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

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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