a) Simplify the equations for the x- and y-momentum for this case. = uu. b) Calculate the x-momentum fluxes for the cell 2, 2. Use the x-momentum convective flux as fa Number the cell faces clockwise from k = 1 representing the interface to cell 2, 3. c) Calculate the residual for the x-momentum divided by velocity, i.e. u, for the cell 2, 2. 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. ui refers to the solution for the i-th point in the x-, and j-th point in the y-direction. i-1,j+1 i,j+1 i-1,j i-1,j-1 i,j i,j-1 i+1, j+1 i+1,j i+1,j-1 Figure 4: Two-dimensional grid with equal spacing. The fluid has a density of 1000. 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.j = 1.5, U3.j = 2.5 for all j except cell 2, 2, and u₁,1 = 0.3, U₁,2 = 0.5, ui,3 = 0.8 for all i except cell 2,2. In cell 2,2 the velocity is u2,2 = [2, 0.6]¹.
a) Simplify the equations for the x- and y-momentum for this case. = uu. b) Calculate the x-momentum fluxes for the cell 2, 2. Use the x-momentum convective flux as fa Number the cell faces clockwise from k = 1 representing the interface to cell 2, 3. c) Calculate the residual for the x-momentum divided by velocity, i.e. u, for the cell 2, 2. 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. ui refers to the solution for the i-th point in the x-, and j-th point in the y-direction. i-1,j+1 i,j+1 i-1,j i-1,j-1 i,j i,j-1 i+1, j+1 i+1,j i+1,j-1 Figure 4: Two-dimensional grid with equal spacing. The fluid has a density of 1000. 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.j = 1.5, U3.j = 2.5 for all j except cell 2, 2, and u₁,1 = 0.3, U₁,2 = 0.5, ui,3 = 0.8 for all i except cell 2,2. In cell 2,2 the velocity is u2,2 = [2, 0.6]¹.
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
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Problem 1.1MA
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I need help on this mock question:
![a) Simplify the equations for the x- and y-momentum for this case.
= uu.
b) Calculate the x-momentum fluxes for the cell 2, 2. Use the x-momentum convective flux as fa
Number the cell faces clockwise from k = 1 representing the interface to cell 2, 3.
c) Calculate the residual for the x-momentum divided by velocity, i.e. u, for the cell 2, 2.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F507f99da-9967-4c1f-a8fd-4e55d78bcba3%2F2c26a1b7-76f6-4b12-8348-67db4e09aba9%2F1ib2xad_processed.png&w=3840&q=75)
Transcribed Image Text:a) Simplify the equations for the x- and y-momentum for this case.
= uu.
b) Calculate the x-momentum fluxes for the cell 2, 2. Use the x-momentum convective flux as fa
Number the cell faces clockwise from k = 1 representing the interface to cell 2, 3.
c) Calculate the residual for the x-momentum divided by velocity, i.e. u, for the cell 2, 2.
![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. ui refers to the solution for the i-th point in the x-, and
j-th point in the y-direction.
i-1,j+1 i,j+1
i-1,j
i-1,j-1
i,j
i,j-1
i+1, j+1
i+1,j
i+1,j-1
Figure 4: Two-dimensional grid with equal spacing.
The fluid has a density of 1000. 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.j = 1.5, U3.j = 2.5
for all j except cell 2, 2, and u₁,1 = 0.3, U₁,2 = 0.5, ui,3 = 0.8 for all i except cell 2,2. In cell 2,2 the
velocity is u2,2 = [2, 0.6]¹.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F507f99da-9967-4c1f-a8fd-4e55d78bcba3%2F2c26a1b7-76f6-4b12-8348-67db4e09aba9%2F7y3jyv_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. ui refers to the solution for the i-th point in the x-, and
j-th point in the y-direction.
i-1,j+1 i,j+1
i-1,j
i-1,j-1
i,j
i,j-1
i+1, j+1
i+1,j
i+1,j-1
Figure 4: Two-dimensional grid with equal spacing.
The fluid has a density of 1000. 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.j = 1.5, U3.j = 2.5
for all j except cell 2, 2, and u₁,1 = 0.3, U₁,2 = 0.5, ui,3 = 0.8 for all i except cell 2,2. In cell 2,2 the
velocity is u2,2 = [2, 0.6]¹.
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