An immersed boundary method for unstructured meshes in depth averaged shallow water models. (6th December 2015)

• Record Type: Journal Article
• Authors: Ouro, Pablo; Cea, Luis; Ramírez, Luis; Nogueira, Xesús
• Is Part Of: International journal for numerical methods in fluids. Volume 81:Number 11(2016)
• Page Start: 672
• Page End: 688
• Publication Date: 2015-12-06
• Subjects: immersed boundary method -- moving least‐squares -- unstructured grids -- shallow water equations -- direct forcing -- finite volumes; Fluid dynamics -- Mathematics -- Periodicals; 532
• DOI: 10.1002/fld.4201
• Languages: English
• ISSNs: 0271-2091

Abstract

Summary: The representation of geometries as buildings, flood barriers or dikes in free surface flow models implies tedious and time‐consuming operations in order to define accurately the shape of these objects when using a body fitted numerical mesh. The immersed boundary method is an alternative way to define solid bodies inside the computational domain without the need of fitting the mesh boundaries to the shape of the object. In the direct forcing immersed boundary method, a solid body is represented by a grid of Lagrangian markers, which define its shape and which are independent from the fluid Eulerian mesh. This paper presents a new implementation of the immersed boundary method in an unstructured finite volume solver for the 2D shallow water equations. Moving least‐squares is used to transmit information between the grid of Lagrangian markers and the fluid Eulerian mesh. The performance of the proposed implementation is analysed in three test cases involving different flow conditions: the flow around a spur dike, a dam break flow with an isolated obstacle and the flow around an array of obstacles. A very good agreement between the classic body fitted approach and the immersed boundary method was found. The differences between the results obtained with both methods are less relevant than the errors because of the intrinsic shallow water assumptions. Copyright © 2015 John Wiley & Sons, Ltd. Abstract : An immersed boundary method for use on unstructured meshes is proposed, with particular focus on its application to depth averaged shallow water models. Moving least‐squares is used to generate the interpolation functions. The method is applied to the flow around a spur dike, a dam break with an isolated obstacle and the flow around an array of obstacles, and results are compared with simulations using classic body fitted meshes and experimental data. Good agreement is found between the numerical methods.