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Questions and Answers
What does the Stokes equation describe?
What does the Stokes equation describe?
- Compressible flow
- Low Reynolds number flow (correct)
- High Reynolds number flow
- Non-viscous flow
Which equation governs steady heat conduction with heat generation in a solid body?
Which equation governs steady heat conduction with heat generation in a solid body?
- Laplace equation
- Fourier equation
- Tricomi equation
- Poisson equation (correct)
What type of equation is the viscous Burger's equation?
What type of equation is the viscous Burger's equation?
- Elliptic equation (correct)
- Parabolic equation
- Algebraic equation
- Hyperbolic equation
Which topic is categorized under post-processing?
Which topic is categorized under post-processing?
Which variable transport equation is used for the vorticity transport equation?
Which variable transport equation is used for the vorticity transport equation?
The score and accepted answers hint at which type of information?
The score and accepted answers hint at which type of information?
In the Thomas algorithm, what is the order in which the values of $x$ are found?
In the Thomas algorithm, what is the order in which the values of $x$ are found?
What is the shape of the coefficient matrix after the forward elimination step of the Gauss elimination method?
What is the shape of the coefficient matrix after the forward elimination step of the Gauss elimination method?
What is the order of accuracy of the nine-point formula for discretizing using a uniform step size?
What is the order of accuracy of the nine-point formula for discretizing using a uniform step size?
What type of equations is discussed in Week 4 of the Computational Fluid Dynamics course?
What type of equations is discussed in Week 4 of the Computational Fluid Dynamics course?
In which week is the topic of Stability Analysis covered in the Computational Fluid Dynamics course?
In which week is the topic of Stability Analysis covered in the Computational Fluid Dynamics course?
What is the topic of Unit 7 in the Computational Fluid Dynamics course?
What is the topic of Unit 7 in the Computational Fluid Dynamics course?
What type of partial differential equation is discussed in 'Lecture Notes'?
What type of partial differential equation is discussed in 'Lecture Notes'?
What is the value that makes the 'Parabolic equations' become parabolic?
What is the value that makes the 'Parabolic equations' become parabolic?
Under what condition does the 'steady compressible flow' become hyperbolic?
Under what condition does the 'steady compressible flow' become hyperbolic?
What nature does the 'Tricomi equation' show under a certain condition?
What nature does the 'Tricomi equation' show under a certain condition?
What is the topic of 'Computational Fluid Dynamics For Incompressible Flows - - Unit 5 - Week 2'?
What is the topic of 'Computational Fluid Dynamics For Incompressible Flows - - Unit 5 - Week 2'?
What is the nature of the second order partial differential equation discussed in 'Lecture Notes' (unit?unit=25&lesson=28)?
What is the nature of the second order partial differential equation discussed in 'Lecture Notes' (unit?unit=25&lesson=28)?
Which type of problem is associated with parabolic equations?
Which type of problem is associated with parabolic equations?
Which statement is true about parabolic equations?
Which statement is true about parabolic equations?
Which type of conditions are associated with parabolic equations?
Which type of conditions are associated with parabolic equations?
Which numerical method is used for solving parabolic equations?
Which numerical method is used for solving parabolic equations?
Which of the following is a characteristic of elliptic equations?
Which of the following is a characteristic of elliptic equations?
Which of the following schemes is inconsistent for solving a one-dimensional parabolic equation?
Which of the following schemes is inconsistent for solving a one-dimensional parabolic equation?
What type of equations are being focused on in Week 6?
What type of equations are being focused on in Week 6?
Which method is used to solve a one-dimensional wave equation and requires two sets of initial values?
Which method is used to solve a one-dimensional wave equation and requires two sets of initial values?
What type of method is the Lax-Wendroff technique?
What type of method is the Lax-Wendroff technique?
Which of the following schemes is unconditionally unstable?
Which of the following schemes is unconditionally unstable?
How many real characteristic lines do the equations in question have?
How many real characteristic lines do the equations in question have?
In which week is the Lec 1: Finite difference formulations of the first order wave equation: Explicit Method taught?
In which week is the Lec 1: Finite difference formulations of the first order wave equation: Explicit Method taught?
Study Notes
Computational Fluid Dynamics for Incompressible Flows
- The Stokes equation is best described by Low Reynolds number flow.
Classification of PDEs
- Parabolic equations are associated with initial and boundary conditions.
- Unsteady heat conduction is a parabolic problem.
- Parabolic equations have one real characteristic line.
Numerical Methods
- The Thomas algorithm is used to solve systems of equations.
- Forward elimination in the Gauss elimination method reduces the coefficient matrix to an upper triangular matrix.
- The five-point formula for discretizing using a uniform step size has an order of accuracy of finite domain of dependence and finite domain of influence.
- The nine-point formula for discretizing using a uniform step size has an order of accuracy of 2.
Vorticity Transport Equation
- The general variable transport equation used in vorticity transport equation is the forward variable transport equation.
Computational Fluid Dynamics
- Flow visualization is a part of post-processing in CFD.
- The vorticity-streamfunction formulation is used in Week 8.
- The MAC algorithm is used in Week 9.
Difference Methods
- The Lax-Wendroff technique is an explicit method for solving one-dimensional hyperbolic equations.
- The leap frog scheme requires two sets of initial values to solve a one-dimensional wave equation.
- The FTCS scheme is unconditionally unstable while solving a one-dimensional wave equation.
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Description
Test your knowledge on fluid dynamics and heat conduction with questions about Stokes equation and steady heat conduction in solid bodies with heat generation. See if you can identify the correct answers.
