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Due to the variety of wave-equations and source-time functions one can use in Salvus Compute, the question of "which units are my results out put in?" can be non-trivial. If you are interested in precicely determining the units of input and output, please read on.

Acoustic simulations

Within Salvus we consider a formulation of the acoustic wave equation based on a scalar displacement potential. The strong form of this equation is:

ρ1c2t2ϕ=(ρ1ϕ)+f. \rho ^{-1} c ^{-2} \partial _t^2 \phi = \nabla \cdot (\rho ^{-1} \nabla \phi) + f.

Here ρ\rho represents density, cc is the speed of sound, and by definition the units of the state variable ϕ\phi are m2\text{m}^2. Depending on the units of our forcing term ff, physically useful units can be extracted from the solution as follows.

Source in units of Volume Density Injection Rate (s1\text{s}^{-1})

Desired outputSymbolField to saveFurther operations
Pressure (Nm2\text{N}\cdot \text{m}^{-2})ϕt\phi _t["phi_t"]None
Particle velocity (ms1m \cdot s^{-1})ϕρ1\nabla \phi \cdot \rho ^{-1}["gradient-of-phi"]Multiply by the inverse density

Source in units of Force Density (Nm3\text{N} \cdot \text{m}^{-3})

Desired outputSymbolField to saveFurther operations
Pressure (Nm2\text{N}\cdot \text{m}^{-2})ϕρ1\phi \cdot \rho^{-1}["phi"]Multiply by the inverse density
Particle velocity (ms1\text{m}\cdot s^{-1})ϕ  dtρ2\int \nabla \phi\;dt \cdot \rho ^{-2}["gradient-of-phi"]Multiply by the inverse density squared

For more information on the physical equations solved in Salvus, please check out our paper here. Additionally, a complete list of fields which can be output can be found in the documentation.