Multigrid methods for compressible Navier-Stokes equations in low-speed flows

AbstractThe multigrid performance of pointwise, linewise and blockwise Gauss-Seidel relaxations for compressible laminar and turbulent Navier-Stokes equations is illustrated on two low-speed test problems: a flat plate and a backward facing step. The line method is an Alternating Symmetric Line Gauss-Seidel relaxation. In the block methods, the grid is subdivided into geometric blocks of n × n points with one point overlap. With in the blocks, the solution is obtained by a direct method or with an alternating modified incomplete lower-upper decomposition. The analysis is focused on flows typical for boundary layers, stagnation and recirculation regions. These are characterized by very small Mach numbers, high Reynolds numbers and high mesh aspect ratios

Analysis of robust multigrid methods for steady viscous low Mach number flows.

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Multigrid methods for compressible Navier-Stokes equations. Proceedings second Seminar on Euler and Navier-Stokes Equations (Theory, Numerical Solution, Applications), Prague, April 1996, Academy of Sciences of the Czech Republic, 1996, ISBN 80-85918 -18-8, p. 63-64.

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Effect of constant strain rate, composed of varying amplitude and frequency, of early loading on peri-implant bone (re)modelling.

Item does not contain fulltextAIM: Examine the effect of varying components of strain rate -- amplitude versus frequency -- while maintaining a constant strain rate of early controlled mechanical loading on implant stability, peri-implant bone mass and bone-to-implant contact. MATERIAL AND METHODS: Three groups of guinea-pigs received TiO2 -blasted implants in both tibiae. One week after installation test implants were loaded 5 days/week during 4 weeks. The contra-lateral implants were the unloaded controls. Strain rate was kept constant (1600 micro epsilon/s), while amplitude and frequency were varied per group. Implant stability was followed by resonance frequency analysis. Animals were sacrificed, and ground sections were prepared to rate bone-to-implant contact and bone mass. RESULTS: All implants (n=78) integrated uneventfully. A significant positive effect (p=0.03) of early loading on bone mass was observed in the distal medullar cavity. A significant difference in bone mass between test and control implants was evidenced between the groups (p=0.03 and 0.04). A significant increase in implant stability and bone-to-implant contact could not be shown. CONCLUSIONS: Early controlled stimulation of peri-implant bone is related to amplitude/frequency and not to strain rate as such, considering a constant stimulation time. An increase of bone mass around early-loaded implants was shown. This cortical bone model is most sensitive to low-frequency/high-amplitude stimulation