非线性大气化学动力学方程组数值解法的比较

The comparison of numerical schemes for nonlinear atmospheric chemical kinetic equations

大气化学模式中描述化学反应动力学的是一组高度耦合、刚性、非线性的常微分方程组,高效精确的计算方法在空气质量模拟预测、气候化学相互作用研究中尤为重要。本文介绍了求解此类非线性常微分方程组(ODEs)的七种常见的数值计算方法,包括QSSA、MQSSA、HYBRID、MHYBRID、LSODE、Gong&Cho以及TWOSTEP方法,并基于同一反应机理进行24 h的数值模拟,通过对模拟结果的讨论分析,比较了各种方法的优劣。研究结果表明,就计算效率而言,QSSA方法最为省时。就计算精度而言,LSODE方法最优。若综合考虑计算精度和效率,HYBRID、MHY-BRID是比较适中的数值解法。

The chemical reactions in atmospheric chemistry models are described by a group of highly coupled,stiff and non-linear ordinary differential equations（ODEs）,to which a high-accuracy and fast numerical method is particularly important.In this paper,we present and compare the results of several methods,including QSSA,MQSSA,HYBRID,MHYBRID,LSODE,Gong Cho and TWOSTEP by a 24 h numerical simulation using the same chemical mechanism.Among all those methods,QSSA,TWOSTEP,MHYBRID,HYBRID and MQSSA are relatively faster than LSODE and Gong Cho,while LSODE is the best in terms of accuracy and QSSA costs the least amount of cup-time.In balance,we recommend HYBRID and MHYBRID to be the better choices with satisfactory performance in both precision and efficiency.