List the different methods used to solve the algebraic simultaneous equations. Explain anyone method with suitable example.

Solve the following algebraic equations using Gauss-Seidel iterative method

7xl +x2 +2x3 =17

3xl 8x2 2x3 =14

4xl+ 2x2 9x3 20

What are the different types of panels used in the analysis of flow using panel method?

Explain in detail about the source panel method.

3. The first order partial differential equation is given u0 ux uy u 0 with the initial condition, 10. Determine:

Characteristic equation

Compatibility equation

4. Define isentropic flow. What do you mean by quasi-one dimensional flow Derive the expression for governing equations of quasi-one dimensional steady, isentropic flow by considering equation of state.

What are the theoretical aspects of transonic flows

Using Taylor's series, derive the backward difference expression for du/dy.

6. Explain the need for turbulence modeling in dealing with CFD problems. What are the various turbulence models used in CFD problems

7. Briefly write about shock fitting and shock capturing techniques using neat and appropriate sketches. Explain how shock capturing technique is used for conserved form of equations.

8. Using Vortex panel method, obtain the lift generated by a flat plate considering N Vortex panels. Make necessary assumptions.

9. Write short notes on the following:

Stability'

Consistency

Lax-equivalence theorem

Round-off and discrimination errors