
Computational mechanics 187
structure and the dissipation of energy into the surrounding space is negligible.
Assuming small motions, the equilibrium of a compressible fluid inside a
cavity is governed by the Euler equation derived in Section 10.5
ρ¨u = −∇p,
where ¨u is the acceleration of the particles and p is the pressure in the fluid.
Furthermore, ρ is the density and ∇ is the differential operator.
We also assume locally linear pressure-velocity behavior of the fluid as
p = −b∇u,
where b is the so-called bulk modulus related to the density of the fluid and
the speed of sound. Differentiating twice with respect to time and substitut-
ing the Euler equation ...