1 edition of **Finite element approximation of the shallow water equations on the MasPar** found in the catalog.

Finite element approximation of the shallow water equations on the MasPar

Beny Neta

- 4 Want to read
- 13 Currently reading

Published
**1993**
by Naval Postgraduate School, Available from National Technical Information Service in Monterey, Calif, Springfield, Va
.

Written in

- NONLINEAR DIFFERENTIAL EQUATIONS,
- HYPERBOLIC DIFFERENTIAL EQUATIONS,
- SHALLOW WATER,
- FINITE ELEMENT ANALYSIS

Here we report on development of a high order finite element code for the solution of the shallow water equations on the massively parallel computer MP-1104. We have compared the parallel code to the one available on the Amdahl serial computer. It is suggested that one uses a low order finite element to reap the benefit of the massive number of processors available.... Finite element approximation, Shallow water equations.

**Edition Notes**

Other titles | NPS-MA-93-014. |

Statement | by Beny Neta, Rex Thanakij |

Contributions | Thanakij, Rex, Naval Postgraduate School (U.S.). Dept. of Mathematics |

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

Pagination | 16 p. ; |

Number of Pages | 16 |

ID Numbers | |

Open Library | OL25512053M |

Key words: Shallow water, well-balanced approximation, invariant domain, friction term, second-order accu-racy, nite element method, positivity preserving. Abstract The Shallow Water Equations (SWEs) are popular for modeling non-dispersive incompressible water waves where the horizontal wavelength is much larger than the vertical scales. Finite volume solver for Shallow Water Equations. Contribute to Paulms/ShallowWaters development by creating an account on GitHub.

Neta, B., Analysis of finite elements and finite differences for shallow water equations: A review, Mathematics and Computers in Simulation 34 () In this review article we discuss analyses of finite-element and finite-difference approximations of the shallow water equations. element methods for the shallow water equations with bottom topography and friction terms M. Luk´aˇcov´a - Medvid’ ova´1 and U. Teschke2 Abstract We present a comparison of two discretization methods for the shallow water equa-tions, namely the ﬁnite volume method and the ﬁnite element scheme. A reliable.

A new method to solve the quasi-3D shallow water equations is proposed. This method combines a suitable mass-preserving finite element approach in the horizontal plane with a conventional conforming finite element (or finite difference) scheme along the . The resulting equations belong to the class of systems of hyperbolic partial differential equations of first order with zero order source terms, the so‐called balance laws. In order to approximate correctly steady equilibrium states we need to derive a well‐balanced approximation of the source term in the finite volume framework.

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Finite Element Approximation of the Shallow Water Equations on the MASPAR Article (PDF Available) March with 23 Reads How we measure 'reads' A 'read' is counted each time someone views. FINITE ELEMENT APPROXIMATION OF THE SHALLOW WATER EQUATIONS ON THE MASPAR by Beny Neta Rex Thanakij Technical Report For Period November -March Approved for public release; distribution unlimited Prepared for: Naval W Mn t•y,/'TA Postgraduate School lllll~tll•ll~il MASPAR Computer Corporation N.

Mary Ave. Sunnyvale, CA 2. Finite Element Solution The barotropic nonlinear shallow-water equations on a limiLed-area. domain of a. earLh (using the ;'planc assumption) have the following form: llt + 'U.'U.:r + l'lly + 'fx. FINITEELEMENTAPPROXIMATION OFTHESHALLOWWATER EQUATIONSONTHEMASPAR by BenyNeta RexThanakij TechnicalReportForPeriod NovemberMarch Approvedforpublicrelease;distributionunlimited FedDocs D/2 NPS-MA NavalPostgraduateSchool Monterey,CA Finite element approximation of the shallow water equations on the MasPar by Neta, Beny.;Thanakij, Rex.

We here employ the idea where we use different finite elements for the approximation of geometric variables (forms) describing an infinite-dimensional system, to spatially discretize the system and obtain a finite-dimensional port-Hamiltonian system.

In particular we take the example of a special case of the shallow water equations. A standard test set for numerical approximations to the shallow water equations in spherical geometry.

Journal of Computational Physics–]. Optimal rates of convergence for the P 1 NC - P 1 finite element pair are obtained, for both global and local quantities of interest. A least-squares finite-element method (LSFEM) for the non-conservative shallow-water equations is pre- sented.

