Computational Fluid Dynamics
Course Objectives
The JNTUH R25 curriculum aims to develop the student’s ability to:
- Understand computational techniques for fluid-flow and heat-transfer problems.
- Formulate and discretize the continuity, Navier–Stokes and energy equations.
- Apply Finite Difference Method (FDM) and Finite Volume Method (FVM).
- Implement boundary conditions and understand stability and convergence.
- Apply CFD techniques to practical engineering problems and use CFD software. (JNTU Hyderabad)
UNIT–I: Governing Equations and Numerical Methods
Governing Equations
- Conservation laws
- Differential form of governing equations
- Governing equations for:
- Fluid flow
- Heat transfer
- Characteristics of governing equations
- Boundary conditions
Solution Methods
- Analytical methods
- Experimental methods
- Numerical methods
- Comparison of analytical, experimental and numerical approaches
Numerical Methods
- Finite Difference Method (FDM)
- Finite Element Method (FEM)
- Finite Volume Method (FVM)
- Solution of linear algebraic equations
- Direct methods
- Iterative methods
Partial Differential Equations
- Classification of PDEs
- Elliptic equations
- Parabolic equations
- Hyperbolic equations
- Physical interpretation and examples
Finite Difference Method
- Taylor’s series
- Derivation of finite-difference formulae
- Partial derivative approximations
- 1D elliptic PDEs
- 1D steady-state heat-transfer problems
- Cartesian coordinates
- Cylindrical coordinates
- Spherical coordinates
- Boundary conditions
UNIT–II: Finite Difference Method
Two-Dimensional Problems
- 2D elliptic PDEs
- 2D steady-state heat-conduction problems
- Finite-difference formulation
Parabolic PDEs
- Transient heat conduction
- Explicit method
- Stability analysis
- Errors in numerical solutions
- Implicit method
- Crank–Nicolson method
Two-Dimensional Transient Problems
- 2D parabolic PDEs
- Finite-difference formulation
- ADI method
- Explicit method
Hyperbolic PDEs
- 1D hyperbolic equations
- Finite-difference formulation
- Wave equation
UNIT–III: Finite Volume Method
Fundamentals of FVM
- Basic principles of the Finite Volume Method
- Control-volume approach
- Formation of basic FVM equations
- General nodal equation
Thermal Conductivity
- Interface thermal conductivity
- Treatment of thermal conductivity at interfaces
Source Terms and Non-linearity
- Treatment of source terms
- Treatment of non-linear terms
Applications
- 1D elliptic PDEs
- 2D elliptic PDEs
- Heat-conduction problems
- 1D parabolic PDEs
- Explicit method
- Implicit method
- Transient heat-conduction problems
UNIT–IV: FVM Applied to Convection and Diffusion
Governing Equations
- General form of governing equations
- Fluid-flow equations
- Heat-transfer equations
- Convection
- Diffusion
Burgers’ Equation
- Introduction to Burgers’ equation
- Numerical treatment
Convection-Diffusion
- Steady 1D convection-diffusion equation
- Finite-volume formulation
- Discretization
- Discretization schemes
- Assessment of discretization schemes
- Treatment of boundary conditions
UNIT–V: Calculation of Flow Field
Stream Function and Vorticity
- Vorticity formulation
- Stream-function method
- Advantages
- Limitations
- Boundary-condition treatment
Staggered Grid
- Representation of flow field
- Need for staggered grids
- Staggered-grid concept
Pressure–Velocity Coupling
- Pressure-velocity coupling problem
- Pressure correction
- Velocity correction
SIMPLE Algorithm
- SIMPLE algorithm
- Formulation
- Pressure correction equation
- Velocity correction
- Iterative solution procedure
SIMPLER Algorithm
- SIMPLER algorithm
- Revised pressure-velocity coupling
- Comparison with SIMPLE
Compressible Flow
- Introduction
- Pressure–velocity coupling
- Pressure–velocity–density coupling
JNTUH R25 Course Outcomes
After completing CFD, students should be able to:
- Classify different types of PDEs and select appropriate numerical techniques.
- Solve basic heat-transfer and fluid-flow problems using numerical methods.
- Understand the importance of validation of numerical solutions.
- Apply Finite Difference and Finite Volume Methods to steady and unsteady heat-conduction and fluid-flow problems.
- Implement and analyze SIMPLE and SIMPLER pressure-velocity coupling algorithms for incompressible and compressible flows. (JNTU Hyderabad)
Target Students:
M.Tech Thermal Engineering students
Prerequisites:
Fluid Mechanics + Heat Transfer
Training Mode:
One-to-One / Online / Offline
Recommended Duration:
35–45 hours
Training methodology
Theory → Mathematical formulation → Numerical method → Derivation → Hand calculation → Coding/implementation → CFD software → Validation
Practical CFD component
Although the JNTUH theory syllabus focuses on numerical methods, you can add practical sessions covering:
- CFD problem definition
- Geometry preparation
- Computational domain
- Mesh generation
- Boundary conditions
- Solver selection
- Convergence criteria
- Residual monitoring
- Post-processing
- Velocity and pressure contours
- Temperature contours
- Streamlines
- Validation against analytical/experimental results
- Basic CFD case studies
This would make the course particularly useful for M.Tech students working on dissertations and thermal/fluid engineering projects.
Suggested Website Description
Computational Fluid Dynamics (CFD) – M.Tech Thermal Engineering
Master the fundamentals of Computational Fluid Dynamics through concept-oriented and problem-solving based training aligned with the JNTUH R25 M.Tech Thermal Engineering curriculum. The course covers governing equations, PDE classification, Finite Difference Method, Finite Volume Method, convection-diffusion problems, numerical stability, boundary conditions, pressure-velocity coupling, SIMPLE and SIMPLER algorithms, and compressible-flow calculations.
The training also emphasizes practical CFD methodology, numerical validation and engineering applications to help students connect mathematical formulations with real-world fluid-flow and heat-transfer problems.
Official JNTUH R25 syllabus: JNTUH R25 M.Tech. Thermal Engineering syllabus (JNTU Hyderabad)
