## Dimensional Scaling

Elmer(/Ice) does not know about unit systems. You can create your mesh and run your case in any unit system you like. The user is responsible to define a dimensionally consistent setup. This gives the oportunity to switch from the usually used SI units, metres-kilogramm-seconds (m-kg-s) to a unit system that still has a unit lengths of metres, but yields pressures in Megapascal and measures unit-time in years (m-MPa-a). If using the value the value 3.1556926E+07 s/a (seconds per year), we get the following entries for density in the Material section:

```! In SI units it would be
! Density = 910.0
! In m-Mpa-a
Density = \$910.0*1.0E-06*(31556926.0)^(-2.0)```

The acceleration by gravity should be given inside the Body Force section as

```! In SI units it would be
! Flow BodyForce 3 = -9.81
! In m-Mpa-a
Flow BodyForce 3 = \$-9.81*(31556926.0)^(2.0)```

Eventually external imposed pressure and traction should scale in MPa (hence be mulitplied with 1.0E-06 if given in Pascal). For instance, if we impose an external normal pressure caused by a water body of density 1000 kg m^-3, we would write the hydrostatic pressure distribution in a Boundary Condition as

```External Pressure = Variable Coordinate 3
Real MATC "(tx < 0.0)*(1000.0 * 9.81 * tx)*1.0E-06"```

Consequently, slip coefficients (here linear) shall be scaled from SI units as

`Slip Coefficient 2 = \$1.0E10*1.0E-06/31556926.0 `

with typical values for faster sliding of about 1.0E-04 m a^-1 MPa^-1 .

Also the units of the thermodynamic properties need to be converted to the m-MPa-a unit system:

```Temp Heat Capacity = Variable Temp
Real MATC "capacity(tx)*(31556926.0)^2" !capacity in SI units, input in K
Temp Heat Conductivity = Variable Temp
Real MATC "conductivity(tx)*31556926*1.0e-6"  !conductivity in SI units, input in K
Temp Heat Flux = Real MATC "0.063*(31556926.0)*1.0E-06" !heat flux of 63mW/m2
pressuremeltingpoint=273.15-(9.8E-08*1.0E06*P) ! if pressure in MPa```

Conversion factor for units in general (y2s = yeartosecond = 31556926):

• 1kg=1e-6MPa*m*yr^2*y2s^-2
• 1J=1e-6MPa*m^3
• 1W=1e-6MPa*m^3/yr*y2s