2 edition of **fast numerical method for explicit integration of the primitive equations near the poles** found in the catalog.

fast numerical method for explicit integration of the primitive equations near the poles

M. E. Schlesinger

- 335 Want to read
- 22 Currently reading

Published
**1976** by Rand Corporation in Santa Monica .

Written in English

- Atmospheric circulation -- Mathematical models.,
- Numerical integration.

**Edition Notes**

Statement | Michael E. Schlesinger. |

Series | Rand paper series ; P5507 |

Contributions | Rand Corporation. |

The Physical Object | |
---|---|

Pagination | 50 p. ; |

Number of Pages | 50 |

ID Numbers | |

Open Library | OL16462933M |

Methods and technology have been developed to solve a wide range of problems in the dynamics of sea currents and to assess their “impact” on objects in the marine environment. Technology can be used for monitoring and forecasting sea currents, for solving the problems of minimizing risks and analyzing marine disasters associated with the choice of the optimal course of the ship, and Cited by: 3. Governing equations and numerical methods Unsteady primitive equations of motion, for all scales Terms in equations are added/removed depending on scale User selected physical and numerical schemes (e.g., split-explicit finite difference), both hydrostatic and non-hydrostatic Operational configuration and performance. I'm working on a numerical analysis problem that requires me to find an iterative solution to (1). The resulting integral should take the form (2). However, I cannot figure out what method to use. I. Before the primitive equations can be solved, they have to be discretized with respect to space and time. Discretization means that the atmosphere (or the part of it that you want to study) is represented by a finite number of numerically approximated values. The most common numerical time integration scheme in meteorology is the leapfrog scheme.

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A Fast Numerical Method for Explicit Integration of the Primitive Equations near the Poles., Santa Monica, Calif.: RAND Corporation, P, Add tags for "A fast numerical method for explicit integration of the primitive equations near the poles".

Be the first. A fast numerical method for explicit integration of primitive equations near the poles: Authors: Schlesinger, M.

Affiliation: AA(RAND Corp., Santa Monica, CA.) In this paper the three-point method is analyzed and compared to the Fourier method for the numerical solution of the primitive equations in the polar regions. It is shown that.

The impact of potential abrupt climate changes on near-term policy choices A Fast Numerical Method for Explicit Integration of the Primitive Equations near the Poles. About RAND Reports. PDF | A Lagrangean-type numerical forecasting method is developed in which the computational (grid) points are advected by the wind and the necessary | Find, read and cite all the research you Author: Fedor Mesinger.

We study integral methods applied to the resolution of the Maxwell equations where the linear system is solved using an iterative method which requires only matrix–vector products. The fast multipole method (FMM) is one of the most efﬁ-cient methods used to perform matrix–vector products and accelerate the resolution of the linear Size: KB.

We have presented a class of integral equation methods for fast numerical method for explicit integration of the primitive equations near the poles book solution to the modified Helmholtz equation in bounded or unbounded multiply-connected domains.

Using a fast-multipole accelerated iterative method, our solution procedure requires O (N) operations, where N is the number of nodes in the discretization of the by: An explicit time integration of the primitive equations, which are often used for numerical ocean simulations, would be subject to a short time step limit imposed by the rapidly varying external.

The resulting numerical equation is solved with GMRES (generalised minimum residual method) in connection with FMM (fast multipole method). It is found that the obtained code is faster than a conventional one when the number of unknowns is greater than about Cited by: SECOND ORDER METHOD OF THE PRIMITIVE EQUATIONS OF THE OCEAN 5 We denote by A1 the Stokes-type operator associated with the primitive equa- tions(see [3, 13, 14]), that is A1 = PL1, where P is the L2-orthogonal projection from L2(Ω)2 to Hwe write A2.

Then methods for solving the first-order differential equations, including the fourth-order Runge–Kutta numerical method and the direct integration methods (finite difference method and Newmark method) as well as the mode superposition fast numerical method for explicit integration of the primitive equations near the poles book are presented.

