Consider the 2-D incompressible, invisicid Navier-Stokes equation in the horizontal plane. Recall that the momentum equations are simply solving the transport of the velocity on a frozen velocity field. Use a finite volume method on a structured grid numbered i, j with uniform h = 0.3 in x and y, as shown in Fig. 4. Use typical numbering, e.g. ujj refers to the solution for the i-th point in the x-, and j-th point in the y-direction.
Consider the 2-D incompressible, invisicid Navier-Stokes equation in the horizontal plane. Recall that the momentum equations are simply solving the transport of the velocity on a frozen velocity field. Use a finite volume method on a structured grid numbered i, j with uniform h = 0.3 in x and y, as shown in Fig. 4. Use typical numbering, e.g. ujj refers to the solution for the i-th point in the x-, and j-th point in the y-direction.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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can you help me answer this question please.
![Calculate the x-momentum fluxes for the cell 2, 2. Use the x-momentum convective flux as fx = uu.
Number the cell faces clockwise from k
=
1 representing the interface to cell 2, 3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f7fd42a-4300-4da8-8f14-b18670105553%2Fe257de0e-11be-416c-9ea7-cb9b74954443%2Fs6e3ho_processed.png&w=3840&q=75)
Transcribed Image Text:Calculate the x-momentum fluxes for the cell 2, 2. Use the x-momentum convective flux as fx = uu.
Number the cell faces clockwise from k
=
1 representing the interface to cell 2, 3.
![Consider the 2-D incompressible, invisicid Navier-Stokes equation in the horizontal plane. Recall that
the momentum equations are simply solving the transport of the velocity on a frozen velocity field.
Use a finite volume method on a structured grid numbered i, j with uniform h = 0.3 in x and y, as
shown in Fig. 4. Use typical numbering, e.g. uż,¡ refers to the solution for the i-th point in the x-,
and
j-th point in the y-direction.
Ay
i-1,j+1 i,j+1
=
i-1,j
i+1,j+1
X
i,j i+1,j
i-1,j-1 i,j-1 i+1,j-1
Figure 4: Two-dimensional grid with equal spacing.
The fluid has a density of 1000 kg. Use first-order upwinding for the fluxes.
The pressure field of the initial solution is taken as uniform pij 0.
=
Assume that you have computed the first step of the SIMPLE scheme from an initial solution, and the
resulting velocity field u* is given by the components u = [u, v]T with u₁,j 1.1, U2,5 = 1.5, U3,j = 2.5
for all j except cell 2, 2, and ui,1
[2, 0.6] ¹.
0.3, ui,2 = 0.5, Uį,3
=
= 0.8 for all i except cell 2, 2. In cell 2,2 the
velocity is u2,2 =
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5f7fd42a-4300-4da8-8f14-b18670105553%2Fe257de0e-11be-416c-9ea7-cb9b74954443%2Ffifiq59_processed.png&w=3840&q=75)
Transcribed Image Text:Consider the 2-D incompressible, invisicid Navier-Stokes equation in the horizontal plane. Recall that
the momentum equations are simply solving the transport of the velocity on a frozen velocity field.
Use a finite volume method on a structured grid numbered i, j with uniform h = 0.3 in x and y, as
shown in Fig. 4. Use typical numbering, e.g. uż,¡ refers to the solution for the i-th point in the x-,
and
j-th point in the y-direction.
Ay
i-1,j+1 i,j+1
=
i-1,j
i+1,j+1
X
i,j i+1,j
i-1,j-1 i,j-1 i+1,j-1
Figure 4: Two-dimensional grid with equal spacing.
The fluid has a density of 1000 kg. Use first-order upwinding for the fluxes.
The pressure field of the initial solution is taken as uniform pij 0.
=
Assume that you have computed the first step of the SIMPLE scheme from an initial solution, and the
resulting velocity field u* is given by the components u = [u, v]T with u₁,j 1.1, U2,5 = 1.5, U3,j = 2.5
for all j except cell 2, 2, and ui,1
[2, 0.6] ¹.
0.3, ui,2 = 0.5, Uį,3
=
= 0.8 for all i except cell 2, 2. In cell 2,2 the
velocity is u2,2 =
-
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