COMPUTATIONAL FLUID DYNAMICS (PE – IV) B.Tech. IV Year I Sem JNTUH R-18

• Differentiate between parabolic, elliptic, and hyperbolic partial differential equations and classify governing equations for heat transfer and fluid flow accordingly.

• Explain the need for Computational Fluid Dynamics (CFD) and its advantages as a research and design tool across various engineering disciplines.

• Compare and contrast the main working principles of different numerical techniques like FDM, FEM, and FVM.

• Analyze the mathematical behavior of partial differential equations (PDEs) and its significance in understanding the physical and numerical aspects of the solution.

• Explain the concepts of well-posed problems and boundary conditions, and their importance in obtaining accurate numerical solutions.

Unit II: Finite Difference Method (FDM)

• Describe the basic discretization process in FDM and derive finite difference formulas for first and second order terms.

• Solve physical problems with elliptic governing equations using FDM for different boundary conditions in heat conduction, beams, etc.

• Explain the numerical treatment of curvilinear coordinates and singularities in FDM solutions.

• Derive and apply finite difference equations to solve 1D heat conduction problems with complex geometries.

Unit III: FDM for Parabolic and Hyperbolic Equations

• Solve physical problems with parabolic governing equations using FDM, explaining implicit, explicit, and semi-implicit methods.

• Analyze the concepts of stability and consistency in FDM, applying the Von Neumann stability criterion to simple physical problems.

• Derive and explain the Lax-Wendroff technique for FDM solution of first-order wave equations.

• Analyze the Maccormack's technique for hyperbolic equations and its advantages over Lax-Wendroff.

Unit IV: FDM for Unsteady Inviscid Flows

• Solve 2D viscous incompressible flow problems using FDM in vorticity and stream function formulation.

• Apply FDM to the lid-driven cavity problem and interpret the results.

• Formulate and numerically solve the flow over infinitely long cylinder and sphere using cylindrical coordinates.

• Explain the process of obtaining elliptic equations from the 2D Navier-Stokes equations.

Unit V: Advanced FDM Applications and Fluid Flow Modeling

• Use the Finite Difference approach to model fluid flow behavior using the Burger's equation.

• Analyze the FDM solution of the Burger's equation with respect to upwind schemes and transport properties.

• Explain the staggered grid and Marker and Cell (MAC) formulations for solving the Navier-Stokes equations.

• Discuss the pressure correction method (SIMPLE algorithm) and its importance in numerical stability for incompressible fluid flows.

Bonus Questions:

• Compare and contrast the advantages and limitations of explicit and implicit methods in FDM.

• Discuss the role of grid generation and discretization schemes in the accuracy and efficiency of CFD solutions.

• Analyze the importance of validation and verification in CFD simulations to ensure their reliability and accuracy.