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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The GRAIL mission determined the internal structure of the Moon in great detail for nine months during 2012. Armed with this the new information, GRAIL astronomers were able to redefine the sizes of the largest impact basins on the lunar surface. Dr. Porco further believes that Enceladus's orbit could have been much more eccentric in the past. The greater the eccentricity, the greater the tidal squeezing, and the resulting structural variations produce heat. In this case, the heat would have been saved inside the icy moon, melting some of the ice to replenish the liquid water sea. Dr. Porco continued to explain that "(T)he tidal flexing occurring now is not enough to account for all the heat presently coming out of Enceladus. One way out of this dilemma is to assume that some of the heat observed today was generated and stored internally in the past... (N)ow that the orbit's eccentricity has lessened, the heat emanating from the interior is a combination of heat produced today and in the past." Despite this oddball moon's many exotic attributes, it actually sports one of the most Earth-like surfaces in our Solar System. Titan may also experience volcanic activity, but its volcanoes would erupt with different ingredients than the molten-rock lava that shoots out from the volcanoes of Earth. In dramatic contrast to what occurs on our own planet, Titan's volcanoes erupt icy water "lava" (cryovolcanism). Titan's entire alien surface has been sculpted by gushing methane and ethane, which carves river channels, and fills its enormous great lakes with liquid natural gas.