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:

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

Here ρ{`\\rho`} represents density, c{`c`} 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 f{`f`}, 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 (ms1{`m \\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.

PAGE CONTENTS