Dear All,

please, note that I do not want to push all your patience to the limit, by being another one posting concerning “LB Units”!

Presently I’m struggling with some unit conversion issue, and I’m well aware of the excellent “Unit Howto” of jlatt, and some other sources in papers, books. To be honest: I don’t get it concerning the following…

Assume a simple 3D flow, oriented in z-direction, within a rectangular domain with obstacles. I use a MRT LB, and besides qualitative flow visualization (which already looks quite good), I need to evaluate the pressure loss in the channel.

First I define some reference values:

```
reference length d_0 = 1.000E-03 [ m ]
reference time t_0 = 1.000E-04 [ s ]
reference mass m_0 = 1.200E-09 [ kg ]
```

this gives…

```
reference density rho_0 = 1.200E+00 [ kg / m³ ]
reference kinematic viscosity nu_0 = 1.000E-02 [ m² / s ]
```

The physical domain is defined by

```
length in x-direction = .001 [ m ]
length in y-direction = .001 [ m ]
length in z-direction = .001 [ m ]
density = 1.2 [ kg / m³ ]
Re number = 1 000. [ - ]
kinematic viscosity = .00001 [ m² / s ]
characteristic length = .001 [ m ]
characteristic time = .0001 [ s ]
characteristic velocity = 10. [ m / s ]
```

This leads me to the following non-dimensional system…

```
length in x-direction = 1. [ - ]
length in y-direction = 1. [ - ]
length in z-direction = 1. [ - ]
density = 1. [ - ]
Re number = 1 000. [ - ]
kinematic viscosity = .001 [ - ]
characteristic length = 1. [ - ]
characteristic time = 1. [ - ]
characteristic velocity = 1. [ - ]
```

and using

```
spatial resolution Nx = 5.000E+01 [ - ]
temporal resolution Nt = 1.000E+03 [ - ]
```

I start with the discret system (lb units)

```
lattice spacing in x-direction = .02 [ m ]
lattice spacing in y-direction = .02 [ m ]
lattice spacing in z-direction = .02 [ m ]
rho = 1. [ - ]
Re-number = 1 000. [ - ]
kinematic viscosity = .0025 [ - ]
cell spacing d_x = .02 [ - ]
time step d_t = .001 [ - ]
lb velocity u_lb = .05 [ - ]
```

The computation converges well, and at z-const. planes at channel inlet and outlet I got two average densities

```
density inlet 1.099E+00 [ - ]
density outlet 1.084E+00 [ - ]
```

Well, now I’m struggling with getting meaningful physical values (in terms of Pascal) from these numbers. Referring to threads like Example of Units… and other sources, I tried the following…

```
using... p_phys = p_lb * d_0^2 / t_0^2 * rho_0 with p_lb = cs^2 * rho
pressure inlet = 44. [ Pa ]
pressure outlet = 43.4 [ Pa ]
```

Currently I assume there is some mistake (seems to be a to small pressure difference in-out compared to NaSt computation and analytical estimate). I’m not sure if my scaling and unit conversion is done well/correct, and if I get it right with the conversion of pressure.

Please, any help and discussion is appreciated!

Thanks in advance,

Francois