The model is capable of handling complex topography, steady and unsteady flows. Finite element approximation of initial boundary value problems. Energy dissi-pation, conservation and stability.

Analysis of ﬁnite element methods for evolution problems. Reading List 1. Brenner & R. Scott, The Mathematical Theory of Finite Element Methods.

Springer-Verlag, Corr. 2nd printing [Chapters 0,1,2,3; Chapter 4. The finite element method (FEM), or finite element analysis (FEA), is a computational technique used to obtain approximate solutions of boundary value problems in engineering. Boundary value problems are also called field problems.

The field is the domain of interest. CiteSeerX - Document Details (Isaac Councill, Lee Giles, Pradeep Teregowda): Here we report on development of a high order nite element code for the solution of the shallow water equations on the massively parallel computer MP We have compared the parallel code to the one available on the Amdahl serial computer It is suggested that one uses a low order nite element to reap the benet of the.

The shallow water equations are a set of hyperbolic partial differential equations (or parabolic if viscous shear is considered) that describe the flow below a pressure surface in a fluid (sometimes, but not necessarily, a free surface).The shallow water equations in unidirectional form are also called Saint-Venant equations, after Adhémar Jean Claude Barré de Saint-Venant (see the related.

Galerkin finite-element techniques have been applied to the shallow-water equations by many Writers (see refer- ences ). llere we are concerned with the solution of tile evolu- tionary shallow-water equations for a limited-area domain on a fl-plane.

A Galerkin finite-element method (FEM) is employed. Abstract. In the chapter we consider a linearized system of shallow water equations.

Since this problem should be solved in domains being seas and oceans (or their parts), then solving this problem should use unstructured meshes to approximate domains under consideration properly. A wave-structure interaction model based on the least-squares finite-element formulation of the depth-averaged, nonlinear, non-conservative 2D shallow-water equations is developed.

Advantages of the model include: (1) a single approximating space can be used for all variables, and its choice of approximating space is not subject to the Ladyzhenskaya-Babuska-Brezzi (LBB) condition; (2) upwind. ilar techniques to the shallow water equations, e.g. Glaister [14] using nite di erences, or V azquez Cend on [31], with nite volumes.

Donea and Huerta [12] apply the Finite Element Method, in permanent and non-permanent problems, both to compressible and incompressible uids. The Shallow Water Equations The behavior of a viscous. () A positive and bounded finite element approximation of the generalized Burgers–Huxley equation.

Journal of Mathematical Analysis and Applications() NUMERICAL SOLUTION OF THE TIME-DEPENDENT NAVIER–STOKES EQUATION FOR VARIABLE DENSITY–VARIABLE VISCOSITY.

The paper reports the current progress in developing a finite element method for the shallow water equations. The main feature of the method is the special care given to the advective and diffusive parts of the equations, so that it can be of interest to use it when dealing with flows strongly influenced by convective and boundary layer effects.

the shallow water equations. The shallow water equations are pre-sented in nondimensional form. The ﬁnite element discretization of the equations is discussed.

Chapter 4 introduces the ALE moving mesh method that is used to approximate the moving boundary problems outlined in chapter 2. The method used to derive the. LUO Zhen-dong, ZHU Jiang, ZENG Qing-cun,et al.

Mixed finite element methods for the shallow water equations including current and silt sedimentation (I)—The continuous-time case[J]. Applied Mathematics and Mechanics (English Edition),24 (1)–.

In this paper we present a space-time finite element formulation for problems governed by the shallow water equations. A linear time-discontinuous approximation is adopted, and linear three node triangles are used for the spatial discretization. Computational aspects are also discussed.G.R.

Liu, S.S. Quek, in The Finite Element Method (Second Edition), Abstract. Finite element equations for such truss members will be developed in this chapter. The one-dimensional element developed is commonly known as the truss element or bar elements are applicable for analysis of skeletal-type truss structural systems both in two-dimensional planes and in three.1 Introduction to the equations of fluid dynamics and the finite element approximation General remarks and classification of fluid dynamics problems discussed in this book The governing equations of fluid dynamics Inviscid, incompressible flow Incompressible (or nearly incompressible) flows Numerical solutions: weak forms, weighted residual and finite element approximation.