Numerical Simulation in Fluid Dynamics: A Practical Introduction

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The fluid solver I am using for this project is based on [Griebel et al. The Navier-Stokes equations are discretized on a staggered grid. After computing a tentative velocity field, a pressure correction term to make the field divergence free is computed using successive over-relaxation SOR. Boundaries are assumed to lie along the grid edges at boundary cells.

I never got around to trying the fluid solver used by [Stam ].

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In particular, I would like to compare the amount of numerical dissipation that occurs from the semi-lagrangian advection step used in Stam's solver. Sediment Transport Model There are two modes of sediment transport. Bed-load transport occurs when particles of sediment slide, roll, or saltate along the bottom. These particles move along in a region above the bed called the bed-load layer. The bed-load layer has a height corresponding to the maximum height achieved by a saltating particle. When the velocity of the fluid is high enough particles begin to move into the second mode of transport, suspended transport.

Ebook Numerical Simulation In Fluid Dynamics A Practical Introduction

Suspended particles entrained at the top of the bed-load layer move through the fluid by advection and diffusion. There are a large number of empirical models for sediment transport see [Chanson ] which do not necessarily agree. Since I was more concerned about getting the visual aspect of sediment transport than physically accurate simulation I decided to start with a simplified model.

I did away with the complicated expressions for coefficients based on physical parameters and replaced them with a single coefficient that could be set with a slider to achieve the desired effect.

The model does not include bed-load transport. Though the contribution of bed-load transport to the total sediment transport is not neglible, suspended transport is the most important factor. The main idea behind the model I used is that the capacity for a fluid to carry suspended sediment is related to the velocity of the fluid and the fall-rate of the sediment.

A sediment particle has a terminal fall velocity that depends on its shape, size, and density relative to the fluid. Smaller particles such as clay and silt tend to have smaller fall velocities and thus remain suspended longer, whereas gravel and sand have much higher fall velocities. The critical velocity at which sediment begins to move into suspension is related to the fall-velocity. A smaller disturbance in the fluid is required to suspend particles with a low fall velocity. Similarly, the sediment capacity is also related to fall velocity.

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