Encyclopaedia Index

### Imbalance Patch

#### The general idea

PHOENICS solves equations which express, cell-by-cell throughout the computational grid, the balances of conserved quantities such as mass, momentum and energy.

A 'patch' in PHOENICS terms, is a group of contiguous cells, defined by the PIL PATCH command.

An "imbalance patch" is such a patch of cells for which the imbalances of the conserved quantities, at a defined instant in the calculation, are computed and printed.

Such patches provide interesting information of the following kinds:

1. If the patch encloses a volume of material which is free from any source of the quantity in question, if the flow is steady, and if the solution is converged, the printed-out imbalance should be as close to zero as round-off error permits.

Larger imbalances are therefore a measure of lack of convergence which it may be useful to know about.

2. In like circumstances except that the flow is transient, the printed imbalance represents the contribution of the transient terms of the equations, integrated over the patch volume.

3. If the patch encloses a volume of fluid within which a solid object is held at rest, the imbalances of momentum in three different directions represent the forces exerted by the fluid on the body.

#### Implementation in PHOENICS

If a patch name in the Q1 file begins with the four characters IMBL, it will be treated as an imbalance patch. Associated COVAL commands are necessary in order to indicate the variables for which imbalances must be computed; but the values of CO and VAL appearing in them are immaterial.

Core-Library case 805 may serve as an example. It concerns flow around a sphere.

Several imbalance patches enclose the object, as may be seen here.

The extent to which they agree about the z-direction force on the sphere is shown by the following extract from the RESULT file:

```
z-wise force on IMBL3&2  is      4.07574
z-wise force on IMBL4&3  is      4.06488
z-wise force on IMBL5&4  is      4.04868
z-wise force on IMBL810  is      4.04253
z-wise force on IMBL815  is      3.90546  ```
wherein the +/- 1% variations are probably indicative of incomplete convergence.

#### Future developments

It is intended to extend the imbalance-patch concept so as to enable it to compute turning moments as well as forces.

This will be useful for 'virtual-wind-tunnel' applications.