Description: Computational Fluid Dynamics
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Computational Fluid Dynamics
- Motivation for CFD & Introduction to the CFD approach
- Illustration of the CFD approach through a worked out example
- Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation Part 1
- Eulerian approach, Conservation Equation, Derivation of Mass Conservation Equation Part 2
- Forces acting on a Control Volume: Stress tensor
- Kinematics of deformation in fluid flow: Stress vs Strain Rate Relation
- Equations governing flow of incompressible flow
- Spatial discretization of a simple flow domain
- Finite Difference Approximation of pth Order of Accuracy for qth Order Derivative
- One-sided high order accurate approximations, Explicit & Implicit Formulations
- Numerical solution of the unsteady advection equation using different finite
- Need for analysis of a discretization scheme
- Statement of the stability problem
- Consistency and stability analysis of the unsteady diffusion equation
- Stability analysis of the generic scalar equation
- Template for the generic scalar transport equation and its extension to the solution
- Illustration of application of the template using the MacCormack scheme
- Stability limits of MacCormack scheme
- Artificial compressibility method and the streamfunction-vorticity method
- Pressur e equation method for the solution of NS equations
- Pressure-correction approach to the solution of NS equations on a staggered grid
- Need for effici ent solution of linear algebraic equations
- Direct methods for linear algebraic equations & Gaussian elimination method
- Gauss-Jordan method, LU decomposition method, TDMA & Thomas algorithm
- Basic iterative methods for linear algebraic equations
- Convergence analysis of basic iterative schemes, Diagonal dominance condition
- Application to the Laplace equation
- Advanced iterative methods: Alternating Direction Implicit Method; Operator splitting
- Advanced iterative methods, Strongly Implicit Procedure, Conjugate gradient method
- Illustration of the Multigrid method for the Laplace equation
- Numerical solution of NS equations for simple domains
- Derivation of the energy conservation equation
- Derivation of the species conservation equation & Dealing with chemical reactions
- Turbulence, Characteristics of turbulent flow, Dealing with fluctuations
- Derivation of the Reynolds – averaged Navier – Stokes equations
- Reynolds stresses in Turbulent flow, Time & Length scales of Turbulence
- One-equation model for turbulent flow
- Two -equation model for turbulent flow & Numerical calculation of turbulent
- Calculation of near-wall region in turbulent flow & wall function approach
- Need for special methods for dealing with irregular fl ow geometry
- Transformation of the governing equations & Illustration for the Laplace equation
- Finite volume method for complicated flow domain
- Finite volume method for the general case
- Generation of a structured grid for irregular flow domain & Algebraic methods
- Unstructured grid generation & Domain nodalization
- Delaunay triangulation method for unstructured grid generation
- Co-located grid approach for irregular geometries & Pressure correction equations
