Max. Marks: 100
Duration: 3 Hours
PART A
Answer any three full questions, each carries 10 marks.
Marks
(2)
1
a) Can we use CFD as research tool? Justify your answer with example.
b) Derive the differential Governing equation for fluid motion according to
Newton’s second law in conservation form.
(8)
2
3
a) Discuss on source panel method, list its merits and de-merits.
b) Derive an expression for shape function 3 noded bar element
a) Show that the second order wave equation is hyperbolic.
(5)
(5)
(2)
b) Classify the following system of PDE’s according to eigen value method
(5)
where, u and v are the two dependent variables
c) Write a short note on well-posed problems.
(3)
4
a) Consider a viscous flow of air over a flat plate. At a given station in the flow
(10)
direction the variation of the flow direction u in the direction perpendicular to
-y/L
the plate is given by an expression u=1582 (1-e ) where L is the characteristic
length 1m. The viscosity coefficient of air is (1.775 x 107 N/m-s). Assume u at
discrete grid points equally spaced in the y direction with Δy=0.1m. Calculate the
wall shear stress first, second and third order accuracy.
PART B
Answer any three full questions, each carries 10 marks.
5
6
a) Consider 1-D wave equation Ut + a Ux = 0. Discretize the equation and hence
deduce dissipative term and dispersive term.
(10)
a) What are the differences between explicit and implicit methods? (5) b) Distinguish
between truncation error , round-off error and discretization error. (5) 7 a) Derive an
expression for truncation error in the Implicit scheme for 1-D (7)
conduction equation
if α=1.
b) What is the significant of ‘Courant number’ and CFL condition in stability
analysis?
(3)