Embedded domain Reduced Basis Models for the shallow water hyperbolic equations with the Shifted Boundary Method
arXiv:2201.09546 · doi:10.1016/j.cma.2022.115143
Abstract
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.
References in corpus (9)
- The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
- The Neural Network shifted-Proper Orthogonal Decomposition: a Machine Learning Approach for Non-linear Reduction of Hyperbolic Equations
- A Reduced Basis approach for PDEs on parametrized geometries based on the Shifted Boundary Finite Element Method and application to a Stokes Flow
- Reduction of Nonlinear Embedded Boundary Models for Problems with Evolving Interfaces
- A Reduced-Order Shifted Boundary Method for Parametrized incompressible Navier-Stokes equations
- Enhancing CFD predictions in shape design problems by model and parameter space reduction
- Discrete Empirical Interpolation and unfitted mesh FEMs: application in PDE-constrained optimization
- A Reduced Order Approach for the Embedded Shifted Boundary FEM and a Heat Exchange System on Parametrized Geometries
- Galerkin finite element methods for the Shallow Water equations over variable bottom