All Questions
Tagged with crank-nicolson advection-diffusion
7
questions
1
vote
0
answers
207
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Solving PDE on a non-uniform grid with Crank-Nicolson scheme
I am solving a 1D diffusion-type equation with the finite-difference Crank-Nicolson (CN) scheme, and I need to densify the spatial grid around the central point. One could change the spatial variable ...
- 21
2
votes
0
answers
145
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Advection diffusion equation using Crank-Nicolson with total flux and Diriclet BCs
I am trying to model the 1D advection-diffusion equation:
$${\partial c \over \partial t} = D_c{\partial^2 c \over \partial x^2} -u{\partial c \over \partial x}.$$
With Robin boundary conditions that ...
- 81
2
votes
0
answers
86
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Linearising Nonlinear Coupled Partial Differential Equations - Alfvénic Diffusion
I am trying to solve the following coupled partial differential equations with a finite difference scheme:
$$\partial_tf+v\partial_zf+\partial_z\frac{1}{W}\partial_zf=0$$
$$\partial_tW+v\partial_zW-\...
- 21
1
vote
1
answer
323
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Crank-Nicholson for diffusion-advection vs diffusion equation
Let's consider the following 1D diffusion equation:
$\frac{\partial u}{\partial t} = xk \frac{\partial}{\partial x}(\frac{1}{x}\frac{\partial u}{\partial x})$
where we assume that the diffusion ...
- 172
5
votes
1
answer
779
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Finite Differencing schemes for Convection-Diffusion equation
I'm using the Convection(/advection)-Diffusion(-Reaction) equation to calculate the temperature over time in different hydraulic parts like a pipe or a heat exchanger.
The flow/convection is always 1D,...
- 265
1
vote
1
answer
631
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How can I numericaly solve a convection-diffusion equation with a large diffusion term?
I want to numerically solve the advection-diffusion equation:
\begin{equation}
u_t(x,t) + cu_x(x,t) = v u_{xx}(x,t)
\end{equation}
for $x \in [0,1]$ and $t \geq 0$ subject to the boundary conditions ...
- 113
4
votes
1
answer
628
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My algorithm for the heat equation is unstable
I have implemented the 2D heat equation with what I thought was the Crank-Nicolson algorithm in the following way:
...
- 85