局部非侵入式约化基模型在瑞利-泰勒不稳定中的应用

Application of local non-intrusive reduced basis method in Rayleigh-Taylor instability

局部的非侵入式约化基模型用于模拟瑞利-泰勒不稳定性(Rayleigh-Taylor instability,RTI)随时间演化的过程,其中初始小扰动的振幅和时间可视为自由参数。约化基模型把解看作一组基函数的线性组合,其中,基函数由本征正交分解获得,人工神经网络用于建立参数与基函数系数之间的映射关系。由于RTI随着时间的增加,相应的结构越来越复杂,尤其是后期会产生小规模旋涡的卷曲结构,因此考虑将RTI分为早期发展(线性)和中后期(拟非线性和弱非线性体制)发展阶段,即分段考虑时间参数。将时间参数分为3、5、6段,局部的非侵入式约化基模型与全局的非侵入式约化基模型相比,在精度相似的情况下,计算时间最快可以提高4倍左右。

A local non-intrusive reduced basis method(RBM)is proposed to simulate the evolution of Rayleigh-Taylor instability(RTI),in which the amplitude and time of initial small perturbations are considered as free parameters.RBM regards the solution as a linear combination of a set of reduced basis functions,which can be obtained by the proper orthogonal decomposition.Furthermore,the artificial neural network is used to establish the mapping relationship between the parameters and the coefficients of the reduced basis functions.Due to the structures of RTI becoming more and more complex with the increasing time,especially the rollup structures of small-scale vortices in the late stage,RTI is considered being divided into the early stage(linear)and the middle and late stage(quasi-non-linear and weak non-linear systems),i.e.time parameter is considered in stages.The time parameter is divided into three,five and six segments and the local RBM allows a potential speedup up to a factor of about four times faster than the global RBM with similar accuracy.