High-resolution scheme
(重定向自High Resolution)
High-resolution schemes are used in the numerical solution of partial differential equations where high accuracy is required in the presence of shocks or discontinuities. They have the following properties:
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.