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$2\odot 2=4$: Temporal-Spatial Coupling and Beyond in Computational Fluid Dynamics (CFD). (arXiv:1810.02971v1 [math.NA])
来源于:arXiv
With increasing engineering demands, there need high order accurate schemes
embedded with precise physical information in order to capture delicate small
scale structures and strong waves with correct "physics". There are two
families of high order methods: One is the method of line, relying on the
Runge-Kutta (R-K) time-stepping. The building block is the Riemann solution
labeled as the solution element "1". Each step in R-K just has first order
accuracy. In order to derive a fourth order accuracy scheme in time, one needs
four stages labeled as "$1\odot 1\odot 1\odot 1=4$". The other is the one-stage
Lax-Wendroff (L-W) type method, which is more compact but is complicated to
design numerical fluxes and hard to use when applied to highly nonlinear
problems.
In recent years, the pair of solution element and dynamics, labeled as "$2$",
are taken as the building black. The direct adoption of the dynamics implies
the inherent temporal-spatial coupling. With this type of building blocks, a 查看全文>>