The space-time adaptive ADER finite element DG method with a posteriori correction technique of solutions on subcells by the finite-volume ADER-WENO limiter was used to simulate non-stationary compressible multicomponent reactive flows. The multicomponent composition of the reacting medium and the reactions occurring in it were described by expanding the original system of Euler equations by a system of non-stationary convection-reaction equations. The use of this method to simulate high stiff problems associated with reactions occurring in a multicomponent medium requires the use of the adaptive change in the time step. The solution of the classical problem related to the formation and propagation of a ZND detonation wave is carried out. It was shown that the space-time adaptive ADER finite element DG method with a posteriori correction technique of solutions on subcells by the finite-volume ADER-WENO limiter can be used to simulate flows without using of splitting in directions and fractional step methods.

翻译：采用基于后验子单元有限体积ADER-WENO限制器修正技术的时空自适应ADER有限元DG方法，对非定常可压缩多组分反应流动进行了数值模拟。通过在原欧拉方程组基础上扩展非定常对流-反应方程组，描述了反应介质的多组分构成及其内部发生的化学反应。应用该方法模拟多组分介质中化学反应相关的高刚性问题时，需采用自适应时间步长调整策略。针对ZND爆轰波形成与传播的经典问题开展了数值求解。研究表明，结合后验子单元有限体积ADER-WENO限制器修正技术的时空自适应ADER有限元DG方法，能够在无需方向分裂和分步法的情况下实现流动模拟。