 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 outputSymbolField to saveFurther 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 outputSymbolField to saveFurther 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. PAGE CONTENTS