The discontinuous Galerkin domain decomposition (DGDD) method couples subdomains of high-fidelity polynomial approximation to regions of low-dimensional resolution for the numerical solution of systems of conservation laws. In the low-fidelity regions, the solution is approximated by empirical modes constructed by Proper Orthogonal Decomposition and a reduced-order model is used to predict the solution. The high-dimensional model instead solves the system of conservation laws only in regions where the solution is not amenable to a low-dimensional representation. The coupling between the high-dimensional and the reduced-order models is then performed in a straightforward manner through numerical fluxes at discrete cell boundaries. We show results from application of the proposed method to parametric problems governed by the quasi-1D and 2D compressible Euler equations. In particular, we investigate the prediction of unsteady flows in a converging-diverging nozzle and over a NACA0012 airfoil in presence of shocks. The results demonstrate the stability and the accuracy of the proposed method and the significant reduction of the computational cost with respect to the high-dimensional model.

不连续的Galerkin域分解（DGDD）方法将高保真多项式逼近的子域耦合到低维分辨率区域，以实现守恒定律系统的数值解。在低保真度区域中，解决方案通过适当正交分解构建的经验模式进行近似，并使用降阶模型来预测解决方案。高维模型仅在解决方案不适合低维表示的区域中求解守恒定律系统。高维模型和降阶模型之间的耦合随后通过离散单元边界处的数值通量以直接的方式执行。我们显示了将所提出的方法应用于由准1D和2D可压缩Euler方程控制的参数问题的结果。特别是，我们研究了在存在冲击的情况下，在渐缩式发散喷嘴中以及在NACA0012机翼上的非定常流动的预测。结果证明了该方法的稳定性和准确性，并且相对于高维模型而言，其计算成本显着降低。