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4 | 4 | SUNDIALS and Time Integrators |
5 | 5 | ============================= |
6 | 6 |
|
7 | | -This example code shows how to use the AMReX TimeIntegrator class |
8 | | -with SUNDIALS backend for integration. It also include two example |
9 | | -of AMReX native integrators, Forward Euler, and Explicit Runge Kutta. |
10 | | -Each integration type can be chosen by selecting the corresponding |
11 | | -inputs file: |
| 7 | +These example codes demonstrate how to use the AMReX TimeIntegrator class |
| 8 | +with SUNDIALS backend for integration. |
12 | 9 |
|
13 | | - - ``inputs_forward_euler`` -- Native AMReX Forward Euler integrator |
| 10 | +The first example code at ``amrex-tutorials/ExampleCodes/SUNDIALS/Single-Rate`` |
| 11 | +solves the heat equation: |
14 | 12 |
|
15 | | - - ``inputs_rk3`` -- Native AMReX Explicit Runge Kutta |
| 13 | +.. math:: \frac{\partial\phi}{\partial t} = \nabla^2\phi. |
16 | 14 |
|
17 | | - - ``inputs_sundials_erk`` -- SUNDIALS backend |
| 15 | +The inputs file contains a template for single process time integration strategies. |
18 | 16 |
|
19 | | -Both Runge Kutta and SUNDIALS have additional options which can |
20 | | -be set by modifying the inputs file. Please see each respective inputs |
21 | | -file or `AMReX User Guide:Time Integration`_ for more details. |
| 17 | +The second example code at ``amrex-tutorials/ExampleCodes/SUNDIALS/Reaction-Diffusion`` |
| 18 | +solves the reaction-diffusion equation, where :math:`R` and :math:`D` are |
| 19 | +user-supplied reaction and diffusion coefficients: |
| 20 | + |
| 21 | +.. math:: \frac{\partial\phi}{\partial t} = D \nabla^2\phi - R \phi. |
| 22 | + |
| 23 | +The inputs file contains a template for MRI approaches, where the diffusion process |
| 24 | +can be treated as a "fast" partition relative to the reaction process. |
| 25 | +Please see each respective inputs file or |
| 26 | +`AMReX User Guide:Time Integration`_ for more details. |
22 | 27 |
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23 | 28 | .. _`AMReX User Guide:Time Integration`: https://amrex-codes.github.io/amrex/docs_html/TimeIntegration_Chapter.html# |
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