The computational details of most of the methods are illustrated with examples. The Use of the Primitive Equations of Motion in Numerical Prediction By J.

Fast numerical method for explicit integration of the primitive equations near the poles book, The Institute for Advanced Stady, Princeton1 (Manuscript received September I 5, ) Abstract An obstacle to the use of the primitive hydrodynamical equations for numerical pre.

Since there are no poles in the contour, we have by Cauchy's integral formula ∫z = 1 z2 + 3z + 2i (z + 4) (z − 1)dz = 0 We can break the contour up into ∫z = 1 z2 + 3z + 2i (z + 4) (z − 1)dz = ∫ − ϵ − π / 2 z2 + 3z + 2i (z + 4) (z − 1)dz + ∫0 π (ϵeiθ + 1)2 + 3 (ϵeiθ + 1) + 2i [ (ϵeiθ + 1) + 4] [.

Implicit-explicit (IMEX) linear multistep methods are examined with respect to their suitability for the integration of fast-wave-slow-wave problems in which the fast wave has relatively low.

Framework for Atmospheric Numerical Models Prognostic Equation: dθ/dt = F Model Equations • Primitive Equations (PE)- the basic set of eqs derived by using minimal assumptions o Prognostic Equations:.

Horizontal momentum equations (u and v) rather than the stability of the numerical Size: 1MB. This banner text can have markup.

web; books; video; audio; software; images; Toggle navigation. A numerical solver for the primitive equations of the ocean using term-by-term stabilization Article in Applied Numerical Mathematics 55(1) September with 20 Reads How we measure 'reads'.

differentiation formula (BDF) is a family of implicit methods for the numerical integration of ordinary differential equations.

They are linear multistep methods They are linear multistep methods Singular boundary method (1, words) [view diff] exact match in snippet view article find links to article.

This scheme, which is based on the Laplace transform (LT), has been implemented in a baroclinic primitive equation model, PEAK (Ehrendorfer, ). Analysis shows that the LT scheme is more accurate than SI for both linear and nonlinear terms of the equations.

Numerical experiments confirm the superior performance of the LT : Eoghan Harney, Peter Lynch. Masuda, Y., and H. Ohnishi, An integration scheme of the primitive equations model with an icosahedral-hexagonal grid system and its application to the shallow water equations.

Short- and Medium-Range Numerical Weather Prediction, T. Matsuno, Ed., Japan Meteorological Society, – Google ScholarCited by: A fully discrete second-order decoupled implicit/explicit method is proposed for solving 3D primitive equations of ocean in the case of Dirichlet boundary conditions on the side, where a second.

Masuda, Y., and H. Ohnishi, An integration scheme of the primitive equation model with an icosahedral-hexagonal grid system and its application to the shallow-water equations. In Short-and Medium-Range Numerical Weather Prediction, WHO/IUGG NWP, Tokyo, –Cited by: An explicit two-step method exact for the scalar test equation y′ = λy, Re(λ) method to systems of ordinary differential by: 9.

Three types of method are available for the horizontal discretization of the governing equations of large-scalemod-els of the atmosphere.

These are the ﬁnite-difference method, the spectral method and the ﬁnite-elementmethod. The basics of these methods have been introduced in the preceding course on numerical methods. Interval integration is used to obtain inclusions of integral operators of the form g(u)(s) = / T g(s,t,u(s),u(t))dt (1) which can be carried out on a computer.

The resulting inclusions, combined with interval iteration, are used to compute guaranteed upper and lower bounds for solutions of integral equations of the form u = g(u) (2) for s ɛ S. The Numerical Method of Lines: Integration of Partial Differential Equations by William E.

Schiesser () on *FREE* shipping on qualifying cturer: Academic Press. In this paper, we propose a numerical method based on semi-Lagrangian approach for solving quasi-geostrophic (QG) equations on a sphere. Using potential vorticity and stream-function as prognostic variables, two-order centered difference is suggested on the latitude-longitude grid.

