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started on Jun 11, 2018
Solute Transport Feature
This milestone will conclude when a higher order scheme for the Solute Transport equation is fully proposed, implemented, and tested within DORiE.
 Propose a numeric scheme.
 Implement it in DORiE.
 Validate and test it against analytic and other numeric solutions.
To achieve this, Prof. Peter Bastian proposed to do it in the following sequence of steps:

Implement the flux reconstruction with
\mathcal{RT}_0
finite elements: Implement an easy and straightforward low order reconstruction.

Solution with Finite Volume Method:
 Move the dunemodelling code to dorie.
 Prepare few benchmarks to test the code in order to compare later with the dG method.

Implement the dG method for
\mathcal{Q}_1/\mathcal{P}_1
: Firstly try with the averaged saturation (
\theta \in \mathcal{P}_0, C_w\in\mathcal{Q}_1/\mathcal{P}_1
), compensate the balance of mass, and investigate its behaviour.  Later, try with the continuous saturation (
\theta \in \mathcal{P}_k, C_w\in\mathcal{Q}_1/\mathcal{P}_1
), and check whether we get numerical problems in the time discretization.
 Firstly try with the averaged saturation (

Increase the order dG.
 Do the flux reconstruction in higher order, that is,
j_w^*\in\mathcal{RT}_s, s\in \{k,k1\}
.  Solve with for polynomials of order
k
, that is,C_w\in\mathcal{Q}_k/\mathcal{P}_k
.
 Do the flux reconstruction in higher order, that is,