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Nondimensionalization

Create a nondimensionalization object in which we specify characteristic values, which are later employed to non-dimensionalize (or dimensionalize) all model parameters. Choose between GEO, SI or NO units:

  • SI units assume all input and output is in SI units. Very general, but for typical geodynamic simulations often not so useful (as a million years has many seconds, resulting in large numbers).
  • GEO units uses SI units throughout but assumes that input/output are in a format that is more convenient for typical geodynamic use cases, such as Myrs,km or MPa
  • NO units are nondimensional units. Note that for parameters to be correctly non-dimensionalized in this case, you still have to indicate units (such as that velocity is given in m/s).

A dimensional parameter can be transformed into a non-dimensional one with Nondimensionalize.

Specify characteristic values

Characteristic values can be defined in 3 ways.

GeoParams.Units.GEO_units — Function
GEO_units(;length=1000km, temperature=1000C, stress=10MPa, viscosity=1e20Pas)

Creates a non-dimensionalization object using GEO units.

GEO units implies that upon dimensionalization, time will be in Myrs, length in km, stress in MPa, etc. which is more convenient for typical geodynamic simulations than SI units The characteristic values given as input can be in arbitrary units (km or m), provided the unit is specified.

Examples:

julia> CharUnits = GEO_units()
Employing GEO units 
Characteristic values: 
         length:      1000 km
         time:        0.3169 Myrs
         stress:      10 MPa
         temperature: 1000.0 °C
julia> CharUnits.velocity
1.0e-7 m s⁻¹

If we instead have a crustal-scale simulation, it is likely more appropriate to use a different characteristic length:

julia> CharUnits = GEO_units(length=10km)
Employing GEO units 
Characteristic values: 
         length:      10 km
         time:        0.3169 Myrs
         stress:      10 MPa
         temperature: 1000.0 °C
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GeoParams.Units.SI_units — Function
CharUnits = SI_units(length=1000m, temperature=1000K, stress=10Pa, viscosity=1e20)

Specify the characteristic values using SI units

Examples:

julia> CharUnits = SI_units(length=1000m)
Employing SI units 
Characteristic values: 
         length:      1000 m
         time:        1.0e19 s
         stress:      10 Pa
         temperature: 1000.0 K

Note that the same can be achieved if the input is given in km:

julia> CharUnits = SI_units(length=1km)
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GeoParams.Units.NO_units — Function
CharUnits = NO_units(length=1, temperature=1, stress=1, viscosity=1)

Specify the characteristic values in non-dimensional units

Examples:

julia> using GeoParams;
julia> CharUnits = NO_units()
Employing NONE units 
Characteristic values: 
         length:      1
         time:        1.0 
         stress:      1
         temperature: 1.0
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(Non)-dimensionalize parameters

Once characteristic values have been defined, you can use them to non-dimensionalize or dimensionalize any parameter.

GeoParams.Units.Nondimensionalize! — Function
Nondimensionalize!(param::GeoUnit, CharUnits::GeoUnits{TYPE})

Nondimensionalizes param (given as GeoUnit) using the characteristic values specified in CharUnits in-place

Example 1

julia> using GeoParams;
julia> CharUnits =   GEO_units();
julia> v         =   GeoUnit(3cm/yr)
3 cm yr⁻¹ 
julia> Nondimensionalize!(v, CharUnits) 
0.009506426344208684

Example 2

julia> CharUnits =   GEO_units();
julia> A         =   GeoUnit(6.3e-2MPa^-3.05*s^-1)
0.063 MPa⁻³·⁰⁵ s⁻¹
julia> A_ND      =   Nondimensionalize(A, CharUnits) 
7.068716262102384e14
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Nondimensionalize!(MatParam::AbstractMaterialParam, CharUnits::GeoUnits{TYPE})

Non-dimensionalizes a material parameter structure (e.g., Density, CreepLaw)

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Nondimensionalize!(phase_mat::MaterialParams, g::GeoUnits{TYPE})

Nondimensionalizes all fields within the Material Parameters structure that contain material parameters

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GeoParams.Units.Dimensionalize! — Function
Dimensionalize!(param::GeoUnit, CharUnits::GeoUnits{TYPE})

Dimensionalizes param again to the values that it used to have using the characteristic values specified in CharUnits.

Example

julia> CharUnits =   GEO_units();
julia> x = GeoUnit(3cm/yr)
julia> Nondimensionalize!(x, CharUnits)
julia> Dimensionalize!(x, CharUnits) 
3.0 cm yr⁻¹
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Dimensionalize!(MatParam::AbstractMaterialParam, CharUnits::GeoUnits{TYPE})

Dimensionalizes a material parameter structure (e.g., Density, CreepLaw)

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Dimensionalize!(phase_mat::MaterialParams, g::GeoUnits{TYPE})

Dimensionalizes all fields within the Material Parameters structure that contain material parameters

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GeoParams.Units.Nondimensionalize — Function
Nondimensionalize(param, CharUnits::GeoUnits{TYPE})

Nondimensionalizes param using the characteristic values specified in CharUnits

Example 1

julia> using GeoParams;
julia> CharUnits =   GEO_units();
julia> v         =   3cm/yr
3 cm yr⁻¹ 
julia> v_ND      =   Nondimensionalize(v, CharUnits) 
0.009506426344208684

Example 2

In geodynamics one sometimes encounters more funky units

julia> CharUnits =   GEO_units();
julia> A         =   6.3e-2MPa^-3.05*s^-1
0.063 MPa⁻³·⁰⁵ s⁻¹
julia> A_ND      =   Nondimensionalize(A, CharUnits) 
7.068716262102384e14

In case you are interested to see how the units of A look like in different units, use this function from the Unitful package:

julia> uconvert(u"Pa^-3.05*s^-1",A) 
3.157479571851836e-20 Pa⁻³·⁰⁵

and to see it decomposed in the basic SI units of length, mass and time:

julia> upreferred(A)
3.1574795718518295e-20 m³·⁰⁵ s⁵·¹ kg⁻³·⁰⁵
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GeoParams.Units.Dimensionalize — Function
Dimensionalize(param, param_dim::Unitful.FreeUnits, CharUnits::GeoUnits{TYPE})

Dimensionalizes param into the dimensions param_dim using the characteristic values specified in CharUnits.

Example

julia> CharUnits =   GEO_units();
julia> v_ND      =   Nondimensionalize(3cm/yr, CharUnits) 
0.031688087814028945
julia> v_dim     =   Dimensionalize(v_ND, cm/yr, CharUnits) 
3.0 cm yr⁻¹
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