A point source is theoretically formed by taking a mass injection/ejection, (SI unit: kg/(m
3·s)), in a small volume
δV and then letting the size of the volume tend to zero while keeping the total mass flux constant. Given a point source strength,
(SI unit: kg/s), this can be expressed as
is added to a point in the geometry. As can be seen from Equation 3-56,
must tend to plus or minus infinity as
δV tends to zero. This means that in theory the pressure also tends to plus or minus infinity.
The finite element representation of Equation 3-56 corresponds to a finite pressure in a point with the effect of the point source spread out over a region around the point. The size of the region depends on the mesh and on the strength of the source. A finer mesh gives a smaller affected region, but also a more extreme pressure value. It is important not to mesh too finely around a point source since the resulting pressure can result in unphysical values for the density, for example. It can also have a negative effect on the condition number for the equation system.
A line source can theoretically be formed by assuming a source of strength (SI unit: kg/(m
3·s)), located within a tube with cross-sectional area
δS and then letting
δS tend to zero, while keeping the total mass flux per unit length constant. Given a line source strength,
(SI unit: kg/(m·s)), this can be expressed as