General methods are often not adequate for accurate resolution of steep gradient phenomena; they usually introduce non-physical effects such as smearing of the solution or spurious oscillations. Since publication of Godunov’s order barrier theorem, which proved that linear methods cannot provide non-oscillatory solutions higher than first order (Godunov 1954, Godunov 1959), these difficulties have attracted a lot of attention and a number of techniques have been developed that largely overcome these problems. To avoid spurious or non-physical oscillations where shocks are present, schemes that exhibit a Total Variation Diminishing (TVD) characteristic are especially attractive. Two techniques that are proving to be particularly effective are MUSCL (Monotone Upstream-Centered Schemes for Conservation Laws) a flux/slope limiter method (van Leer 1979, Hirsch 1990, Tannehill 1997, Laney 1998, Toro 1999) and the WENO (Weighted Essentially Non-Oscillatory) method (Shu 1998, Shu 2009). Both methods are usually referred to as high resolution schemes (see diagram).
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Beneath The Icy Crust Of Enceladus. The research paper written by scientists with the Cassini mission, published in the journal Science, suggests the presence of hydrogen gas. Hydrogen gas, that could potentially provide a chemical energy source for life, is pouring into the subsurface ocean of Enceladus from hydrothermal activity on the seafloor of this bewitching, distant moon-world. Dr. Carolyn Porco, a planetary scientist and leader of the Imaging Science team for Cassini, explained to the press in March 2012 that "More than 90 jets of all sizes near Enceladus's south pole are spraying water vapor, icy particles, and organic compounds all over the place. Cassini has flown several times now through this spray and has tasted it. And we have found that aside from water and organic material, there is salt in the icy particles. The salinity is the same as that of Earth's oceans." Several possibilities could provide an answer as to why the moon would have charcoal-black surface patches, even though it is circling a dwarf planet that is as bright as freshly fallen snow. One theory that has been suggested proposes that, unlike larger objects such as Makemake, its own little companion moon is so small that it cannot gravitationally keep a grip onto a bright and icy crust, which then sublimates, undergoing a sea-change from solid to gas under the melting influence of warming sunlight. This would make the little moon akin to comets and other KBOs, many of which are well-coated with very dark material.