A Rapid Prediction Model of Urban Flood Inundation in a High-Risk Area Coupling Machine Learning and Numerical Simulation Approaches

Climate change has led to increasing frequency of sudden extreme heavy rainfall events in cities,resulting in great disaster losses.Therefore,in emergency management,we need to be timely in predicting urban floods.Although the existing machine learning models can quickly predict the depth of stagnant water,these models only target single points and require large amounts of measured data,which are currently lacking.Although numerical models can accurately simulate and predict such events,it takes a long time to perform the associated calculations,especially two-dimensional large-scale calculations,which cannot meet the needs of emergency management.Therefore,this article proposes a method of coupling neural networks and numerical models that can simulate and identify areas at high risk from urban floods and quickly predict the depth of water accumulation in these areas.Taking a drainage area in Tianjin Municipality,China,as an example,the results show that the simulation accuracy of this method is high,the Nash coefficient is 0.876,and the calculation time is 20 seconds.This method can quickly and accurately simulate the depth of water accumulation in high-risk areas in cities and provide technical support for urban flood emergency management.

Immersed Finite Element Method for Interface Problems with Algebraic Multigrid Solver

This article is to discuss the bilinear and linear immersed finite element(IFE)solutions generated from the algebraic multigrid solver for both stationary and moving interface problems.For the numerical methods based on finite difference formulation and a structured mesh independent of the interface,the stiffness matrix of the linear system is usually not symmetric positive-definite,which demands extra efforts to design efficient multigrid methods.On the other hand,the stiffness matrix arising from the IFE methods are naturally symmetric positive-definite.Hence the IFE-AMG algorithm is proposed to solve the linear systems of the bilinear and linear IFE methods for both stationary and moving interface problems.The numerical examples demonstrate the features of the proposed algorithms,including the optimal convergence in both L 2 and semi-H1 norms of the IFE-AMG solutions,the high efficiency with proper choice of the components and parameters of AMG,the influence of the tolerance and the smoother type of AMG on the convergence of the IFE solutions for the interface problems,and the relationship between the cost and the moving interface location.