论文标题
嵌入式结构域还原浅水双曲方程的基本模型，具有移位边界方法
Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method
论文作者
论文摘要
我们考虑针对浅水双曲问题及其减少阶模型的完全离散的嵌入式有限元近似值。我们的方法基于固定的背景网格和嵌入式的减少基础。空间离散化的移动边界方法与明确的预测指标/多校正时间积分相结合，以随着时间的及时整合到浅水方程的数值解，包括全阶模型和还原模型。为了改善在离线阶段未经测试的几何形状的溶液歧管的近似值，该快照已通过插值程序进行了预处理，该程序先于减少基础计算。该方法对具有不同大小和位置的几何参数形状进行了测试。
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.
