Periodic boundary conditions for auxiliary physics (#1456)

Description
The Cahn-Hilliard physics solver did not allow periodic boundary conditions yet, as well as heat transfer and tracer physics.

Solution
Using an approach similar to the VOF physics solver, Cahn-Hilliard, heat transfer and tracer physics now allow periodic boundary conditions. The periodic boundary conditions parameters for all auxiliary physics (including VOF) are now explicit; the syntax is the same as for the fluids dynamics solver.

Testing
A new test has been added and all past tests still pass.

lethe-fluid/cahn_hilliard_periodic_boundaries
lethe-fluid/heat_transfer_periodic_boundaries
lethe-fluid/tracer_periodic_boundaries

Documentation
The documentation has been adjusted to mention how to use periodic boundary conditions with auxiliary physics solvers.


Co-authored-by: Bruno Blais <blais.bruno@gmail.com>
Co-authored-by: hepap <47506601+hepap@users.noreply.github.com>

Author: 3 people

CHANGELOG.md

@@ -3,6 +3,12 @@
 All notable changes to the Lethe project will be documented in this file.
 The format is based on [Keep a Changelog](http://keepachangelog.com/).
 
+## [Master] - 2025-03-20
+
+### Added
+
+- MINOR Addition of the periodic boundary conditions for the Cahn-Hilliard, heat transfer and tracer physics solvers. Parameters for periodic boundary conditions for all auxiliary physics (including VOF) now follow the same syntax as for the fluid dynamics solvers. [#1456](https://github.com/chaos-polymtl/lethe/pull/1456)
+
 ## [Master] - 2025-03-19
 
 ### Added
@@ -20,12 +26,13 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/).
 ### Added
 
 - MINOR This PR adds the (almost) empty architecture of the SignedDistanceSolver and its coupling in the VOF solver (geometric reinitialization method), following the structure of the already existing vof_advection prototype. The parameters associated to the geometric reinitialization method for the VOF solver are also added. [#1451](https://github.com/chaos-polymtl/lethe/pull/1451)
-- 
+
 ## [Master] - 2025-03-11
 
 ### Added
 
 - MINOR Remove muParser and custom parsed function class (reversal of [#1143](https://github.com/chaos-polymtl/lethe/pull/1143), [#1153](https://github.com/chaos-polymtl/lethe/pull/1153), [#1160](https://github.com/chaos-polymtl/lethe/pull/1160)). [#1452](https://github.com/chaos-polymtl/lethe/pull/1452)
+
 ## [Master] - 2025-03-06
 
