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 X i+1,j+1 i,j i+1,j 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,j 1.5, U3.j = 2.5 for all j except cell 2, 2, and Ui, 1 = 0.3, ui,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]T. =
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 X i+1,j+1 i,j i+1,j 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,j 1.5, U3.j = 2.5 for all j except cell 2, 2, and Ui, 1 = 0.3, ui,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]T. =
Elements Of Electromagnetics
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Author:Sadiku, Matthew N. O.
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![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
X
i,j
i+1, j+1
i+1,j
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,j
1.5, U3,j = 2.5
for all j
cell 2, 2, and u₁,1 = 0.3, ui,2 = 0.5, U₁,3 = 0.8 for all i except cell 2, 2. In cell 2,2 the
velocity is u2,2 = [2, 0.6]T.
a) Simplify the equations for the x- and y-momentum for this case.
-](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F819262e1-c67a-4578-ac8f-cebe2479cda8%2F378edc3f-7479-4aa8-9ac1-8f77b6fd2fa4%2Fe4qhadh_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
X
i,j
i+1, j+1
i+1,j
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,j
1.5, U3,j = 2.5
for all j
cell 2, 2, and u₁,1 = 0.3, ui,2 = 0.5, U₁,3 = 0.8 for all i except cell 2, 2. In cell 2,2 the
velocity is u2,2 = [2, 0.6]T.
a) Simplify the equations for the x- and y-momentum for this case.
-
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