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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.
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This paper presents experimental and numerical studies on the erosion of a horizontal granular bed by a two-dimensional plane vertical impinging jet to predict the eroded craters’ size scaling (depth and width). The simulations help understand the microscopic processes that govern erosion in this complex flow. A modified jet-bed distance, accounting for the plane jet virtual origin, is successfully used to obtain a unique relationship between the crater size and a local Shields parameter. This work develops a two-phase flow numerical model to reproduce the experimental results. The numerical techniques are based on a finite volume formulation to approximate spatial derivatives, a projection technique to calculate the pressure and velocity for each phase, and a staggered grid to avoid spurious oscillations. Different options for the sediment’s solid-to-liquid transition during erosion are proposed, tested, and discussed. One model is based on unified equations of continuum mechanics, others on modified closure equations for viscosity or momentum transfer. A good agreement between the numerical solutions and the experimental measurements is obtained.