Space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting for multidimensional detonation waves simulation

I. S. Popov
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Abstract

The space-time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting was used for simulation of multidimensional reacting flows with detonation waves. The presented numerical method does not use any ideas of splitting or fractional time steps methods. The modification of the LST-DG predictor has been developed, based on a local partition of the time step in cells in which strong reactivity of the medium is observed. This approach made it possible to obtain solutions to classical problems of flows with detonation waves and strong stiffness, without significantly decreasing the time step. The results obtained show the very high applicability and efficiency of using the ADER-DG-PN method with a posteriori sub-cell limiting for simulating reactive flows with detonation waves. The numerical solution shows the correct formation and propagation of ZND detonation waves. The structure of detonation waves is resolved by this numerical method with subcell resolution even on coarse spatial meshes. The smooth components of the numerical solution are correctly and very accurately reproduced by the numerical method. Non-physical artifacts of the numerical solution, typical for problems with detonation waves, such as the propagation of non-physical shock waves and weak detonation fronts ahead of the main detonation front, did not arise in the results obtained. The results of simulating rather complex problems associated with the propagation of detonation waves in significantly inhomogeneous domains are presented, which show that all the main features of detonation flows are correctly reproduced by this numerical method. It can be concluded that the space-time adaptive ADER-DG-PN method with a posteriori sub-cell ADER-WENO finite-volume limiting is perfectly applicable to simulating complex reacting flows with detonation waves.
带有 LST-DG 预测器和后验子单元 ADER-WENO 有限体积限制的时空自适应 ADER-DG 有限元法用于多维爆轰波模拟
采用带有 LST-DG 预测器和后验子单元 ADER-WENO 有限体积限制的时空自适应 ADER-DG 有限元方法模拟了带有爆轰波的多维反应流。所提出的数值方法没有使用任何分割或分时步骤方法。对 LST-DG 预测器进行了改进,其基础是在观察到介质强烈反应的单元中对时间步进行局部分割。这种方法可以在不显著减小时间步长的情况下,解决具有爆轰波和强刚度的经典流动问题。所获得的结果表明,使用 ADER-DG-PN 方法和后验子单元限制来模拟带有爆轰波的反应流具有很高的适用性和效率。数值解显示了 ZND 爆轰波的正确形成和传播。该数值方法即使在粗网格上也能以子单元分辨率解析爆轰波的结构。数值方法正确和非常精确地再现了数值解的平滑分量。数值求解中的非物理假象是爆轰波问题的典型特征,如非物理冲击波的传播和主爆轰前沿前的微弱爆轰前沿,在所获得的结果中没有出现。本文介绍了在明显不均匀域中与爆轰波传播有关的相当复杂问题的模拟结果,结果表明该数值方法正确地再现了爆轰流的所有主要特征。可以得出结论,带有后验子单元 ADER-WENO 有限体积限制的时空自适应 ADER-DG-PN 方法完全适用于模拟带有爆轰波的复杂反应流。
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