# Computational Fluid Dynamics Questions and Answers – Mathematical Behaviour of PDE – Well Posed Problems

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This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Mathematical Behaviour of PDE – Well Posed Problems”.

1. When can we say that a problem is suitable to be solved using CFD?
a) The PDE has no solution
b) The solution to PDE is unique and it depends continuously on the initial and boundary conditions
c) The PDE has more than one solution
d) The solution to PDE is unique and independent of the initial and boundary conditions

Explanation: We say a problem to be well suited for CFD when the partial differential equation representing the problem has a unique solution and that solution depends on the specified initial and boundary conditions.

2. What is the difficulty in modelling supersonic blunt body problem?
a) The PDE cannot be solved
b) A PDE cannot be formed
c) Mixed flow behaviour
d) Boundary conditions cannot be formed

Explanation: Supersonic flow over a blunt body creates a bow shock. This behaves as a normal shock near the leading edge and as an oblique shock downstream. So, the flow becomes a mixture of subsonic-supersonic flow based on spatial coordinates and makes the mathematical behaviour also mixed.

3. Which of these mathematical models suit unsteady Navier-Stokes equations?
a) Elliptic
b) Hyperbolic
c) Parabolic
d) Mixed

Explanation: The equations reduced from the Navier-Stokes equations have a particular behaviour. But, the pure unsteady Navier-Stokes equations do not have a particular behaviour. They exhibit mixed behaviour.

4. Which kind of flows need an initial condition?
a) Parabolic and hyperbolic
b) Hyperbolic and elliptic
c) Elliptic and Parabolic
d) Elliptic

Explanation: Parabolic and hyperbolic equations are marching problems. So, they need initial conditions. Elliptic equations need only boundary conditions.

5. The flow variables for a/ an _____________ should be solved simultaneously with the flow variables at all other points in the domain.
a) Hyperbolic flow
b) Elliptic flow
c) Parabolic flow
d) Mixed flow

Explanation: Elliptic equations do not march from any condition. They completely rely on the boundary conditions and to solve an elliptic problem, the whole domain should be solved simultaneously.

6. CFD solutions are excellent for flows with _____________
Note: ‘M’ is the Mach number of the flow.
a) M > 1
b) M < 1
c) M = 1
d) M > 5

Explanation: CFD solutions suit problems with Mach numbers well less than 1. When the Mach number is near or more than 1, they pose difficulties for the solution.

7. What is the problem in modelling flows with high Reynolds number?
a) A mixture of viscous and inviscid flow regions
b) A mixture of subsonic and supersonic flow regions
c) A mixture of elliptic and parabolic flows
d) A mixture of elliptic and hyperbolic flows

Explanation: At high Reynolds numbers, the viscous regions are very thin. The part of the flow where the boundary conditions are specified behaves different (inviscid) from the part near the body.

8. Under-specification of boundary conditions gives rise to _____________
a) solution equal to zero
b) no solution
c) a unique solution
d) n-number of solutions

Explanation: If enough boundary conditions are not specified, the number of solutions becomes more. A unique solution to the problem cannot be found.

9. What happens with the over-specification of boundary conditions?
a) Infinite solutions
b) Unique solutions
c) Unphysical solutions
d) No solution

Explanation: When boundary conditions are over-specified, it leads to severe unphysical solutions near the boundaries. It will not reinforce the solution.

10. What is the problem in solving flows with Mach numbers around and above 1?
a) Mach number
b) Compressibility
c) Continuity
d) Pressure 