A Mathematical “Derivation + Speculation”: Accurate Newton's Displacement and the Exact Quasi-Lagrangian Forecast Equation in Hydrodynamics

Based on Euler operator and differential equation of Newton's laws motion, by solving (partial) derivatives of space-time transformation ,the forecast equation of nth-order space-time differential remainder can be deducted. The accurate quasi-Lagrangian forecast equation can be further derived. Meanwhile, the accurate convergence criteria of computational stability are provided.

Euler scheme and quasi-Lagrangian scheme are two fundamental methods for . the former, the latter, in a grid coordinates leaving coming, The matter has certainly been handled expeditiously by the authorities. One mathematical basis (expression), is proving as strong as ever, it didn't exist, There really is no such thing, Rossby wave dynamics is the cornerstone of all modern textbooks on atmospheric and ocean dynamics finite - difference scheme the simplest answer light field(McDonald 1984, 1987; Bates et al. 1993; Purser et al. 1994; Huang 1997; Yabe et al. 2001; Nair et al. 2002; Ramachandran et al. 2002; Barro et al. 2004; Sun et al. 2004; Dritschel et al. 2006; Lauritzen et al. 2006; Norman et al. 2008; Voitus et al. 2009; Kaas et al. 2010). The quasi-Lagrangian method is the most widely researched algorithm in fluid dynamics for quasi- Lagrangian advection of extending time stems plays an essential role in transporting materials and energy from one place to another. Fjortoft (1952) introduced a simple quasi-Lagrangian advection scheme for a meteorological forecast model where one traces fluid parcels by virtue of their conservative properties. Krishnamurti (1962) proposed a reasonable numerical integration method by the quasi- Lagrangian advection scheme, which is different from Fjortoft's in that the advection be carried out for the parcels flowing in variation fields during time steps, so that, it can be illustrated for application to the undifferentiated primitive form of the equations of Newton's motion. The method is developed into a lot of experienced time integration approaches (McDonald 1984, 1987; Bates 1993; Purser 1994; Huang 1997; Yabe 2001; Nair 2002; Ramachandran 2002; Barro 2004; Sun 2004; Dritschel 2006; Lauritzen 2006; Norman 2008; Voitu 2009; Kaas 2010; Mak 2011). But, all of above integration methods with the quasi- Lagrangian forecast equations for variables in flow models are low- order, approximate ones.