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What are the differences between explicit and implicit methods?

Distinguish between truncation error , round-off error and discretization error.

Derive an expression for truncation error in the Implicit scheme for 1-D
Ou _ au

conduction equation at “2௨ if a=1.

What is the significant of ‘Courant number’ and CFL condition in stability

analysis?

Derive the expressions for explicit FTCS and CTCS for a parabolic PDE.

Check the consistency of the following model equation using CTCS method.

PART C
Answer any four full questions, each carries 10 marks.
Discretize and estimate the density in a unsteady, inviscid 2-D flow field one

forward time step ahead with the help of conservative equation by using
McCormack technique.

Differentiate Jacobi and gauss — seidel iterative methods.

Define staggered grid and explain the need for Staggered grid.

Define upwind type discretization.

Describe point Gauss-Seidel method.

Solve the equation by using Runge kutta method in steps of time ‘At’

Describe the node-centred and vertex-centred finite volume schemes with
suitable sketches.
Differentiate lax Wendroff time stepping with Runge- kutta time stepping .

Describe the important features of Finite Volume method.

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