lecnotes23

lecnotes23 - 13.472J/1.128J/2.158J/16.940J COMPUTATIONAL...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 13.472J/1.128J/2.158J/16.940J COMPUTATIONAL GEOMETRY Lecture 23 Dr. W. Cho Prof. N. M. Patrikalakis Copyright c 2003 Massachusetts Institute of Technology Contents 23 F.E. and B.E. Meshing Algorithms 2 23.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 23.1.1 Finite Element Method (FEM) . . . . . . . . . . . . . . . . . . . . . . 2 23.1.2 Mesh . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 23.1.3 Some Criteria for a Good Meshing . . . . . . . . . . . . . . . . . . . . 3 23.1.4 Finite Element Analysis in a CAD Environment . . . . . . . . . . . . . 4 23.1.5 Background Information . . . . . . . . . . . . . . . . . . . . . . . . . . 4 23.1.6 Mesh Conformity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 23.1.7 Mesh Refinement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 23.2 Mesh Generation Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 23.2.1 Mapped Mesh Generation [23, 10, 11, 5] . . . . . . . . . . . . . . . . . 10 23.2.2 Topology Decomposition Approach [20, 3] . . . . . . . . . . . . . . . . 12 23.2.3 Geometry Decomposition Approach [6, 17, 13] . . . . . . . . . . . . . . 13 23.2.4 Volume Triangulation Delaunay Based [7, 15] . . . . . . . . . . . . . 14 23.2.5 Spatial Enumeration Methods [21, 22] . . . . . . . . . . . . . . . . . . 15 Bibliography 16 1 Lecture 23 F.E. and B.E. Meshing Algorithms 23.1 General 23.1.1 Finite Element Method (FEM) FEM solves numerically complex continuous systems for which it is not possible to construct any analytic solution, see Figure 23.1. Physical Problem Law of Physics PDE Weighted Residual Methods Integral Formulation Algebraic System of Equations Unknown Function Approximation (using finite element mesh and matrix organization) Approximate Solution Numerical Solution Formulation of Equations Transformation of Equations Solution Figure 23.1: FEM Procedure 2 23.1.2 Mesh Mesh is the complex of elements discretizing the simulation domain, eg. triangular or quadri- lateral mesh in 2D, tetrahedral or hexahedral mesh in 3D. Why Use Mesh ? To construct a discrete version of the original PDE problems. Types of Mesh See Figure 23.2. Figure 23.2: Structured ( n = 6) and unstructured ( n 6 = constant ) mesh Structured mesh The number of elements n surrounding an internal node is constant . The connectivity of the grid can be calculated rather than explicitly stored . simpler and less computer memory intensive Lack of geometric flexibility Unstructured mesh The number of elements surrounding an internal node can be arbitrary . Greater geometric flexibility crucial when dealing with domains of complex geometry or when the mesh has to be adapted to complicated features of computational domain or to complicated features of the solution (eg. boundary layers, internal layers, shocks, etc)....
View Full Document

This note was uploaded on 11/08/2011 for the course AERO 16.872 taught by Professor Danielhastings during the Fall '03 term at MIT.

Page1 / 17

lecnotes23 - 13.472J/1.128J/2.158J/16.940J COMPUTATIONAL...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online