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).
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.
Water in its life-sustaining liquid phase exists beyond our own planet, both in our Solar System--and elsewhere. With oceans of water sloshing around on 71% of our own planet's surface, Earth still remains the only planet known to have stable bodies of liquid water. Liquid water is essential for all known life forms on Earth. The existence of water on the surface of Earth is the outcome of its atmospheric pressure and a stable orbit in our Sun;s circumstellar habitable zone. The habitable zone is that Goldilocks region, surrounding a star, where the temperature is not too hot, not too cold, but just right for life sustaining water to exist in its liquid phase. However, the origin of Earth's water still remains unknown.
"If there are plumes on Europa, as we now strongly suspect, with the Europa Clipper we will be ready for them," commented Dr. Jim Green in the April 13, 2017 NASA Press Release. Dr. Green is Director of Planetary Science at NASA Headquarters.