Introduction:
CFD ideas to understand, CFD Application, Governing Equations (no derivation) of flow; continuity, momentum, energy. Conservative & Non-conservative forms of equations, Integral vs Differential Forms of Equations. Form of Equations particularly suitable for CFD work. Shock capturing, Shock fitting, Physical Boundary conditions.
Mathematical Behavior of Partial Differential Equations and Discretization:
Classification of partial differential equations and its Impact on computational fluid dynamics; case studies. Essence of discretization, order of accuracy and consistency of numerical schemes, Lax’s Theorem, convergence, Reflection Boundary condition.
Mathematical Behavior of Partial Differential Equations and Discretization:
Higher order Difference quotients. Explicit & Implicit Schemes. Error and analysis of stability, Error Propagation. Stability properties of Explicit & Implicit schemes.
'Solution Methods of Finite Difference Equations:
Time & Space Marching. Alternating Direction Implicit (ADI) Schemes. Relaxation scheme, Jacobi and Gauss-Seidel techniques, SLOR technique. Lax-Wendroff first order scheme, Lax-Wendroff with artificial viscosity, upwind scheme, midpoint leap frog method.
Grid Generation:
Structured Grid Generation: Algebraic Methods, PDE mapping methods, use of grid control functions, Surface grid generation, Multi Block Structured grid generation, overlapping and Chimera grids. Unstructured Grid Generation: Delaunay-Voronoi Method, advancing front methods (AFM Modified for Quadrilaterals, iterative paving method, Quadtree & Octree method).
Adaptive Grid Methods:
Multi Block Adaptive Structured Grid Generation, Unstructured adaptive Methods. Mesh refinement methods, and Mesh enrichment method. Unstructured Finite Difference mesh refinement.
Approximate Transformation & Computing Techniques:
Matrices & Jacobian. Generic form of governing Flow Equations with strong conservative form in transformed space. Transformation of Equation from physical plane into computational Plane -examples. Control function methods. Variation Methods. Domain decomposition. Parallel Processing.
Finite Volume Techniques:
Finite volume Discritisation-Cell Centered Formulation. High resolution finite volume upwind scheme Runge-Kutta stepping, Multi-Step Integration scheme. Cell vertex Formulation. Numerical Dispersion.
CFD Application to Some Problems:
Aspects of numerical dissipation & dispersion. Approximate factorization, Flux Vector splitting. Application to Turbulence-Models. Large eddy simulation, Direct Numerical Solution. Post-processing and visualization, contour plots, vector plots etc.
Course outcomes:
At the end of the course the student will be able to:
1. Develop grids around given shapes and transform the physical domain in to computational domain
2. Develop adaptive structured and unstructured grids
3. Apply knowledge to solve CFD problems through finite difference and finite volume techniques
Question paper pattern:
The SEE question paper will be set for 100 marks and the marks scored will be proportionately reduced to 60.
Textbook/ Textbooks
1 Computational Fluid Dynamics John D Anderson Jr McGraw Hill International 2 nd edition &1995
2 Computational Fluid Dynamics T J Chung Cambridge University Press 2 nd edition &2008
Reference Books
1 Computational Fluid Dynamics - An Introduction F. Wendt Springer 3 rd edition &2009.
2 Numerical Computation of Internal and External Flows, Vols. I and II Charles Hirsch John Wiley & Sons, New York 1 st edition &1988.
3 Computational Fluid Dynamics- A Practical Approach JiyuanTu, Guan HengYeoh, and Chaoqun Liu Elsevier Inc 2008