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).
Therefore, the results of the new study support the idea that primitive life could potentially have evolved on Ganymede. This is because places where water and rock interact are important for the development of life. For example, some theories suggest that life arose on our planet within hot, bubbling seafloor vents. Before the new study, Ganymede's rocky seafloor was believed to be coated with ice--not liquid. This would have presented a problem for the evolution of living tidbits. The "Dagwood sandwich" findings, however, indicate something else entirely--the first layer on top of Ganymede's rocky core might be made up of precious, life-sustaining salty water.
For this reason, astronomers have for years considered the possibility that hydrocarbon lakes and seas might exist on the surface of this misty moisty moon. The data derived from Cassini/Huygens validated this prediction. During its long and productive mission, now over, Cassini revealed that almost 2% of Titan's entire bizarre surface is coated wth gasoline-like liquids.
"We are just beginning to try and figure out quantitatively how all this might smooth a surface," Dr. Thomas said in the May 17, 2013 New Scientist.