The topics include a posteriori error estimation via nonlinear error transport with application to shallow water, enforcing discrete mass conservation in incompressible flow simulations with continuous velocity approximation, the stability of partitioned methods for magnetohydrodynamic flows at small

magnetic Reynolds number, an immersed finite element method of lines for moving interface problems with non-homogeneous flux jumps, and full Eulerian modeling and effective numerical studies for the dynamic fluid-structure interaction problem.

A low magnetic Reynolds number means that the dynamo is weak and could soon dissipate.

Some of the flows zip along at nearly 10 kilometers per second, allowing them to achieve very high magnetic Reynolds numbers.

The magnetic field B0 is applied perpendicular to the stretching sheet and the effect of the induced magnetic field is neglected since the

magnetic Reynolds number is assumed to be small and have constant physical properties.

The

magnetic Reynolds number is assumed to be small so that the induced magnetic field can be neglected and a constant magnetic field

Assuming that the

magnetic Reynolds number to be small, we neglect the induced magnetic field in comparison with the applied magnetic field.

The

magnetic Reynolds number is assumed to be small which implies that the induced magnetic field can be neglected compared to the applied magnetic field.

The

magnetic Reynolds number is so small that the induced magnetic field can be neglected.

They demonstrated that the rate of dipole moment decay is weakly sensitive to the particular mixing flow pattern, but varies with the magnetic Reynolds number, a measure of the velocity of the flow.

In particular, the researchers found that a mixing flow in the outer core with magnetic Reynolds number in the range of 200, which they suggest is a physically reasonable range, could account for the historically measured rate of decrease of the geomagnetic dipole moment.

Since the fluid is slightly conducting, the

magnetic Reynolds number is much less than unity and hence the induced magnetic field is neglected in comparison with the applied magnetic field following Sparrow and Cess [14].