The
ellipsis model input parameters are scaled from real world values into
dimensionless values in order to minimise computation time and increase
the
accuracy of the solution. We use the non-dimensional scaling approach
given by: |
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where
E
is a dimensionless Ellipsis variable, N
is the dimensional real world parameter and S
is a dimensional scaling factor. As an example, scaling from real world model length dimensions of 450km wide by 150km deep may be carried out using a length scaling factor (SL) of 1.5 x 105 m resulting in non-dimensional model geometry of 3 units wide by 1 unit deep. Using a Thermal diffusivity scaling factor (Sκ) of 1 x 10-6, a time scaling factor (St) can be found using: |
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With a viscosity scaling factor (Sη) of 1 x 1021 Pa and a gravity scaling factor (Sg) of 1 m/s2, a density scaling factor (Sρ) can be found: |
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A stress scaling factor (Ss) can now be defined as: |
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Using a velocity scale (Su) defined by: |
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The strain rate scaling factor (Sε) is subsequently given by: |
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Temperature is scaled between non-dimensional values of 0.17 and 1 corresponding to temperatures of 273K and 1603K respectively using a temperature scale (ST) of 1603K. Scaling factors for thermal properties heat generation (SHgen), thermal expansion coefficient (Sα) and heat flux (SQ) can be defined as: |
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