Question 22.6: Now suppose that the amount of computer time required to sol......

Introduction to Nuclear Reactor Physics [1368692]

Now suppose that the amount of computer time required to solve the transport equation in one dimensional space increases as the square of the number of ordinates that are used. How many times longer will it take to solve the one-group transport equation with an $S_8$ method than an $S_4$ approximation if this is the case?

Step-by-Step

The 'Blue Check Mark' means that this solution was answered by an expert.
Learn more on how do we answer questions.

From our discussion earlier, there are a total of 3 times more ordinates at each mesh point in an $S_8$ method than there are in an $S_4$ method. Therefore, the amount of computer time needed to solve the transport equation with an $S_8$ method will be 3² = 9 times greater in this case.

Related Answered Questions

Question: 22.2

In the P1 approximation, the angular neutron flux ϕ(r, E, u) can be written as the sum of two terms: Φ(r , E, u) = Φo(r ,E)Po(μ) + Φ1(r ,E)P1(μ) or Φ(r , E, u) = Φo + μΦ1 where Po(μ) and P1(μ) are the first two Legendre polynomials. What is the physical meaning of ϕo and ϕ1 in this case? ...

Verified Answer:

In the

P_1

approximation,

ϕ_...

Question: 22.1

Suppose that the components of the angular neutron current along the x-axis, the y-axis, and the z-axis in a Cartesian coordinate system are given by Jx = 0.25 × 10^14 neutrons/cm²/s, Jy = 0.433 × 10^14 neutrons/cm²/s, and Jz = 0.866 × 10^14 neutrons/cm²/s. What is the neutron density n(r, E, Ω, t) ...

Verified Answer:

The magnitude of the neutron density n(r, E, Ω, t)...

Question: 22.9

A bare homogeneous reactor is surrounded by a reflector that has almost no measureable reflectivity. If it then follows that Σs ≈ 0 in the area occupied by the reflector, how far from the edge of the core must we set the neutron flux equal to zero if we want to obtain an accurate solution to the ...

Verified Answer:

In this case, the extrapolated boundary condition ...

Question: 22.8

In an S8 method, how many different angular directions is the particle flux discretized along in a one-dimensional problem and in a two-dimensional problem with a single energy group? ...

Verified Answer:

Most versions of the

S_N

method use...

Question: 22.7

Suppose that we have solved the neutron transport equation in a Cartesian coordinate system using the SN or PN methods. The results reveal that the neutrons are moving at an angle of 30° with respect to the z-axis and 60° with respect to the x-axis. If the neutron flux ϕ(r, E, Ω, t) at the origin ...

Verified Answer:

From our previous discussion, we know that the dir...

Question: 22.5

Write down an explicit expression for the three components Ωx, Ωy, and Ωz of the angular unit vector Ω that appears in the neutron transport equation when the transport equation is to be solved in the x and z directions and the azimuthal angle φ is zero. ...

Verified Answer:

In this case, the angular directional vector Ω = i...

Question: 22.4

Suppose that an S8 method is to be used to solve the neutron transport equation in one dimension instead of an S4 method. How many more discrete angles will have to be used at each mesh point in this case? ...

Verified Answer:

From the equations we presented earlier, the numbe...

Question: 22.3

Suppose that the general equation for a Legendre polynomial is (n + 1)Pn+1(μ) = (2n + 1)μPn(μ) – nPn – 1(μ) where the first two polynomials are P0(μ) = 1 and P1(μ) = μ. Write out the Legendre polynomials that are needed in a simple P3 approximation in one dimension. ...

Verified Answer:

The

P_3

approximation involves expa...