Skip to main content
Computational Science

Return to Question

added 18 characters in body
Source Link
Matt
Matt
  • 1
  • 1

I am working on 1-D mass transient diffusion in a radial domain (spherical object) using finite volume method. My equation reads $$\frac{\partial C}{\partial t} = D\left[\frac{\partial^2 C}{\partial r^2} + \frac{2}{r}\frac{\partial C}{\partial r}\right]\, .$$

In a sense of conservative mass within the the radial domain, plus a closed BC ( constant concentration of A species on the surface), does that mean I should end up with concentration gradient among the discretized nodes? In other words, at first time step, (forward in time) for internal nodes, Should I haveget distributed concentrations that the sum of whole domaininternal nodes will give me the initial concentration on the surface?

I am working on 1-D mass transient diffusion in a radial domain (spherical object) using finite volume method. My equation reads $$\frac{\partial C}{\partial t} = D\left[\frac{\partial^2 C}{\partial r^2} + \frac{2}{r}\frac{\partial C}{\partial r}\right]\, .$$

In a sense of conservative mass within the the radial domain, plus a closed BC ( constant concentration of A species on the surface), does that mean I should end up with concentration gradient among the discretized nodes? In other words, at first time step, (forward in time) Should I have distributed concentrations that the sum of whole domain will give me the initial concentration on the surface?

I am working on 1-D mass transient diffusion in a radial domain (spherical object) using finite volume method. My equation reads $$\frac{\partial C}{\partial t} = D\left[\frac{\partial^2 C}{\partial r^2} + \frac{2}{r}\frac{\partial C}{\partial r}\right]\, .$$

In a sense of conservative mass within the the radial domain, plus a closed BC ( constant concentration of A species on the surface), does that mean I should end up with concentration gradient among the discretized nodes? In other words, at first time step (forward in time) for internal nodes, Should I get distributed concentrations that the sum of whole internal nodes will give me the concentration on the surface?

LaTeX-ing equations
Source Link
nicoguaro ♦
nicoguaro ♦
  • 8.6k
  • 6
  • 26
  • 51

I am working on 1-D mass transient diffusion in a radial domain (spherical object) using finite volume method. My equation reads $$\frac{\partial C}{\partial t} = D\left[\frac{\partial^2 C}{\partial r^2} + \frac{2}{r}\frac{\partial C}{\partial r}\right]\, .$$

In a sense of conservative mass within the the radial domain, plus a closed BC ( constant concentration of A species on the surface), does that mean I should end up with concentration gradient among the discretized nodes? In other words, at first time step, (forward in time) Should I have distributed concentrations that the sum of whole domain will give me the initial concentration on the surface?
enter image description here

I am working on 1-D mass transient diffusion in a radial domain (spherical object) using finite volume method. In a sense of conservative mass within the the radial domain, plus a closed BC ( constant concentration of A species on the surface), does that mean I should end up with concentration gradient among the discretized nodes? In other words, at first time step, (forward in time) Should I have distributed concentrations that the sum of whole domain will give me the initial concentration on the surface?
enter image description here

I am working on 1-D mass transient diffusion in a radial domain (spherical object) using finite volume method. My equation reads $$\frac{\partial C}{\partial t} = D\left[\frac{\partial^2 C}{\partial r^2} + \frac{2}{r}\frac{\partial C}{\partial r}\right]\, .$$

In a sense of conservative mass within the the radial domain, plus a closed BC ( constant concentration of A species on the surface), does that mean I should end up with concentration gradient among the discretized nodes? In other words, at first time step, (forward in time) Should I have distributed concentrations that the sum of whole domain will give me the initial concentration on the surface?

Source Link
Matt
Matt
  • 1
  • 1

The physical meaning of conservative mass in diffusion equation

I am working on 1-D mass transient diffusion in a radial domain (spherical object) using finite volume method. In a sense of conservative mass within the the radial domain, plus a closed BC ( constant concentration of A species on the surface), does that mean I should end up with concentration gradient among the discretized nodes? In other words, at first time step, (forward in time) Should I have distributed concentrations that the sum of whole domain will give me the initial concentration on the surface?
enter image description here