Timeline for Finite-difference form of the reaction-term in the solute transport equation
Current License: CC BY-SA 3.0
8 events
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| Nov 13, 2016 at 20:26 | comment | added | Peter Frolkovič | OK, thanks for the answer. I have added a reference where also analytical solution to these equations is given. I think it is too complicated to implement only for the purpose of comparing numerical solution with the analytical one. You might prefer to reproduce plots of analytical solution that have been published for some particular parameters. | |
| Nov 13, 2016 at 20:21 | history | edited | Peter Frolkovič | CC BY-SA 3.0 |
added 751 characters in body
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| Nov 13, 2016 at 18:51 | comment | added | ToNoY | I'm not having any trouble understanding your solution but I also requested for a reproducible example of the scheme if possible. Once I can apply the whole scheme to a problem I'll accept the answer, but I'm working on it. | |
| Nov 13, 2016 at 18:27 | comment | added | Peter Frolkovič | Can you specify, please, which part in my answer is still unclear to you? Is the first differential equation for $C$ unclear? Is the second differential equation for $S$ unclear? Is the first numerical scheme for $C$ unclear? Is the second numerical scheme for S unclear? | |
| Nov 9, 2016 at 9:01 | comment | added | Peter Frolkovič | The link to the book you provided does not work for me, the pages are not visible. My first partial differential equation (PDE) for $C$ is obtained from your PDE simply by replacing $\frac{\partial S}{\partial t}$ there with the right hand side of ordinary differential equation (ODE) for $S$ that you have to multiply firstly by $\frac{\rho}{\theta}$. The second numerical scheme for $S_{x,t}$ is obtained by so called backward (explicit) Euler (time discretization) method that is the simplest possible one, you can use more sophisticated ones, but in fact you use it for the first PDE. | |
| Nov 9, 2016 at 3:21 | comment | added | ToNoY | can you explain a little why is it $C_{x,t-\Delta t}$ & $S_{x,t-\Delta t}$? Not involved with concentrations from any other nodes; e.g. $C_{x+\Delta x,t-\Delta t}$? The link I provided indicates a difference between two nodal concentrations divided by 2. Also, the $\theta$ term was with $C$, how come its with $S$ in your final equation? | |
| Nov 8, 2016 at 15:50 | history | edited | Peter Frolkovič | CC BY-SA 3.0 |
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| Nov 8, 2016 at 15:43 | history | answered | Peter Frolkovič | CC BY-SA 3.0 |