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Correct option is (b) The first CORRECTOR step

Explanation: The pressure-correction equation is obtained by applying the CORRECTED VELOCITIES to the CONTINUITY equation. This pressure-correction equation is then used to get the first pressure correction value.

Right option is (C) Initial guesses for pressure and velocity are obtained

For explanation I would say: In the FIRST STEP of the PISO algorithm, an initial guess is made on the pressure and the velocity VALUES. This is corrected later in the following corrector STEPS. This is exactly the same for the SIMPLE algorithm.

The correct option is (B) DISSIPATIVE term

To elaborate: TWO different grid STENCILS are used in the Rhie-Chow interpolation method. The difference between the values obtained from these two grid stencils is added as a dissipative term in the RESULT.

Right OPTION is (d) Absolute pressure is not IMPORTANT

Best explanation: There is no NEED for the absolute value of pressure in an incompressible flow. This is because the flow is not AFFECTED by this value. But, their gradients in all the directions are important as it will affect the flow.

Right option is (d) Convective TERM in the momentum equation is non-linear

For explanation: The convective term in the momentum equation is given by \(\FRAC{\partial(\rho u_i u_j)}{\partial x_j}\). Where, ρ and U are density and velocity respectively. This term is a non-linear term. The RATE of change and the body force TERMS are linear.

The CORRECT choice is (C) BULK viscosity

For explanation I would say: In the incompressible flows, the bulk viscosity term is omitted as the density is constant. But, in the compressible flows, this cannot be omitted. This is an additional term in the momentum EQUATION of the compressible flows.

The correct OPTION is (b) Predictor-corrector method

The best explanation: The algorithm is a guess and correct method used to calculate the pressure values in a staggered grid ARRANGEMENT. It involves continuous iterations of PREDICTING the values and correcting them.

Correct option is (c) an accurate TIME history of the flow is needed

Explanation: Explicit METHODS are used to solve the Navier-Stokes equations when accurate time history of the flow VARIABLES is needed. The explicit time advancement METHOD is more accurate than the first-order EULER method.

The correct option is (b) the product of momentum equations and VELOCITIES

The EXPLANATION: Momentum is the product of mass and velocity. Kinetic energy is half of the product of mass and the square of velocities. THEREFORE, by multiplying the momentum EQUATION with the velocity and further SIMPLIFYING the resultant equations, we can get the conservation equations of kinetic energy.

Correct choice is (d) It produces oscillatory pressure or velocity fields

To ELABORATE: One of the main disadvantages of the Arbitrary Lagrangian-Eulerian method is the possibility of PRODUCING oscillatory pressure or velocity fields. It is advantageous only in some SPECIAL cases.

The correct choice is (d) SUMMATION of fluxes over the faces

The best explanation: The bulk viscosity term in the momentum EQUATION is a volume INTEGRAL. This is CONVERTED into a surface integral. This surface integral is then discretized as the summation of fluxes over the faces of the control volume.

Right answer is (C) Computation is stable but CONVERGENCE is slow

To elaborate: When the under-relaxation factor is SMALL, the speed of computation is very slow. Because, to get the solutions CONVERGED, a large number of iterations are needed. But, this small under-relaxation factor will lead to a stable computation.

Correct option is (c) Pressure-correction equation

To EXPLAIN I would say: The equation for the pressure correction arises from the discretized continuity equation. It CONTAINS a SOURCE TERM which is the result of the continuity imbalance from the incorrect velocity field.

Correct ANSWER is (a) Semi-Implicit Method for Pressure-Linked Equations

To elaborate: The SIMPLE in SIMPLE ALGORITHM EXPANDS as “Semi-Implicit Method for Pressure-Linked Equations”. This method was introduced by Suhas Patankar and Brian Spalding in the year 1972 at Imperial College.

The CORRECT option is (C) second-order accurate

Easy explanation: The coefficient approximation in the Rhie-Chow interpolation RESULTS in an EQUATION which is the same as the one obtained using the staggered grids. This coefficient approximation is of second-order ACCURACY.

Correct answer is (c) Incompressible ISOTHERMAL flows

Explanation: When the flow is not isothermal, THERMAL energies play an IMPORTANT role in energy conservation. When the flow is compressible, internal energies play an important role. Only when the flow is incompressible and isothermal, kinetic energies become significant.

The correct choice is (a) DECOUPLING of PRESSURE and velocities

The best explanation: The UNCOUPLING between pressure and velocities cause a number of problems. Coupling can be enforced if the different flow variables are stored in the STAGGERED GRID form. Here, pressure and velocity are stored in different places.

Correct choice is (a) Mass, momentum and energy conservations and EQUATION of STATE

To explain: For the compressible flows, the BASIC governing equations – the mass, momentum and energy conservations are solved first. From these known values, to FIND the unknowns, an extra governing equation – the equation of state is ALSO used.

The correct ANSWER is (b) discretized momentum equation

To explain: The discretized momentum equation is taken. From this equation, the pseudo-velocities of the SIMPLER ALGORITHM are obtained. The momentum equation is then WRITTEN in TERMS of these pseudo-velocities for further use.

