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51.	Consider the equation \((\frac{\partial u}{\partial y})_{i,j}=(\frac{u_{i,j}-u_{i,j-1}}{\Delta y})\) formulated using the Taylor series expansion. Find the type of equation.(a) first-order forward difference(b) first-order rearward difference(c) second-order forward difference(d) second-order rearward differenceThe question was asked in examination.My question is taken from Finite Difference Method in section Finite Difference Methods of Computational Fluid Dynamics
Answer» Correct choice is (b) first-order rearward difference The explanation is: The equation USES the terms ui,j and its rearward TERM ui,j-1. So, it represents a rearward difference. The order of accuracy of the equation depends on its TRUNCATION error. The truncation error has the least order term \(\frac{-\Delta y}{2}\). So, it is first order ACCURATE.

52.	Which is the major error occurring due to the finite difference approximations?(a) Discretization error(b) Round-off error(c) Iteration error(d) Modelling errorsThe question was asked in an internship interview.My enquiry is from Errors in Finite Difference Approximations topic in division Finite Difference Methods of Computational Fluid Dynamics
Answer» Right ANSWER is (a) Discretization error To explain I would say: The major error occurring in the finite DIFFERENCE method is the discretization error. This error occurs due to both TEMPORAL and spatial discretization USING an APPROXIMATION for the discretization. This is also called a numerical error.

53.	MacCormack’s technique is __________(a) explicit, finite-difference method(b) implicit, finite-difference method(c) explicit, finite volume method(d) implicit, finite volume methodI got this question by my school principal while I was bunking the class.This intriguing question originated from Finite Difference Methods in portion Finite Difference Methods of Computational Fluid Dynamics
Answer» Correct ANSWER is (a) explicit, finite-difference method The EXPLANATION: Like the Lax-Wendroff technique, MacCormack’s technique is also particularly SUITABLE for marching solutions of hyperbolic and parabolic PARTIAL differential equations. It is also an explicit finite difference scheme for marching solutions.

54.	Which is the technique used to overcome the disadvantages of the Lax-Wendroff technique?(a) Upwind scheme(b) MacCormack’s technique(c) Downwind scheme(d) Richtmeyer methodThe question was asked in exam.Enquiry is from Finite Difference Methods in chapter Finite Difference Methods of Computational Fluid Dynamics
Answer» Correct answer is (B) MacCormack’s TECHNIQUE The explanation: To OVERCOME the lengthy algorithm of the Lax-Wendroff technique, MacCormack’s technique is USED which can produce results of the same order of accuracy with a SIMPLER method which does not want the second-order derivative.

55.	What causes aliasing in Spectral methods?(a) Small grid sizes(b) Fourier series(c) Arbitrary values for Fourier series(d) Periodic natureThe question was posed to me during an interview.My question comes from Finite Difference Methods in portion Finite Difference Methods of Computational Fluid Dynamics
Answer» Right OPTION is (c) Arbitrary values for Fourier series Easiest explanation: For Fourier EXPANSION, there is a nearly arbitrary value to be assumed. The results DEPEND on this arbitrary value. If this value is not chosen PROPERLY, it will lead to aliasing error. This means pointing the same element more than one time.

56.	The time-step size in explicit schemes depends upon _____________(a) Grid size(b) Number of iterations(c) Total time interval(d) Given mathematical equationI had been asked this question by my college professor while I was bunking the class.The origin of the question is Explicit and Implicit Finite Difference Methods topic in chapter Finite Difference Methods of Computational Fluid Dynamics
Answer» The correct option is (a) Grid size The explanation is: There is a LIMIT POSED to time-step size in EXPLICIT schemes. This limit depends on the grid size chosen. Once, the grid size is chosen, from the FORMULA given by stability criterion, the maximum POSSIBLE time-step size can be calculated.

57.	Spectral methods are much more accurate than the Finite Difference methods ___________(a) unconditionally(b) conditionally depending on the problem taken(c) conditionally when the number of grid points is small(d) conditionally when grid size is smallI have been asked this question in a job interview.Enquiry is from Finite Difference Methods in section Finite Difference Methods of Computational Fluid Dynamics
Answer» Right choice is (d) conditionally when grid size is small To explain: The error in the solution decreases exponentially with the number of grid POINTS. The results are more precise when the number of grid points is more. So, the grid size should be small. This makes the spectral method with more GRIDS accurate than the Finite Difference methods.

58.	What is the advantage of using fourier series in the spectral method?(a) Less grid size(b) Large number of grid points(c) Continuous results(d) FlexibilityI got this question during an online interview.My doubt is from Finite Difference Methods topic in section Finite Difference Methods of Computational Fluid Dynamics
Answer» Right option is (c) Continuous results Easiest explanation: The Fourier SERIES can be interpolated to get the dependent FUNCTION. This will HELP us to get the results at a continuous space instead of results at particular grid points. This is an advantage over the other DISCRETIZATION techniques.