An immersed boundary method for unstructured meshes in depth averaged shallow water models

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.

Instantaneous transport of a passive scalar in a turbulent separated flow

“…This IB method allows the representation of solid obstacles within the fluid domain without the need for building body conformal meshes. Although the IB method can be used in unstructured meshes [ 34 ], it is commonly used with rectangular Cartesian meshes in conjunction with fast Poisson equation solvers, such as the multi-grid method, which makes LES more feasible as the computational performance is improved, i.e. by reducing the computational resources.…”

Hydrodynamic loadings on a horizontal axis tidal turbine prototype

“…[15] and Bai et al [17] used a continuum IB method, in the following the discrete method developed by Fadlun et al [19] and improved by Uhlmann [20], the so-called direct forcing IB method, is adopted for the simulations. This method has been validated previously for vertical axis tidal turbines [21,22], particle laden flows [20], bluff body representation [23], and several other applications as summarised in [24].…”

An immersed boundary-based large-eddy simulation approach to predict the performance of vertical axis tidal turbines

“…Since then, the IB method has been used in a wide range of applications such as particle laden flows [27], fluid-structure interaction [28], bluff bodies in depth-100 averaged shallow water models [29] or simulation of HATTs [30], and has proven to work well for flows with moving boundaries.…”