Description

Book Synopsis

The Control Volume Finite Element Method (CVFEM) is a hybrid numerical method, combining the physics intuition of Control Volume Methods with the geometric flexibility of Finite Element Methods. The concept of this monograph is to introduce a common framework for the CVFEM solution so that it can be applied to both fluid flow and solid mechanics problems. To emphasize the essential ingredients, discussion focuses on the application to problems in two-dimensional domains which are discretized with linear-triangular meshes. This allows for a straightforward provision of the key information required to fully construct working CVFEM solutions of basic fluid flow and solid mechanics problems.

Table of Contents

Governing Equations; The Essential Ingredients in a Numerical Solution; Control Volume Finite Element Data Structure; Control Volume Finite Element Method (CVFEM) Discretization and Solution; The Control Volume Finite Difference Method; Analytical and CVFEM Solutions of Advection-Diffusion Equations; The CVFEM Solution for Plane Stress and Plane Strain Elasticity; The CVFEM Solution for the Stream-Function Vorticity Form of the Navier-Stokes Equations; Notes for the Extension of CVFEM to Three Dimensions.

Basic Control Volume Finite Element Methods For

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    A Hardback by Vaughan R Voller

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      Book details

      Publisher World Scientific Publishing Co Pte Ltd
      Published 6 February 2009
      ISBN-13 9789812834980
      978-9812834980
      ISBN-10 9812834982
      Also in:
      Mathematical modelling

      Description

      Book Synopsis

      The Control Volume Finite Element Method (CVFEM) is a hybrid numerical method, combining the physics intuition of Control Volume Methods with the geometric flexibility of Finite Element Methods. The concept of this monograph is to introduce a common framework for the CVFEM solution so that it can be applied to both fluid flow and solid mechanics problems. To emphasize the essential ingredients, discussion focuses on the application to problems in two-dimensional domains which are discretized with linear-triangular meshes. This allows for a straightforward provision of the key information required to fully construct working CVFEM solutions of basic fluid flow and solid mechanics problems.

      Table of Contents

      Governing Equations; The Essential Ingredients in a Numerical Solution; Control Volume Finite Element Data Structure; Control Volume Finite Element Method (CVFEM) Discretization and Solution; The Control Volume Finite Difference Method; Analytical and CVFEM Solutions of Advection-Diffusion Equations; The CVFEM Solution for Plane Stress and Plane Strain Elasticity; The CVFEM Solution for the Stream-Function Vorticity Form of the Navier-Stokes Equations; Notes for the Extension of CVFEM to Three Dimensions.

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