In Problem 2, we assume that the two immiscible and
incompressible phases share the same viscosity value but have different densities.
As is shown in Figure 12, there are viscous
incompressible fluids between two infinite-length concentric cylinders.
In this section, we will present the numerical methods for the fractional model of two-phase
incompressible flow.
Let [u.sup.0] be the smooth solution, defined on [0, [T.sub.*]), to the
incompressible Euler equations (1.4) with initial data [u.sup.0.sub.0].
The physical parameters are E = [10.sup.5] and v = 0.4999, hence the problem is nearly
incompressible. In Figure 5.1(b) we plot the mesh of the bent domain.
Li, "
Incompressible limit of the compressible magnetohydrodynamic equations with vanishing viscosity coefficients," SIAM Journal on Mathematical Analysis, vol.
There should also be one additional valve actuator, to control the amount of
incompressible fluid in the lower piston area of all the actuators.
Marliani, "Evolution of current sheets and regularity of ideal
incompressible magnetic fluids in 2D," Communications on Pure and Applied Mathematics, vol.
And the latter three terms can be estimated, noting that [[partial derivative].sub.3] [u.sub.3] = -[[partial derivative].sub.1] [u.sub.1]-[[partial derivative].sub.2][u.sub.2] from the
incompressible condition
The insulation system is a stable
incompressible solid in deep water environments that involve depths of more than 10,000 feet.