# How do I Choose an Advection Method?

## Simulation of Swirling/Rotating Flows Advection Methods Best Practices

There are four momentum advection methods in * FLOW-3D*. The selection of a momentum advection method affects both runtime and accuracy so the proper choice is important.

- IORDER=1 1st Order Momentum Advection
- IORDER=2 2nd Order Centered
- IORDER=3 2nd Order Upwind Monotonicity Preserving
- IORDER=4 3rd Order Upwind Monotonicity Preserving

The 1st order advection method is the default choice and uses only neighboring cell information to advect momentum.

There are two 2nd order methods which perform well for simulations with strong flows and diagonal components relative to the computational mesh. Swirling flows are examples of simulations which can benefit from 2nd order advection methods.

In order to predict flows which have weak secondary features, a 3rd order momentum advection may be required.

Swirling and rotating flows are characterized by primarily diagonal flow in Cartesian mesh and secondary motions are often important. Examples of swirling flows are sedimentation tanks and swirl nozzles.

## Example: Sediment Collection Tank Simulation

The goal of this simulation is to predict the flow in a circular sediment removal tank. Sludge-laden flow enters the tank tangent to the mean flow at about ½ of the tank radius to the edge.

Main Swirling Flow Around Center & Secondary Flows

Utilize "Teacup Effect"

Heavier Solids Collect in Center

The incoming flow establishes a primary flow circulation pattern which is approximately solid body rotation. Once the primary, circular flow is established, centrifugal acceleration causes the flow to move outward, raising the fluid level at the outer wall. The flow surface also dips toward the center of the tank. This creates a pressure gradient from the outer edge of the tank to the center, resulting in a flow inward along the bottom of the tank. The inward flow draws sediments into the sump (sunken region) at the center of the tank.

This effect can easily be seen in teacups with tea leaves. Stirring the tea with a spoon sets up a rotational flow. After a short time, the tea leaves accumulate at the bottom of the cup near the center.

## Experimental Results in Circular Total Velocity

The image on the left shows the velocity measurements in the sump region of the tank. The numbers on the plot represent total velocity magnitudes at the indicated locations and are normalized with respect to the inlet velocity. The experimental results indicate a narrow vortex near the axis of the tank should occur. The velocity magnitude should be 1.2x the inlet velocity.

## Advection Method Choices in *FLOW-3D*: What to Choose?

- First Order (IORDER=1, Default)
- Excessive diffusion of diagonal flow

- Second Order (IORDER=2)
- Unstable with free-surface flows
- Advects diagonal motion well in confined flows

- Second Order Monatonicity Preserving (IORDER= 3)
- Some diffusion of diagonal flow

- Third Order (IORDER = 4)
- Advects diagonal motion well in free surface and confined flows
- Captures secondary flow features

## Simulation Results

Watch an IORDER 1 animation

Watch an IORDER 4 animation

### IORDER=1

- Initally solid-body rotation
- No vortexing seen near axis
- First order advection too dissipative

The default 1st order momentum advection, IORDER=1, is computationally efficient for many problems but is too diffusive of diagonal velocity components to accurately predict a swirling flow.

### IORDER=2

- Velocities are not reasonable – instability
- IORDER=2 not recommended for free surface

Since IORDER=2 is known to be unstable with free-surface flows with strong circulation, it is not expected to perform well in this problem. The simulation quickly becomes unstable and generates unreasonable flow velocities.

To use IORDER=2 for this problem, the user would need to replace the free surface with a symmetry boundary condition. However, the vortexing is not predicted well when the free surface is removed because the flow cannot dip at the tank center. This reduces the angular momentum increase at the axis.

### IORDER = 4

- Solid-body fluid rotation initialized
- Good prediction of vortexing seen near axis
- 3rd order advection captures flow well

The simulation of flow in a rotating flow in a circular tank is predicted well by IORDER=4 (third order accuracy). The fluid motion is initialized as solid body rotation since it is the steady state flow which is of interest rather than the startup.

## Summary of Advection Methods

### IORDER=1

- Best for flow without secondary flows
- Spillway and rivers flows
- Diagonal flows are diffused

### IORDER=2

- Unstable for circular free-surface flows
- Good for circular, confined flows

### IORDER=3

- Stable, not all secondary features captured

### IORDER=4

- Best for simulating rotating flows
- Secondary flow features captured