的加速效果更为显著。
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关键词:
- 湍流燃烧数值模拟 /
- 化学反应计算加速 /
- 动态自适应化学 /
- Krylov子空间近似 /
- 指数积分格式
Abstract: To investigate the methods of accelerating the computation of chemical kinetics in turbulent combustion, the application of Dynamic Adaptive Chemistry (DAC) and exponential integrator with Krylov subspace approximation is discussed. In the large eddy simulation of a turbulent flame, using DAC can accelerate the computation of chemical kinetics. However, in the context of parallel combustion simulation, the loads on the different processors are extremely imbalanced, which limits its performance. For the exponential integrator with Krylov subspace approximation, the acceleration effect acts on each processor, which is beneficial to improve the global computational efficiency. Compared to that of the implicit scheme coupled with DAC and MTS, the accelerating performance of the exponential integrator with Krylov subspace approxi-mation under the same level of accuracy is more obvious. -
图 2 在各处理器核心上的(a) ODE时间(tODE, p)以及(b) ODE时间、(c)温度T、(d) PFA占比(ϕPFA, p)和(e)简化机理中组分数(NS)的局部放大视图[21]
Figure 2. Contour plot of (a) ODE time on each processor (tODE, p) together with zoom-in view of (b) ODE time on each processor, (c) temperature T, (d) percentage of cells performing PFA (ϕPFA, p) and (e) number of selected species in locally reduced mechanism (NS) [21]
图 4 使用反应机理(a)GRI-Mech 3.0[102]和(b)USC Mech Ⅱ[103]得到的表 1中算例的加速因子γ与最大平均相对误差ε的关系。Xsc(εr)，Xsm(α)和Xscm(εr, α)表示表 1所列工况算例，括号中的数值εr和α分别表示CoDAC简化阈值和MTS安全因子[99]
Figure 4. The speedup factor γ as functions of maximum averaged relative error ε for the cases in Table 1 with (a) GRI-Mech 3.0[102] and (b) USC Mech Ⅱ [103]. Xsc (εr), Xsm(α) and Xscm(εr, α) represent the cases in Table 1 and numbers εr and α in the parentheses represent the reduction threshold of CoDAC and the safety factor of MTS, respectively[99]
图 6 使用GRI-Mech 3.0[102]和USC Mech Ⅱ [103]机理时表 1中算例Ascm和Bscm的Krylov子空间维数(mKrylov)随快方程数量(nfast)的变化[99]
Figure 6. The dimension of the Krylov subspace (mKrylov as a function of the number of fast equations (nfast) for cases Ascm and Bscm shown in Table 1 with the mechanisms of GRI-Mech 3.0 [102] and USC Mech Ⅱ [99, 103]
表 1 使用不同加速方法的算例设置
Table 1. Simulated cases for different acceleration methods
加速方法\求解器 DVODE 指数格式 Non R - SC As Bs SC + CoDAC Asc Bsc SC+MTS Asm Bsm SC + CoDAC + MTS Ascm Bscm 
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