Three-Dimensional Hydrostatic Curved Channel Flow Simulations Using Non-Staggered Triangular Grids

Wei Zhang,Miguel Uh Zapata,Damien Pham Van Bang,Kim Dan Nguyen

doi:10.3390/w14020174

Abstract

Non-staggered triangular grids have many advantages in performing river or ocean modeling with the finite-volume method. However, horizontal divergence errors may occur, especially in large-scale hydrostatic calculations with centrifugal acceleration. This paper proposes an unstructured finite-volume method with a filtered scheme to mitigate the divergence noise and avoid further influencing the velocities and water elevation. In hydrostatic pressure calculations, we apply the proposed method to three-dimensional curved channel flows. Approximations reduce the numerical errors after filtering the horizontal divergence operator, and the approximation is second-order accurate. Numerical results for the channel flow accurately calculate the velocity profile and surface elevation at different Froude numbers. Moreover, secondary flow features such as the vortex pattern and its movement along the channel sections are also well captured.

Highlights

Academic Editors: Non-staggered triangular grids have many advantages in river modeling with the finite-volume method (FVM)
This paper proposes a novel three-dimensional hydrostatic method for flows in a curved channel based on an unstructured finite-volume method and a filtered scheme for the case of non-staggered triangular grids to avoid the divergence noise and ensure momentum advection in both horizontal and vertical directions
This paper proposes a novel three-dimensional hydrostatic method for flows in a curved channel based on an unstructured finite-volume method and a filtering technique with non-staggered triangular grids

Summary

Introduction

Academic Editors: Non-staggered triangular grids have many advantages in river modeling with the finite-volume method (FVM). [1], horizontal divergence errors may occur, especially in large-scale hydrostatic calculations with centrifugal acceleration or nonlinear momentum advection [2] These divergence noises, shown as a checker-board patterns, were initially noticed in the numerical experiments as an inherent feature of the staggered triangular C-grid [3]. This phenomenon is significant when the model needs to solve external forces such as centrifugal force or other nonlinear momentum terms. We notice the inaccuracies in the approximation of the divergence operator and instabilities due to spurious pressure modes associated with the unstaggered arrangements that show similar behavior as the divergence noise

Methods

Results

Discussion

Conclusion