This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Discretization”.
1. Discretization of the physical domain of interest results in __________
b) Discretized equations
c) Discrete cells
d) Exponential equations
Explanation: Discretization of the physical domain means dividing the region of interest into discrete elements. This will result in discrete cells on which the rest of the solution process depends.
2. The number of discretized equations is equal to the number of __________
a) Discretized cells
b) Boundary conditions
d) Boundary-side elements
Explanation: Discretized equations are formed for each element obtained after discretizing the domain. So, the number of discretized cells and that of the discretized equations will be the same.
3. Equation discretization is the process of converting ___________ PDEs into discretized equations.
Explanation: Closed form continuous PDEs are converted into discretized equations suitable for numerical solutions. Analytical solution of this closed form PDEs will give continuous equations which can be used to get the flow variable at any desired point in the domain.
4. Which of these methods is not a method of discretization?
a) Finite volume method
b) Finite difference method
c) Gauss-Seidel method
d) Spectral element method
Explanation: Gauss-Seidel method is a method of solving the discretized equations. Finite difference method, finite volume method and spectral element method are all methods of discretization.
5. Discretization of the governing equations result in ___________
a) Integral equations
b) Quasi-linear partial differential equations
c) Partial differential equations
d) Algebraic equations
Explanation: Discretization of the governing equations means converting the partial differential or the integral equations into algebraic equations.
6. The discretized equation connects each element with __________
a) the northern and southern elements
b) the boundary elements
c) the neighbouring elements
d) the eastern and western elements
Explanation: The discretized equation for a particular element connects it with its neighbouring elements in all the sides in general. The particular sides depend upon the problem taken.
7. If the domain and equations are not discretized, which of these will become true?
a) Numerical solution cannot be obtained
b) Analytical solution cannot be obtained
c) Initial conditions cannot be applied
d) Mathematical model cannot be obtained
Explanation: Discretization process is done to make the equations suitable for numerical solution. If not discretized, numerical methods could not be applied.
8. The discretized flow field properties exhibit ___________
a) continuous nature
b) piece-wise nature
c) quadratic nature
d) cubic nature
Explanation: The discretized flow field properties are discontinuous and they have a piece-wise nature. Until discretized, the variables are continuous.
9. The finite volume method ____________ the governing equations in each cell.
b) sums up
Explanation: In the finite volume method, the governing equations are integrated over each cell to form a semi-discretized equation. Then, the variation of flow variables is approximated.
10. In which of these methods, the differential equation is multiplied by a test function?
a) Finite difference method
b) Finite volume method
c) Finite element method
d) Spectral element method
Explanation: Spectral element method multiplies the differential equation by a random test function and then integrates it over the entire domain.
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