In our proposed numerical scheme, advection terms are expressed in a Lagrangian frame of reference to circumvent Author: Quanyong Zhu, Yan Yang. At the poles (i.e., φ = ±π/2), this is a source of numerical problems, caused by the specific coordinate formulation rather than the nature of the primitive equations and its the use of a local Cartesian coordinate system has been used to overcome these problems in the past (Taylor et al.

), we have, guided by the results of previous work (Giraldo ; Giraldo et al Cited by: Geometric numerical integration One-step formulations Introducing the velocity ˙q = v turns equation () into a ﬁrst-order system of doubled dimension q˙ = v, v˙ = f(q), () an equation in the so-called phase analogy to this, we introduce.

The barotropic forecast The equations solved by Richardson were obtained by vertical integration of the primitive equations linearized about an isothermal, motionless basic state. We using both analytical and numerical methods, in the previous chapter. For reference, numerical algorithms with explicit use of PV as a prognostic variable are called PV based.

Early attempts in designing PV-based algorithms for the shallow-water equations (Bates et al. ; Thuburn ; Dritschel et al. ) used only the material conservation of PV in the absence of forcing and by: The author describes the implementation of a specific model PEAK (Primitive-Equation Atmospheric Research Model Kernel) to illustrate the steps needed to construct a global spectral NWP model.

The book brings together all the spectral, time, and vertical discretization aspects relevant for such a model. becomes zero when, that is, for and K = 2; correspondingly, the equal roots of are given by and λ 1 = λ 2 = Figure 2a shows R plotted as a function of κΔt for the two roots physical mode is stable for 0 equation provided 0 Cited by: 4.

A practical method is proposed to achieve high-order finite-difference schemes on grids that are quasi-homogeneous on the sphere. A family of grids is used that are characterized by the parameter NP, which can take on values of 3, 4, and 5, by: 6. ERA-Interim Horizontal Coordinate Conventions and Numerical Attributes.

the primitive equations are reduced to a set of model equations that are of two types, E., B. Machenhauer, and E. Rasmussen, On a numerical method for integration of the hydrodynamical equations with a spectral representation of the horizontal fields.

Rep. The poles are unique points and may cause violation of global conservation laws within the model. To maintain computational stability near the poles, small integration time-steps could be used, but at great expense. The high resolution in the east-west direction near the poles would be wasted because the model uses lower resolution elsewhere ().Cited by: 1.

GCMs have as their basis the primitive equations which describe atmospheric dynamics and km just north and south of the Equator to km near the poles) Number of horizontal grid points: Eliasen, E., B.

Machenhauer, and E. Rasmussen, On a numerical method for integration of the hydrodynamical equations with a spectral. () A Fast Explicit Operator Splitting Method for Modified Buckley–Leverett Equations.

Journal of Scientific Computing() A higher order Finite Volume resolution method for a system related to the inviscid primitive equations in a complex by: Determining poles and order of $1/\sin(z)$ Ask Question Asked 4 years, Use MathJax to format equations. MathJax reference.

To learn more, see our tips on writing great answers. Is there a fast technique to tell that the poles of $\frac{1}{\sin z}$ are simple.

Thanks for contributing an answer to Mathematics Stack Exchange. Please be sure to answer the question. Provide details and share your research. But avoid Asking for help, clarification, or responding to other answers. Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. Optimized Schwarz methods are a new class of Schwarz methods with greatly enhanced convergence properties.

Pdf converge uniformly pdf than classical Schwarz methods and their convergence rates dare asymptotically much better than the convergence rates of classical Schwarz methods if the overlap is of the order of the mesh parameter, which is often the case in practical by: The GFDL spectral dynamical core solves the download pdf primitive equations on a sphere with no bottom topography (Held & Suarez, ).

The primitive equations are integrated with the spectral-transform method in the horizontal, and in stratified-flow simulations a centered finite-difference scheme is used in the vertical (using sigma coordinate).Cited by: 4.Suppose one has ebook integral of a real (or complex) function that has at least one pole that lies on the contour of integration, for example: $$\int_{-a}^{a}\frac{f(x)}{x}dx$$ Clearly such an integral is undefined in the normal sense.