Kīlauea, Hawai’i, puts on a ‘once-in-a-century’ show

Kīlauea is the youngest of five basaltic shield volcanoes on the island of Hawai’i. It is located to the south-east of the much larger Mauna Loa volcano, and rose above sea level about 100 ka ago. Kīlauea is one of the most monitored, and arguably the best understood volcanoes on Earth, providing scientists with a good understanding of its current eruption, in which magma rises from depth and is stored beneath its 4 × 3.2 km summit caldera in an underground reservoir. The reservoir is connected to a lava lake within a crater called Halema’uma’u, which is situated on the floor of the caldera. When magma drains from the summit area it travels in underground conduits and emerges on the flanks of the volcano at a rift zone, where it erupts through fissures. The magma is sometimes stored in other reservoirs along the way. This link between summit magma storage and fissure eruptions on the flanks has occurred thousands of times at many Hawai’ian volcanoes. The current eruptive episode is, however, a ‘once-in-a-century’ show, because it is the first time since 1924 that fissure-fed lava flow eruptions have been accompanied by significant explosive eruptions within Halema’uma’u Crater. This gives scientists a unique opportunity to use modern methods to understand exactly how such hazardous explosions happen at Kīlauea, a volcano that receives about 2 million visitors a year

Transformation of two and three-dimensional regions by elliptic systems

The research during this period continued to expand the class of numerical algorithms that can be accurately and efficiently implemented on overlapping grids. Whereas previous calculations have been used to solve elliptic equations and to find the steady-state solution of parabolic equations, the present work is aimed towards developing time-accurate solution techniques for parabolic and hyperbolic equations. The primary difficulty here is in the correct treatment of the interior boundary nodes that must be updated at each iteration. The implementation of explicit methods is straightforward. However, the common practice of lagging these values when using an implicit methods leads to inconsistencies in the difference equation. One way to avoid this problem is to alternately calculate with an implicit and an explicit method on each subgrid. With this procedure, the explicit method generates boundary values at the next time level which are then used by the implicit step. It can be shown that when a backward implicit method is combined with a forward explicit method, the composite method is second order accurate and unconditionally stable for linear problems. A second area in which progress can be reported is in the distribution of grid points on curves and surfaces