پروژه CFD با استفاده از متلب

شرح پروژه

با سلام پروژه درس CFD با استفاده از متلب که بخش زیادیش انجام شده و کدها زده شده ماتریس و معادله آن انجام شده فقط مونده نمودار مقدار سرعت در زمان مختلف بر حسب مکان و مقدار خطا و مقدار v

Background: Burgers’ equation is a parabolic PDE, which can serve as a model equation for the boundary-layer equation and the parabolized Navier-Stokes equation.

Consider the one-dimensional generalized Burgers’ viscous equation:

ut+(12−u)ux=μuxxut​+(21​−u)ux​=μuxx​

Where:

uu is the velocity field
μμ is the dynamic viscosity (μ=1 N⋅s/m2)(μ=1N⋅s/m2)
xx and tt represent space and time respectively
Coupled with boundary conditions:

u(x=±t,t)=12(1+tanh⁡(x4μt))at t=1u(x=±t,t)=21​(1+tanh(4μtx​))at t=1

and initial condition:

u(x,0)=e−x−3/2−e−(x+1)/2u(x,0)=e−x−3/2−e−(x+1)/2

Write a computer program to solve the one-dimensional generalized Burgers’ equation using the Keller Box scheme. Follow these guidelines:

a) Replace second and higher derivatives with first derivatives by introducing additional variables.

b) Utilize Taylor-series expansion about the point xj+12xj+21​​ to develop a finite difference representation.

c) Impose the linearization scheme using:

(un+1)j=(un)j+θ(un+1−un)j(un+1)j​=(un)j​+θ(un+1−un)j​j + \theta(u^{n+1} - u^{n})

d) Perform computations for uniform mesh with three different step sizes and analyze mesh dependency.

e) Perform computations for three meshes stretched toward x=0x=0 and investigate mesh dependency.

f) Plot the time evolution of the velocity profile for each case and compare graphically with the exact stationary solution α(x,t)=12(1+tanh⁡(x4))α(x,t)=21​(1+tanh(4x​)).

Implementation Note: Solve the matrix of coefficients using the Thomas algorithm.

مهارت ها و تخصص های مورد نیاز

درباره کارفرما

کاربر631180

عضویت هفده روز پیش

2 پروژه ثبت شده ،

0 پروژه در حال انجام ،

1 پروژه آماده دریافت پیشنهاد ،

نرخ پذیرش پیشنهاد 50%