# 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.