Linked Questions
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Closed (Robin) boundaries in advection-diffusion equation with FDM
I am solving the equation
$$
\frac{\partial \phi}{\partial t} = \frac{\partial}{\partial x} \left( D \frac{\partial \phi}{\partial x} + v\phi \right)
$$
using finite differences. I want to include ...
- 11
3
votes
1
answer
1k
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Implementing Robin Boundary condition (finite difference)
I'm interested in applying Robin boundary condition to a convection-diffusion problem in 1D.
In the following system,
$$\frac{\partial C}{\partial t} = D\frac{\partial ^2 C}{\partial x^2} - v\frac{\...
- 421
2
votes
1
answer
494
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Closed boundary conditions in finite difference method for diffusive-advective equation
I am implementing a finite difference method in solving the diffusive-advective equation:
$$
u_t + v \cdot u_x = D\cdot u_{xx}
$$
(v, D are constants). Planning to use the operator splitting method (...
- 173
3
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1
answer
1k
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Implementation of gradient zero boundary conditon in advection-diffusion equation
My question is about Finite Element Method.
I want to know how to implement "gradient zero" conditions to advection-diffusion equations in conservative form like,
$\frac{\partial \rho}{\partial t} + ...
5
votes
3
answers
4k
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Conservation of Mass in 1D Advection-Diffusion Equation
My long-term goal is to numerically solve the 1D advection-diffusion equation of the form:
$$\frac{\partial u}{\partial t}=\frac{\partial }{\partial x}\left( v(x,t) u+D\frac{\partial u}{\partial x}\...
- 231
8
votes
1
answer
879
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Conservative finite-difference expression for the advection equation
Following on from the earlier question I am trying to derive a finite-difference scheme for the advection equation which is conservative. It was suggested that for advection equation with variable ...
- 5,409
14
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1
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Can the advection equation with variable velocity be conservative?
I am trying to understand the advection equation with variable velocity coefficient a bit better. In particular I don't understand how the equation can be conservative.
The advection equation,
$$
\...
- 5,409
6
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1
answer
3k
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Trouble implementing Neumann boundary conditions because the ghost points cannot be eliminated
Neumann boundary conditions are implemented by introducing ghost points outside the domain and then using the boundary conditions to eliminate the ghost points. For example, see this question.
I ...
- 5,409
5
votes
3
answers
2k
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No flux boundaries for mixed hyperbolic parabolic PDE
I read this post, "Conservation of a physical quantity when using Neumann boundary conditions applied to the advection-diffusion equation" and although it is the same type of equation it does not fit ...
- 343
8
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3
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4k
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Open boundary conditions with the advection-diffusion equation
Following on from my previous equation I'm would like to apply open boundary condition to the advection-diffusion equation (with reaction term),
$$ \frac{\partial \phi}{\partial t} = \frac{\partial}{\...
- 5,409
34
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2
answers
6k
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Strange oscillation when solving the advection equation by finite-difference with fully closed Neumann boundary conditions (reflection at boundaries)
I am trying to solving the advection equation but have a strange oscillation appearing in the solution when the wave reflects from the boundaries. If anybody has seen this artefact before I would be ...
- 5,409