We consider fully discrete embedded finite element approximations for a shallow water hyperbolic problem and its reduced-order model. Our approach is based on a fixed background mesh and an embedded reduced basis. The Shifted Boundary Method for spatial discretization is combined with an explicit predictor/multi-corrector time integration to integrate in time the numerical solutions to the shallow water equations, both for the full and reduced-order model. In order to improve the approximation of the solution manifold also for geometries that are untested during the offline stage, the snapshots have been pre-processed by means of an interpolation procedure that precedes the reduced basis computation. The methodology is tested on geometrically parametrized shapes with varying size and position.

我们考虑了浅水双曲线问题及其降阶模型的完全离散嵌入式有限元近似。我们的方法基于固定的背景网格和嵌入的缩减基础。用于空间离散化的移位边界方法与显式预测器/多校正器时间积分相结合，以及时积分浅水方程的数值解，适用于全阶和降阶模型。为了改进在离线阶段也未测试的几何形状的解流形的近似，快照已经通过在简化基础计算之前的插值过程进行了预处理。该方法在具有不同大小和位置的几何参数化形状上进行了测试。