 ### Added

applications_tests/lethe-fluid/cahn_hilliard_periodic_boundaries.output

@@ -0,0 +1,307 @@
+Running on 1 MPI rank(s)...
+   Number of active cells:       64
+   Number of degrees of freedom: 243
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 162
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+0.000000e+00    9.141646e-18   -7.214176e-18     1.710754e-18     0.000000e+00 
+   Number of active cells:       160
+   Number of degrees of freedom: 567
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 378
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+0.000000e+00    7.841238e-18   -5.939492e-19     1.368603e-18     0.000000e+00 
+   Number of active cells:       388
+   Number of degrees of freedom: 1335
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 890
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+0.000000e+00    2.798299e-18    5.857601e-19     1.276418e-18     0.000000e+00 
+
+*******************************************************************************
+Transient iteration: 1        Time: 0.1      Time step: 0.1      CFL: 0.275885
+*******************************************************************************
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+1.000000e-01    2.798299e-18    5.857601e-19     9.295018e-01     1.773974e-06 
+
+*******************************************************************************
+Transient iteration: 2        Time: 0.2      Time step: 0.1      CFL: 1.43992 
+*******************************************************************************
+   Number of active cells:       340
+   Number of degrees of freedom: 1203
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 802
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+2.000000e-01    9.214761e-02    1.490279e-07     9.313494e-01    -1.251653e-06 
+
+*******************************************************************************
+Transient iteration: 3        Time: 0.3      Time step: 0.1      CFL: 1.43972 
+*******************************************************************************
+   Number of active cells:       529
+   Number of degrees of freedom: 1761
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1174
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+3.000000e-01    1.817110e-01    4.932793e-09     9.432320e-01    -2.555544e-06 
+
+*******************************************************************************
+Transient iteration: 4        Time: 0.4      Time step: 0.1      CFL: 1.45306 
+*******************************************************************************
+   Number of active cells:       649
+   Number of degrees of freedom: 2121
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1414
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+4.000000e-01    2.617497e-01    1.002454e-06     9.462906e-01     2.705503e-06 
+
+*******************************************************************************
+Transient iteration: 5        Time: 0.5      Time step: 0.1      CFL: 1.45465 
+*******************************************************************************
+   Number of active cells:       682
+   Number of degrees of freedom: 2217
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1478
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+5.000000e-01    3.213142e-01    1.442577e-06     9.482278e-01     1.173208e-06 
+
+*******************************************************************************
+Transient iteration: 6        Time: 0.6      Time step: 0.1      CFL: 1.45566 
+*******************************************************************************
+   Number of active cells:       718
+   Number of degrees of freedom: 2337
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1558
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+6.000000e-01    3.523343e-01    1.389488e-06     9.495790e-01     7.290279e-07 
+
+*******************************************************************************
+Transient iteration: 7        Time: 0.7      Time step: 0.1      CFL: 1.45659 
+*******************************************************************************
+   Number of active cells:       697
+   Number of degrees of freedom: 2280
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1520
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+7.000000e-01    3.502705e-01   -1.377413e-05     9.493334e-01    -4.904477e-06 
+
+*******************************************************************************
+Transient iteration: 8        Time: 0.8      Time step: 0.1      CFL: 1.45667 
+*******************************************************************************
+   Number of active cells:       721
+   Number of degrees of freedom: 2352
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1568
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+8.000000e-01    3.156897e-01   -4.985812e-07     9.473282e-01    -1.916337e-03 
+
+*******************************************************************************
+Transient iteration: 9        Time: 0.9      Time step: 0.1      CFL: 1.45375 
+*******************************************************************************
+   Number of active cells:       712
+   Number of degrees of freedom: 2328
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1552
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+9.000000e-01    2.542705e-01   -1.771304e-04     9.447748e-01    -2.447104e-05 
+
+*******************************************************************************
+Transient iteration: 10       Time: 1        Time step: 0.1      CFL: 1.45097 
+*******************************************************************************
+   Number of active cells:       709
+   Number of degrees of freedom: 2319
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1546
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+1.000000e+00    1.743566e-01   -1.825746e-04     9.431318e-01    -1.352193e-05 
+
+*******************************************************************************
+Transient iteration: 11       Time: 1.1      Time step: 0.1      CFL: 1.45092 
+*******************************************************************************
+   Number of active cells:       727
+   Number of degrees of freedom: 2388
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1592
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+1.100000e+00    8.513368e-02   -1.838895e-04     9.435853e-01    -4.044475e-06 
+
+*******************************************************************************
+Transient iteration: 12       Time: 1.2      Time step: 0.1      CFL: 1.45581 
+*******************************************************************************
+   Number of active cells:       727
+   Number of degrees of freedom: 2376
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1584
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+1.200000e+00   -4.533727e-03   -1.914768e-04     9.406825e-01    -4.426158e-04 
+
+*******************************************************************************
+Transient iteration: 13       Time: 1.3      Time step: 0.1      CFL: 1.45306 
+*******************************************************************************
+   Number of active cells:       724
+   Number of degrees of freedom: 2379
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1586
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+1.300000e+00   -8.661074e-02   -2.322010e-04     9.401689e-01     3.168932e-05 
+
+*******************************************************************************
+Transient iteration: 14       Time: 1.4      Time step: 0.1      CFL: 1.45546 
+*******************************************************************************
+   Number of active cells:       715
+   Number of degrees of freedom: 2334
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1556
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+1.400000e+00   -1.547633e-01   -2.253168e-04     9.378217e-01    -5.517296e-04 
+
+*******************************************************************************
+Transient iteration: 15       Time: 1.5      Time step: 0.1      CFL: 1.45265 
+*******************************************************************************
+   Number of active cells:       721
+   Number of degrees of freedom: 2367
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1578
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+1.500000e+00   -2.042688e-01   -2.795846e-04     9.380117e-01    -6.416754e-06 
+
+*******************************************************************************
+Transient iteration: 16       Time: 1.6      Time step: 0.1      CFL: 1.45533 
+*******************************************************************************
+   Number of active cells:       703
+   Number of degrees of freedom: 2292
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1528
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+1.600000e+00   -2.327802e-01   -2.529040e-04     9.367188e-01    -1.470065e-03 
+
+*******************************************************************************
+Transient iteration: 17       Time: 1.7      Time step: 0.1      CFL: 1.45516 
+*******************************************************************************
+   Number of active cells:       715
+   Number of degrees of freedom: 2331
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1554
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+1.700000e+00   -2.401852e-01   -3.914376e-04     9.380837e-01    -2.384484e-05 
+
+*******************************************************************************
+Transient iteration: 18       Time: 1.8      Time step: 0.1      CFL: 1.46098 
+*******************************************************************************
+   Number of active cells:       715
+   Number of degrees of freedom: 2331
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1554
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+1.800000e+00   -2.279344e-01   -3.898199e-04     9.373024e-01    -6.321715e-04 
+
+*******************************************************************************
+Transient iteration: 19       Time: 1.9      Time step: 0.1      CFL: 1.45836 
+*******************************************************************************
+   Number of active cells:       715
+   Number of degrees of freedom: 2331
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1554
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+1.900000e+00   -1.991551e-01   -4.515133e-04     9.384494e-01    -2.738432e-05 
+
+*******************************************************************************
+Transient iteration: 20       Time: 2        Time step: 0.1      CFL: 1.46048 
+*******************************************************************************
+   Number of active cells:       709
+   Number of degrees of freedom: 2310
+   Volume of triangulation:      4
+   Number of Cahn-Hilliard degrees of freedom: 1540
+
+-------------------------
+Cahn-Hilliard Barycenter
+-------------------------
+    time     x_cahn_hilliard y_cahn_hilliard vx_cahn_hilliard vy_cahn_hilliard 
+2.000000e+00   -1.580186e-01   -4.616693e-04     9.372702e-01    -2.957594e-06