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Contents
Contents
List of Tables
List of Figures
Introduction
Objectives
Outline
The Elements
The Triangle
The Quadrilateral
The Tetrahedron
The Pyramid
The Prism
The Hexahedron
Global Assembly
Algorithm 1
Algorithm 2
Algorithm For Connecting Prisms And Tetrahedra
Basis Functions
One-Dimensional Orthogonal Polynomials
Singular Sturm-Liouville Problems on a Simplex in d-Dimensions
Orthogonal (Modal) Bases
The Orthogonal Triangle Basis
The Orthogonal Quadrilateral Basis
The Orthogonal Prism Basis
The Orthogonal Hexahedral Basis
The Decay of Basis Coefficients
Semi-Orthogonal Bases
Modal basis
Triangle Basis:
Quadrilateral Bases:
and
Nodal and Mixed Bases
Quadrilateral Basis:
Triangle Basis:
Comparison of the Bases
Operators
Elemental Spatial Operators
Integration
Flux Integrals
Differentiation
Implementation and Programming
Global Projection Operator
Global Convergence in Skew Elements
Convective Operator
Accuracy of the Convective Operator
Spectrum of the Galerkin 2D Convective Operator
Three-Dimensional Galerkin Convective Operator Spectrums
Spectrum of the Galerkin 3D Convective Operator
Diffusion Operator
The Schur Complement Method of Inverting Global Operators
Optimal Numbering for the Schur Complement Boundary Matrix
Numerical Results
Convergence for the Galerkin Helmholtz Operator
Convergence in 3D Hybrid Elements
Convergence in 3D Skew Elements
Incompressible Flow Simulations
Incompressible Navier-Stokes Equation
Formulation
Summary of Scheme, Boundary Conditions and Implementation
Wannier Flow
Kovasznay Flow
Cylinder Flow
The Robotuna
ALE Incompressible Navier-Stokes
Formulation
Temporal Discretization
Rayleigh Sliding Plate Problem
Design of a Micro-Pump via Simulation
Micro-Pump Geometric Specifications
Efficiency Analysis
Numerical Simulation
Incompressible Viscous Magnetohydrodynamics
Formulation
Numerical Scheme
Magnetic Pearson's Vortex
Orszag-Tang Vortex
Cylinder Flow
Compressible Flow Simulations
Numerical Formulation
Discontinuous Galerkin for Diffusion
Compressible Navier-Stokes Simulations
Convergence
Cylinder Flow
Flow Past a Two-Dimensional NACA0012 Airfoil
Flow Past a Multi-Body Airfoil
Flow Past A NACA0012 Wing With Endplates
Compressible Viscous Magnetohydrodynamics Simulations
Formulation
The
Constraint
Implementation of the Euler Flux Terms
Implementation of the Viscous Terms
Summary of the Compressible MHD Code Implementation
Two-Dimensional Magnetohydrostatic Example
Three-Dimensional Magnetohydrostatic Example
Compressible Orszag-Tang Vortex
Flow Past a Cylinder
Summary
Continuous Expansion Basis
Jacobi Polynomials
Modal Basis
Two-Dimensional Expansions
Quadrilateral Domain
Triangular Domain
Three-Dimensional Expansions
Hexahedral Domain
Prismatic Domain
Pyramidic Domain
Tetrahedral Domain
Nodal Basis
Two-Dimensional Expansions
Quadrilateral Domain
Three-Dimensional Expansions
Hexahedral Domain
References
About this document ...
T. Warburton
10/24/1998
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