The correct OPTION is (a) large and oscillatory ITERATION steps

Easy explanation: The under-relaxation FACTOR should be large enough to MOVE the iteration steps FORWARD at a fast rate. But, if it is too large, the iteration steps will be unstable and oscillatory or even divergent at times.

Correct choice is (C) Helps to avoid CONVERGENCE problems and oscillations

For explanation: The biggest ADVANTAGE of the staggered grid arrangement is the coupling of pressure and velocities. It also helps to avoid convergence problems and oscillations in pressure and VELOCITY fields.

The correct choice is (a) Continuity and MOMENTUM EQUATIONS

Best EXPLANATION: The divergence of the momentum EQUATION is taken. The equation obtained from this is then simplified using the continuity equation to get the pressure values. So, a COMBINATION of continuity and momentum equations is needed here.

The CORRECT choice is (d) Linear interpolation

Explanation: The Rhie-Chow interpolation forms momentum equations. The COEFFICIENTS of this NEW momentum equation cannot be directly computed. They are ASSUMED using interpolation of the VALUES in the neighbouring nodes.

Right option is (b) CORRECT the pressure field

The EXPLANATION: Pressure correction equation resembles the predictor-corrector method. The VELOCITIES are corrected until they satisfy the CONTINUITY equation. Then the corrected velocity is USED to correct the pressure field of the previous time step.

Correct option is (a) a hyperbolic equation

For explanation I would say: The pressure-correction equation in the INCOMPRESSIBLE flows is an ELLIPTIC equation. This is transformed into a hyperbolic equation in the compressible flows which is capable of RESOLVING shock waves.

Correct option is (b) Density

Explanation: In the incompressible flows, the density was constant everywhere. But pressure VALUES were calculated. But, for the compressible flows, the density values VARY at DIFFERENT points. So, at the INTERFACES, they should be interpolated.

Correct choice is (B) No under-relaxation

To explain: In the SIMPLE algorithm, the whole momentum equation is used. So, for the CORRECTION of PRESSURE and velocity, an under-relaxation factor is used. But, as the SIMPLEC algorithm omits all the insignificant TERMS in the momentum equation, this under-relaxation becomes unnecessary.

The CORRECT option is (a) the weighted average of the neighbouring corrections

Explanation: The SIMPLEC ALGORITHM assumes that the velocity correction at the CENTRAL node as the weighted average of the corrections at the neighbouring nodes. This changes the momentum and the velocity-correction EQUATIONS.

The correct option is (a) pseudo-momentum equation with the COEFFICIENTS linearly interpolated

To explain: The Rhie-Chow interpolation is used on collocated grids. It is EQUIVALENT to constructing a pseudo-momentum equation at the face. It has coefficients which are obtained using linear interpolation of the momentum EQUATIONS at the centroids.

The correct OPTION is (d) Surface flux terms

The best I can EXPLAIN: CORRECTIONS based on the surface fluxes become zero when the solution CONVERGES. The other terms of the momentum EQUATION do not become zero here. Therefore, the surface fluxes have no impact on the final solution.

The correct answer is (d) MASS conservation

Best explanation: The pressure correction uses a pressure equation to MAKE sure that mass is CONSERVED at each time step. This is to GET the correct SOLUTION from the assumed initial values at that time step.

Right CHOICE is (b) unsteady COMPRESSIBLE flows

Best explanation: This algorithm was actually built for the unsteady compressible flows. It INCLUDED a non-iterative computation PROCESS. This method was then adapted to SOLVE the incompressible flows with an iterative process.

The correct answer is (C) Cost per iteration

Explanation: As the SIMPLEC algorithm is more converging than the SIMPLE algorithm, the SIMPLEC has more convergence per iteration, less NUMBER of ITERATIONS and HENCE less total computational cost than the SIMPLE algorithm. But, the computational cost per iteration is the same for both.

The correct CHOICE is (d) Velocity-correction equation

The explanation is: The momentum equation USED by the SIMPLEC algorithm is MODIFIED. This modification directly affects the velocity-correction equation. This GIVES an ADVANTAGE to the SIMPLEC algorithm.

Correct answer is (b) velocity field in the continuity equation

The best I can explain: In the STAGGERED grid formation, as the PRESSURE is already stored in a different place from the pressure, there is no need of any INTERPOLATION to FIND the velocity field required for the continuity equation.

Right answer is (B) Non-orthogonal grids

To elaborate: The Arbitrary Lagrangian-Eulerian method has some ADVANTAGES for the non-orthogonal grids. One of these advantages is that the PRESSURE at the BOUNDARIES NEED not be specified here.

Correct ANSWER is (b) MOMENTUM equation

Easy EXPLANATION: The SIMPLEC algorithm uses the same PROCEDURE as the SIMPLE algorithm. The major difference is that the momentum equation which is used by the SIMPLE algorithm is changed in the SIMPLEC algorithm.