No |
Units |
Titles |
Sub Titles |
Chapters |

1 |
Unit 1 |
Introduction to numerical method in fluid dynamics |
Introduction to numerical fluid dynamics - Introduction to governing equations of fluid dynamics and modeling of fluid flow - The substantial derivative and the physical meaning of divergence of a vector, Boundary conditions for various types of fluid flow conditions - Introduction to Introduction to numerical fluid dynamics - Introduction to governing equations of fluid dynamics and modeling of fluid flow - The substantial derivative and the physical meaning of divergence of a vector, Boundary conditions for various types of fluid flow conditions - Introduction to |
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2 |
Unit 2 |
Grid generation |
Introduction to grid generation in computational fluid dynamics - Structured grid generation techniques - algebraic methods, conformal mapping and methods using partial differential equations - Basic ideas in numerical grid generation and mapping - Boundary value problem of
numerical grid generation- grid control functions- branch cut - The boundary conditions of first kind - orthogonality of grid lines- boundary point grid control |
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3 |
Unit 3 |
Solution of fluid flow equations |
Introduction to boundary layer equations and their solution - Description of Prandtl's boundary layer equations and the hierarchy of the boundary layer equations - Transformation of
boundary layer equations and the numerical solution method - Choice of discretization model and the generalized Crank-Nicholson scheme - Discretization of the boundary layer equations and illustration of solution of a tridiagonal system of linear algebraic equations - Solution methods for elliptic, parabolic and hyperbolic equations |
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4 |
Unit 4 |
Time dependent methods |
Introduction to time dependent methods - Explicit time dependent methods - Euler, Backward Euler, One step trapezoidal, Backward differencing, two-step trapezoidal, Leap Frog and Adams-Bashforth Methods - Description of Lax-Wendroff Scheme and Mac Cormack's two step predictor - corrector method - Description of time split methods,
Introduction to implicit methods and respective stability properties of explicit and implicit methods - Construction of implicit methods for time dependent problems - Linearization, choice of explicit operator and numerical dissipation aspects |
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5 |
Unit 5 |
Finite volume method |
Introduction to Finite volume Method - Different Flux evaluation schemes, central, upwind and hybrid schemes - Staggered grid approach - Pressure-Velocity coupling - SIMPLE, SIMPLER algorithms- pressure correction equation (both incompressible and compressible forms) - Application of Finite Volume Method for 1-D and 2-D problems |
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