Recent content by nazmulislam
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Graduate Finite Difference Method for non-square grid
Thanks for your suggestions, specially for the curve boundary. Cheers- nazmulislam
- Post #14
- Forum: Differential Equations
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Graduate Finite Difference Method for non-square grid
Sorry for my typing mistake in writing equations (1) & (2). Thanks for the correction. Also, I tried to write equation in Latex with single $..$ instead of writing with double $. For that reason it didn't work. Thanks for adding the delimiters. I have deleted '\right' from the last equation that...- nazmulislam
- Post #12
- Forum: Differential Equations
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Graduate Finite Difference Method for non-square grid
I have used the following central difference formula for the spatial derivatives: (written in Latex) $$\frac{\partial^2 c}{\partial z^2} = \frac{c_{\rm i+1,j}^{k}-2 c_{\rm i,j}^{k}+c_{\rm i-1,j}^{k}}{(\Delta z)^2}+O[(\Delta z)^2]$$ $$\frac{\partial c}{\partial r} = \frac{c_{\rm...- nazmulislam
- Post #10
- Forum: Differential Equations
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Graduate Finite Difference Method for non-square grid
D0 means double precision. Forexample, 2.D0.- nazmulislam
- Post #8
- Forum: Differential Equations
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Graduate Finite Difference Method for non-square grid
Many thanks for your response. I have imposed symmetry condition, cnew(i,1)=cnew(i,2) at r=0 (since I am calculating concentration within a straight tube). Also, I have used no-flux condition, cnew(i, rsteps+1)=cnew(i, rsteps) at r=r_max (i.e., on the tube surface), and periodic condition...- nazmulislam
- Post #7
- Forum: Differential Equations
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Graduate Finite Difference Method for non-square grid
Thanks for your suggestion.- nazmulislam
- Post #4
- Forum: Differential Equations
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Graduate Finite Difference Method for non-square grid
Hi, I have written some codes for the finite difference solution of diffusion equation (\frac{\partial c}{\partial t}= D {\nabla^2 c}, where c is the species concentration and D is the diffusion coefficient) as follows: DO k= 1, tsteps+1 DO i = 2, zsteps DO j = 2, rsteps...- nazmulislam
- Thread
- Difference Finite Finite difference Finite difference method Grid Method
- Replies: 13
- Forum: Differential Equations
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Graduate Stability condition for solving convection equation by FDM
Thanks.- nazmulislam
- Post #5
- Forum: Differential Equations
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Graduate Stability condition for solving convection equation by FDM
Thanks for your response. I am not sure how to calculate the stability condition. I have used the the formula \Delta t<=((\Delta x)^2+(\Delta y)^2)/(8*D) to make my program stable. But if there is no diffusion term,only convection term, how will I calculate the stability condition? Thanks- nazmulislam
- Post #3
- Forum: Differential Equations
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Graduate Stability condition for solving convection equation by FDM
Hi, I know, there is a stability condition for solving the Convection-Diffusion equation by Finite Difference explicit/implicit technique, which is \Delta t<=(\Delta x)^2/(2*D) for one-dimensional or \Delta t<=((\Delta x)^2+(\Delta y)^2)/(8*D) for two-dimensional problem, where D is the...- nazmulislam
- Thread
- Condition Convection Fdm Stability
- Replies: 4
- Forum: Differential Equations
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Undergrad First Derivative of Periodic Tube Profile | Get Help Now
Yes, I understand the facts. Many thanks. Cheers- nazmulislam
- Post #5
- Forum: Calculus
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Undergrad First Derivative of Periodic Tube Profile | Get Help Now
Hi, I have given the profile below I want to calculate dh/dz. Some data are below: z h -1 1 -0.8 0.823664 -0.6 0.714683 -0.4 0.714683 -0.2 0.823664...- nazmulislam
- Post #3
- Forum: Calculus
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Undergrad First Derivative of Periodic Tube Profile | Get Help Now
Hi, I have some points say, 100 points which come from a periodic tube profile, i.e., (z,r), where z and r are the axial and radial coordinates, respectively. Now, I need to calculate the first derivative at each point. Could you please help me in this regard? Cheers- nazmulislam
- Thread
- Derivative
- Replies: 5
- Forum: Calculus
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Graduate Calculation of particles by integral
So, finally the integral will come into the form \int^{}_{V} C(z,r,t) dV=\pi \int^{}_{z} C(z,r,t) h^2(z) dz.- nazmulislam
- Post #6
- Forum: Calculus