Basic control volume finite element methods for fluids and solids / Vaughan R. Voller.

Includes bibliographical references (pages 167-168) and index.

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1. Introduction. 1.1. Overview. 1.2. Objective and philosophy. 1.3. The basic control volume concept. 1.4. Main topics covered -- 2. Governing equations. 2.1. The Euler equations of motion. 2.2. Specific governing equations -- 3. The essential ingredients in a numerical solution. 3.1. The basic idea. 3.2. The discretization : grid, mesh, and cloud. 3.3. The element and the interpolation shape functions. 3.4. Region of support and control volume. 3.5. The discrete equation -- 4. Control volume finite element data structure. 4.1. The task. 4.2. The mesh. 4.3. The data structure. 4.4. The discrete equation. 4.5. Summary -- 5. Control volume finite element method (CVFEM) discretization and solution. 5.1. The approach. 5.2. Preliminary calculations. 5.3. Steady state diffusion. 5.4. Steady state advection-diffusion. 5.5. Steady state advection-diffusion with source terms. 5.6. Coding issues. 5.7. Boundary conditions. 5.8. Solution. 5.9. Handling variable diffusivity. 5.10. Transients. 5.11. Summary -- 6. The control volume finite difference method. 6.1. The task. 6.2. CVFDM data structure. 6.3. Coefficients and sources. 6.4. Boundary conditions. 6.5. Summary -- 7. Analytical and CVFEM solutions of advection-diffusion equations. 7.1. The task. 7.2. Choice of test problems. 7.3. One-dimensional steady state diffusion in a finite domain. 7.4. One-dimensional transient diffusion in a semi-Infinited domain. 7.5. One-dimensional transient advection-diffusion in a semi-infinite domain. 7.6. Steady state diffusion in an annulus. 7.7. Steady state advection diffusion in an annulus. 7.8. Transient diffusion from a line source. 7.9. The recharge well problem -- 8. A plane stress CVFEM solution. 8.1. Introduction. 8.2. The stress concentration problem. 8.3. CVFEM displacement solution. 8.4. The stress solution. 8.5. Summary -- 9. CVFEM stream function-vorticity solution for a lid driven cavity flow. 9.1. Introduction. 9.2. The governing equations. 9.3. The CVFEM discretization of the stream function equation. 9.4. The CVFEM discretization of the vorticity equation. 9.5. Solution steps. 9.6. Results -- 10. Notes toward the development of a 3-D CVFEM code. 10.1. The tetrahedron element. 10.2. Creating a mesh of tetrahedron elements. 10.3. Geometric features of tetrahedrons. 10.4. Volume shape functions. 10.5. The control volume and face. 10.6. Approximation of face fluxes. 10.7. Summary.

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.

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