Questions related to solving the advection-diffusion equation using numerical methods, including derivation and implementation of boundary conditions.

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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 ...
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### 2d advection-diffusion: cell Péclet number and numerical stability

I am studying the numerical resolution of 2d advection-diffusion problems with finite element methods. $$\frac{\partial u}{\partial t} + \beta\cdot\nabla u = \nabla\cdot(\nabla u) \, .$$ It is said in ...
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### Does the time-dependent 1D advection-diffusion with point sources have an analytical solution?

I am looking for the analytical solution of 1-dimensional advection-diffusion equation with several point sources, Q, along the axial length of a cylinder through which the fluid flow occurs. Neumann ...
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### How to implement point source or volume source in finite element implementations

I'm trying to do a simple implementation to study the advection-diffusion-reaction dynamics in a straight pipe. I have points positioned along the length of the pipe (blue dots in the image above). I ...
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I am trying to model a 1-d advection-convection numerically, using an upwind scheme. I'm using the following equation to calculate the value of internal cells: $$C_x^{t+1} = C_x^{t} + D\frac{\Delta t}{... 2 votes 0 answers 30 views ### Semi-analytical/empirical modelling of wall boundary conditions in advection-diffusion-reaction equation with distributed source Let's suppose I need to numerically solve a 3D steady-state transport equation of the form$$ \nabla \cdot (\mathbf{u} c) = \nabla \cdot (D \nabla c) - \lambda c + S $$where c is the transported ... 2 votes 0 answers 75 views ### Linearising Nonlinear Coupled Partial Differential Equations - Alfvénic Diffusion I am trying to solve the following coupled partial differential equations with a finite difference scheme:$$\partial_tf+v\partial_zf+\partial_z\frac{1}{W}\partial_zf=0\partial_tW+v\partial_zW-\...
i am implementing a Matlab code to solve the following equation numerically : $$(\frac{\partial c}{\partial t} =-D_{e} \frac{\partial^2 c}{\partial z^2} +U_{z}\frac{\partial c}{\partial z})$$ with ...