An Improved Immersed Boundary Method for Simulating Flow Hydrodynamics in Streams with Complex Terrains

Abstract

Three-dimensional (3D) computational fluid dynamic (CFD) simulations have gained substantial popularity in recent years for stream flow modelling. The complex terrain in streams is usually represented by a 3D mesh conforming to the terrain geometry. Such terrain-conforming meshes are time-consuming to generate. In this work, an immersed boundary method is developed in an existing terrain-conforming CFD model named U2RANS as an alternative, in which terrains are represented implicitly in the Cartesian background mesh. An improved two-layer wall function is proposed in the framework of the k-ε turbulence model, with the aim of producing accurate and smooth wall shear stress distribution and paving the way for future model development on sediment transport and scour modeling. The improvement overcomes the inherent discontinuity and nonlinearity of the two-layer velocity profile, which causes error in the estimation of shear velocity. The new algorithm utilizes a distance control on the image point in immersed boundary method and a modification of velocity prediction in the laminar layer. The improved immersed boundary method is tested with 1D, 2D, and 3D cases, and comparisons with flume experiments show promising results.

Keywords

• immersed boundary method
• two-layer wall function
• <i>k</i>-<i>ε</i> turbulence model