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# Computational Fluid Dynamics – Mathematical Behaviour of PDE – Elliptic Equations

1 - Question

The characteristic curves for an elliptic system are ___________

a) real and imaginary

b) both real

c) both imaginary

d) both zeros

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Answer: cExplanation: Elliptic equations have their determinant less than zero and the roots of this determinant are both imaginary. So, the curves are also imaginary.

2 - Question

Under which condition does the inviscid steady flow become elliptic?

a) M=1

b) M<1

c) M>1

d) M>5

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Answer: bExplanation: An inviscid steady flow is elliptic when the flow is subsonic. When the flow becomes supersonic, it changes its behaviour. Hence, it comes under the elliptic category when M<1.

3 - Question

Which of these are correct for an elliptic equation?

a) There is no limited region of influence or domain of dependence

b) There is no region of influence or domain of dependence

c) There is no region of influence, but there exists a domain of dependence

d) There is no domain of dependence, but there exists a region of influence

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Answer: aExplanation: For elliptic equations, the information is spread everywhere in all directions. They have an infinite region of influence or a limited domain of dependence for these equations. But, it cannot be stated that they do not have a region of influence or domain of dependence.

4 - Question

The solution of elliptic equations depends on ___________

a) one of its boundaries

b) all its boundaries

c) its opposite boundaries

d) its adjacent boundaries

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Answer: dExplanation: Any point inside the region of elliptic equations is influenced by the whole closed boundary. So, its solution depends on all of its boundaries.

5 - Question

Which of these statements is true for elliptic equations?

a) The solution can be approximated in some of the points

b) The solution can be marched from some initial conditions

c) The solution at all points must be carried out simultaneously

d) The solution process should be carried out simultaneously for some region and then marching can be done

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Answer: cExplanation: Any change at any point in the domain of elliptic equation influences all other points. So, the solution process should be carried out simultaneously and it cannot be marched.

6 - Question

The solution technique used to solve elliptic equations should ___________

a) allow each point to be influenced by its boundary-side neighbours

b) allow each point to be influenced by its west neighbour

c) allow each point to be influenced by its east neighbour

d) allow each point to be influenced by all its neighbours

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Answer: dExplanation: The solution technique of any problem should depend upon the type of the problem. Elliptic problems are influenced by all points in its domain. So, the solution technique should also allow all of its neighbours to influence each point.

7 - Question

Which of these flows is mathematically elliptic?

a) Transient viscous flow

b) Steady viscous flow

c) Steady inviscid flow

d) Transient inviscid flow

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Answer: bExplanation: Steady viscous flow exhibits elliptic behaviour. Steady inviscid flow behaves elliptic optionally. Transient flows are not elliptic.

8 - Question

Which of these is the prototype elliptic equation?

a) Incompressible irrotational flow

b) Incompressible rotational flow

c) Compressible irrotational flow

d) Compressible rotational flow

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Answer: aExplanation: The prototype elliptic equation is Laplace’s equation. This represents an incompressible irrotational fluid flow.

9 - Question

Which is an elliptic equation?

a) Wave equation

b) Transient heat conduction

c) Transient heat convection

d) Steady state heat conduction

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Answer: dExplanation: Transient problems and wave equations need marching solutions and cannot be elliptic. Steady state heat conduction is elliptic.

10 - Question

The below diagram represents elliptic equations.

The point ‘p’ is influenced by ___________

a) ab and bc

b) ab and cd

c) closed boundary abcd

d) ab

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Answer: cExplanation: The whole closed boundary influences the point ‘p’ along with its domain for elliptic equations. Thus ‘p’ is influenced by the closed boundary abcd.