Fortran Expert

$ 10.00 — 30.00 USD

1.
The partial step velocity (u *, v *) is calculated by Eqs. (4) and (5).
2.
The values on the 1/2 grid of the partial velocity are obtained by linear interpolation (in this case, the average).

The right-hand side source term of the pressure equation (12) is calculated using the partial step velocity on the 1/2 lattice, and the convergent solution (pn) of the equation (12) is obtained by the SOR method.
4.
Using the obtained pressure, the first-order differential term for the pressure in Eqs. (6) and (7) is calculated, and the velocity (un + 1, vn + 1) in the n + 1 time step is obtained.

In this process, use equations 14-18
I need 3 simulation's jpg file and code.
And equation 21,22's solution
analytical solution is equation (19)
then compare velocity u,w(and solve(21,22)) and compare pressure p

conditions:
As the initial conditions, the velocity and pressure in which t = 0 is substituted in Eq(19) are used, and the boundary conditions are all (x, y directions, velocity/ pressure) periodic boundary conditions (see Fig. 2).
However, note that the definition position of the physical quantity shifts by 1/2 grid.
The number of grid points is 64x64 points, Reynolds number is Re = 100 and the time interval is t = 1/100, the numerical solution at t = 1.0 (repeated 100 times) is compared with the analytical solution (19).
However, the convergence test of pressure equation (12) uses L2-residual pL2 as follows.

Here, Nx and Ny are the number of lattice points in the x and y directions, and m and m + 1 represent the iterative steps of the SOR method, which is the solver of the pressure equation.
For the calculation result, draw contour lines of velocity (u, v) and pressure for the analytical solution and the numerical solution.
Also, calculate the L2-error shown in the following equation with respect to the velocity.

However, Eq(21,22)'s shoulder letter (a) represents the analytical solution, and (n) represents the numerical solution.

PythonMatlab and MathematicaSoftware ArchitectureFortranLabVIEW

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