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Units

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: $$ \rho ^{-1} c ^{-2} \partial _t^2 \phi = \nabla \cdot (\rho ^{-1} \nabla \phi) + f. $$ Here \rho represents density, c is the speed of sound, and by definition the units of the state variable \phi are \text{m}^2. Depending on the units of our forcing term f, physically useful units can be extracted from the solution as follows.

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

Desired output Symbol Field to save Further operations
Pressure (\text{N}\cdot \text{m}^{-2}) \phi _t ["phi_t"] None
Particle velocity (m \cdot s^{-1}) \nabla \phi \cdot \rho ^{-1} ["gradient-of-phi"] Multiply by the inverse density

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

Desired output Symbol Field to save Further operations
Pressure (\text{N}\cdot \text{m}^{-2}) \phi \cdot \rho^{-1} ["phi"] Multiply by the inverse density
Particle velocity (\text{m}\cdot s^{-1}) \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.