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Essential Computational Fluid Dynamics | Heimkaup.is
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Essential Computational Fluid Dynamics
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Essential Computational Fluid Dynamics provides an introduction to the principles, basic foundation, and background of Computational Fluid Dynamic (CFD) analysis. Through a non-traditional approach, this deliberately concise text serves as the first part of an applied CFD course, followed by a software tutorial. This book explains the principles and methods of CFD analysis as well as CFD software tool.
Engar takmarkanir á útprentun
1: What Is CFD?
Brief History of CFD
Outline of the Book
References and Suggested Reading
2: Governing Equations of Fluid Dynamics and Heat Transfer
Conservation of Chemical Species
Equations in Integral Form
Equations in Conservation Form
Equations in Vector Form
Rigid Wall Boundary Conditions
Inlet and Exit Boundary Conditions
References and Suggested Reading
3: Partial Differential Equations
Model Equations; Formulation of a PDE Problem
Domain, Boundary, and Initial Conditions
Equilibrium and Marching Problems
Mathematical Classification of PDE of Second Order
Numerical Discretization: Different Kinds of CFD
Finite Difference and Finite Volume Methods
References and Suggested Reading
4: Basics of Finite Difference Approximation
Finite Differences and Interpolation
Truncation Error, Consistency, Order of Approximation
Other Formulas for ?u/?x: Evaluation of the Order of Approximation
Schemes of Higher Order for First Derivative
Truncation Error of Linear Interpolation
Approximation of Partial Differential Equations
Interpretation of Truncation Error: Numerical Dissipation and Dispersion
Boundary and Initial Conditions
Consistency of Numerical Approximation
System of Difference Equations
Implicit and Explicit Methods
Development of Finite Difference Schemes
References and Suggested Reading
5: Finite Volume Method
Introduction and Integral Formulation
Upwind Interpolation of Higher Order
Interpolation on Nonorthogonal Grids
References and Suggested Reading
6: Stability of Transient Solutions
Introduction and Definition of Stability
Discretization and Round-off Error
Implicit versus Explicit Schemes—Stability and Efficiency Considerations
References and Suggested Reading
7: Application to Model Equations
Burgers and Generic Transport Equations
Method of Lines Approach
Implicit Schemes: Solution of Tridiagonal Systems by Thomas Algorithm
References and Suggested Reading
Problems Reducible to Matrix Equations
Implicit Integration of Nonsteady Equations
Band-Diagonal and Block-Diagonal Matrices
Successive Over- and Underrelaxation
Convergence of Iterative Procedures
Systems of Nonlinear Equations
Iteration Methods Using Linearization
References and Suggested Reading
9: Unsteady Problems of Fluid Flows and Heat Transfer
Overview and General Comments
Methods for Purely Hyperbolic Systems
Unsteady Conduction Heat Transfer
Simple Methods for Multidimensional Heat Conduction
References and Suggested Reading
Colocated and Staggered Grids
Projection Method for Unsteady Flows
Projection Methods for Steady-State Flows
SIMPLEC, SIMPLER, and PISO
Vorticity-Streamfunction Formulation for Two-Dimensional Flows
References and Suggested Reading
III Art of CFD
A Few Words About Turbulence
Why Is the Computation of Turbulent Flows Difficult?
Overview of Numerical Approaches
Direct Numerical Simulation (DNS)
Reynolds-Averaged Navier-Stokes (RANS) Models
Numerical Implementation of RANS Models
Implementation of LES in CFD Analysis: Numerical Resolution and Near-Wall Treatment
References and Suggested Reading
Introduction: Need for Irregular and Unstructured Grids
Generation by Coordinate Transformation
Finite Volume Discretization on Unstructured Grids
References and Suggested Reading
13: Conducting CFD Analysis
Overview: Setting and Solving a CFD Problem
Errors in CFD Analysis
References and Suggested Reading
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