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A new approach for reducing error of the volume penalization method is proposed. The mask function is modified by shifting the interface between solid and fluid by toward the fluid region, where v and η are the viscosity and the permeability, respectively. The shift length is derived from the analytical solution of the one-dimensional diffusion equation with a penalization term. The effect of the error reduction is verified numerically for the one-dimensional diffusion equation, Burgers’ equation, and the two-dimensional Navier-Stokes equations. The results show that the numerical error is reduced except in the vicinity of the interface showing overall second-order accuracy, while it converges to a non-zero constant value as the number of grid points increases for the original mask function. However, the new approach is effectivewhen the grid resolution is sufficiently high so that the boundary layer,whose width is proportional to , is resolved. Hence, the approach should be used when an appropriate combination of ν and η is chosen with a given numerical grid.
The electronic properties of the interface between Rh clusters and CeO2 (111), (110) and (100) surfaces were studied using an isothermal-isobaric (NPT) ensemble at 773 K and 101.343 kPa using the tight binding-quantum chemical molecular dynamics (TB-QCMD) method. The amount of electronic exchange by interaction at the interface between the supported Rh55 clusters and each CeO2 surface was investigated quantitatively. A comparison of the mean square displacement (MSD) showed that the topmost oxygens on the Rh-supporting CeO2 surface exhibited higher mobility than those of the bare CeO2 surface. Although the mobility of the topmost oxygens on the bare CeO2 surface was in the order (100) > (110) > (111), this sequence was altered by the presence of Rh, so that the oxygen mobility for the more open (110) surface was the largest. The amount of electron exchange that occurred between Rh and the CeO2 (110) surface was also larger than for the (111) or (100) surface. The Ce 4f orbitals on the CeO2 (110) surface exhibited the strongest mixing with Rh 4d orbitals, which simultaneously caused restructuring and instability of the topmost Ce-O bonds. This enhancement of oxygen migration in the presence of Rh was occurred together with an increase in the number of oxygen vacancies on the ceria surface. This was because the topmost oxygens was shifted to have a stronger affinity with Rh and thus formed stronger bonds with Rh than with Ce.
The sound generated by a circular cylinder in a flow at low Mach numbers is
investigated by direct solution of the two-dimensional unsteady compressible Navier–Stokes equations. Results show that sound pressure waves are generated primarily
by vortex shedding from the cylinder surface into its wake. When a vortex is shed
from one side of the cylinder, a negative pressure pulse is generated from that side
whereas a positive pressure pulse is generated from the other side; alternate vortex
shedding from the upper and lower sides of the cylinder produces negative and
positive pulses alternately and thus produces sound pressure waves on both sides.
The dipolar nature of the generated sound is confirmed; lift dipole dominates the
sound field. The Doppler effect is shown to play an important role at finite Mach
numbers. The direct solutions are also compared with the solutions obtained by
Curle's acoustic analogy. The results show that Curle's solution describes well not
only the generation mechanism of the sound but also the propagation process if we
take the Doppler effect into consideration.
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