Jacobian-free Newton-Krylov methods with GPU acceleration for computing nonlinear ship wave patterns

The nonlinear problem of steady free-surface flow past a submerged source is considered as a case study for three-dimensional ship wave problems. Of particular interest is the distinctive wedge-shaped wave pattern that forms on the surface of the fluid. By reformulating the governing equations with a standard boundary-integral method, we derive a system of nonlinear algebraic equations that enforce a singular integro-differential equation at each midpoint on a two-dimensional mesh. Our contribution is to solve the system of equations with a Jacobian-free Newton-Krylov method together with a banded preconditioner that is carefully constructed with entries taken from the Jacobian of the linearised problem. Further, we are able to utilise graphics processing unit acceleration to significantly increase the grid refinement and decrease the run-time of our solutions in comparison to schemes that are presently employed in the literature. Our approach provides opportunities to explore the nonlinear features of three-dimensional ship wave patterns, such as the shape of steep waves close to their limiting configuration, in a manner that has been possible in the two-dimensional analogue for some time.

The effects of humidity on tin whisker growth by immersion tin plating and tin solder dipping surface finishes

The drive to replace lead (Pb) from electronics has led to the replacement of tin (Sn) alloys as the terminal plating for electronic devices. However, the deposition of Sn based alloys as the component surface finish tends to induce Sn whisker that causes unintended electric shorts when the conductive whiskers grow across to the adjacent conductor. Internal stress is considered as the driving force that causes the growth of Sn whiskers. In this study, stress type of elevated temperature/ humidity exposure at 55C/85%RH with the storage for up to 24 months was conducted to define the acceleration factor in samples with deposition of immersion Sn plating and Sn solder dipping. The addition of Nickel (Ni) under-layer was also applied to examine the correlation to field conditions. The results showed that the whisker length increased in high humidity irrespective of the deposition methods. It was also shown that pure Sn solder dipping mitigated the whisker growth but does not completely prevent it when alloying Sn with 0.4%wtCu. Additionally, Ni under-layer was indicated to be more efficient in mitigating the growth of whisker by prolonging the incubation time for whisker formation.

Effect of surface conditions on flow of a micropolar fluid driven by a porous stretching sheet

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Some surface profiles of a strip after plane-strain indentation by rigid bodies with serrated surfaces

This paper is concerned with the surface profiles of a strip after rigid bodies with serrated (saw-teeth) surfaces indent the strip and are subsequently removed. Plane-strain conditions are assumed. This has application in roughness transfer of final metal forming process. The effects of the semi-angle of the teeth, the depth of indentation and the friction on the contact surface on the profile are considered.