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Finite Difference Method

Tim A. Osswald, Juan P. Hernández-Ortíz · Carl Hanser Verlag GmbH & Co. KG eBooks · 2006

No AccessPolymer ProcessingApr 2006Finite Difference MethodTim A. Osswald, Juan P. Hernández-OrtizTim A. Osswald, Juan P. Hernández-Ortizhttps://doi.org/10.3139/9783446412866.008SectionsAboutPDF ToolsAdd to FavoritesDownload CitationTrack CitationsCopy LTI LinkPDF key 'share (en)' returned an object instead of string.FacebookTwitterEmailLinkedIn previous chapternext chapter FiguresReferencesRelatedDetails 2006Pages: 385-451Print ISBN: 978-3-446-40381-9eISBN: 978-3-446-41286-6 Copyright & Permissions© 2006 Carl Hanser Verlag GmbH & Co. KGPDF downloadLoading ...

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Finite Difference Method

A. Chandrasekar · 2022

All models that are utilized in atmospheric science are formulated based on fundamental physical principles, such as conservation of mass, conservation of momentum, and conservation of energy. These basic physical principles embodied in the atmospheric models are expressed mathematically as a coupled system of nonlinear partial differential equations. As these mathematical equations are complex and cannot be solved analytically, one has to resort to numerical methods to solve them. Numerical methods approximate a continuous model (system of partial differential equations) to a discrete model (system of difference equations). The process of approximating a continuous model to a discrete model by employing a numerical method is called “numerical discretization.”

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Finite Difference Method

R. Panneer Selvam · 2022

There are several numerical methods available to approximate the partial differential equations such as finite difference methods (FDM), finite element methods, and spectral methods. This chapter discusses FDM to approximate the Navier–Stokes equations (NS) equations as algebraic equations. It also discusses Potential flow for two-dimensional application, 1D wave equation, Gauss–Siedel and line iteration and NS equation solution. In the NS equation, the convection term is nonlinear, and further numerical complications are encountered. In Euler Forward Upwinding Method procedure, since traveling wave velocity is positive; the space is approximated by backward difference. For unsteady problems, the two major information needed are boundary conditions and initial conditions. The NS equations are nonlinear, and there are several different segregated or sequential solutions are available because the simultaneous solution of all the variables or coupled solver is time and storage consuming.

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The Finite Difference Method

2010

This chapter contains sections titled: Finite Differencing Formulas One-Dimensional Analysis Two-Dimensional Analysis Yee's FDTD Scheme Absorbing Boundary Conditions Modeling of Dispersive Media Wave Excitation and Far-Field Calculation Summary References Problems

Cited by 7