Add Discontinuous Galerkin capabilities to the Tracer auxiliary physics

CHANGELOG.md

@@ -15,12 +15,13 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/).
 
 - MINOR Change default coarse grid solver to a direct solver for the geometric multigrid preconditioner in the matrix application. [#1322](https://github.com/chaos-polymtl/lethe/pull/1322)
 
-## [Master] - 2024-10-16
-
 ### Fixed
 
 - MINOR Added missing flag to update quadrature points for the FEFaceValues of the tracer physics. [#1323](https://github.com/chaos-polymtl/lethe/pull/1323)
 
+### Added
+
+- MAJOR  Tracer physics can now be solved by using a discontinuous Galerkin method instead of a continuous Galerkin method. [#1320](https://github.com/chaos-polymtl/lethe/pull/1320)
 
 ## [Master] - 2024-10-15
 

applications_tests/lethe-fluid/dg_tracer_advection_tanh.output

@@ -0,0 +1,87 @@
+Running on 1 MPI rank(s)...
+   Number of active cells:       1024
+   Number of degrees of freedom: 3267
+   Volume of triangulation:      1
+   Number of tracer degrees of freedom: 4096
+
+*******************************************************************************
+Transient iteration: 1        Time: 0.02     Time step: 0.02     CFL: 0.567185
+*******************************************************************************
+L2 error velocity : 5.55112e-17
+L2 error tracer : 0.00365901
+
+*******************************************************************************
+Transient iteration: 2        Time: 0.04     Time step: 0.02     CFL: 0.567185
+*******************************************************************************
+L2 error velocity : 5.55112e-17
+L2 error tracer : 0.00705464
+
+*******************************************************************************
+Transient iteration: 3        Time: 0.06     Time step: 0.02     CFL: 0.567185
+*******************************************************************************
+L2 error velocity : 5.55112e-17
+L2 error tracer : 0.0100805
+
+*******************************************************************************
+Transient iteration: 4        Time: 0.08     Time step: 0.02     CFL: 0.567185
+*******************************************************************************
+L2 error velocity : 5.55112e-17
+L2 error tracer : 0.0139666
+
+*******************************************************************************
+Transient iteration: 5        Time: 0.1      Time step: 0.02     CFL: 0.567185
+*******************************************************************************
+L2 error velocity : 5.55112e-17
+L2 error tracer : 0.0167514
+
+*******************************************************************************
+Transient iteration: 6        Time: 0.12     Time step: 0.02     CFL: 0.567185
+*******************************************************************************
+L2 error velocity : 5.55112e-17
+L2 error tracer : 0.0196117
+
+*******************************************************************************
+Transient iteration: 7        Time: 0.14     Time step: 0.02     CFL: 0.567185
+*******************************************************************************
+L2 error velocity : 5.55112e-17
+L2 error tracer : 0.0230336
+
+*******************************************************************************
+Transient iteration: 8        Time: 0.16     Time step: 0.02     CFL: 0.567185
+*******************************************************************************
+L2 error velocity : 5.55112e-17
+L2 error tracer : 0.0251808
+
+*******************************************************************************
+Transient iteration: 9        Time: 0.18     Time step: 0.02     CFL: 0.567185
+*******************************************************************************
+L2 error velocity : 5.55112e-17
+L2 error tracer : 0.0279955
+
+*******************************************************************************
+Transient iteration: 10       Time: 0.2      Time step: 0.02     CFL: 0.567185
+*******************************************************************************
+L2 error velocity : 5.55112e-17
+L2 error tracer : 0.0308831
+ time  error_velocity 
+0.0200   5.551115e-17 
+0.0400   5.551115e-17 
+0.0600   5.551115e-17 
+0.0800   5.551115e-17 
+0.1000   5.551115e-17 
+0.1200   5.551115e-17 
+0.1400   5.551115e-17 
+0.1600   5.551115e-17 
+0.1800   5.551115e-17 
+0.2000   5.551115e-17 
+cells error_tracer 
+ 1024 3.659011e-03 
+ 1024 7.054635e-03 
+ 1024 1.008047e-02 
+ 1024 1.396659e-02 
+ 1024 1.675139e-02 
+ 1024 1.961169e-02 
+ 1024 2.303355e-02 
+ 1024 2.518081e-02 
+ 1024 2.799553e-02 
+ 1024 3.088313e-02 

applications_tests/lethe-fluid/dg_tracer_advection_tanh.prm

@@ -0,0 +1,139 @@
+# SPDX-FileCopyrightText: Copyright (c) 2022-2023 The Lethe Authors
+# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception OR LGPL-2.1-or-later
+
+set dimension = 2
+
+subsection simulation control
+  set method            = bdf1
+  set time end          = 0.2
+  set time step         = 0.02
+  set output name       = stab_tracer
+  set output frequency  = 0
+end
+
+subsection FEM
+  set velocity order = 1
+  set pressure order = 1
+  set tracer order   = 1
+  set tracer uses dg = true
+end
+
+subsection initial conditions
+  set type = nodal
+  subsection uvwp
+    set Function expression = 1; 0; 0
+  end
+  subsection tracer
+    set Function expression = tanh(25-50*x)
+  end
+end
+
+subsection physical properties
+  set number of fluids = 1
+  subsection fluid 0
+    set tracer diffusivity = 0
+  end
+end
+
+subsection mesh
+  set type               = dealii
+  set grid type          = subdivided_hyper_rectangle
+  set grid arguments     = 1, 1 : 0, 0 : 1, 1.0 : true
+  set initial refinement = 5
+end
+
+subsection multiphysics
+  set tracer = true
+end
+
+subsection analytical solution
+  set enable    = true
+  set verbosity = verbose
+  subsection uvwp
+    set Function expression = 1 ; 0 ; 0
+  end
+  subsection tracer
+    set Function expression = tanh(25-50*x+50*t)
+  end
+end
+
+subsection boundary conditions
+  set number = 3
+  subsection bc 0
+    set id   = 0
+    set type = function
+    subsection u
+      set Function expression = 1
+    end
+  end
+  subsection bc 1
+    set id   = 2
+    set type = slip
+  end
+  subsection bc 2
+    set id   = 3
+    set type = slip
+  end
+end
+
+subsection boundary conditions tracer
+  set number = 4
+  subsection bc 0
+    set id   = 0
+    set type = dirichlet
+    subsection dirichlet
+      set Function expression = 1
+    end
+  end
+  subsection bc 1
+    set id   = 1
+    set type = outlet
+  end
+  subsection bc 2
+    set id   = 2
+    set type = outlet
+  end
+  subsection bc 3
+    set id   = 3
+    set type = outlet
+  end
+end
+
+subsection non-linear solver
+  subsection tracer
+    set verbosity      = quiet
+    set tolerance      = 1e-9
+    set max iterations = 1
+  end
+  subsection fluid dynamics
+    set verbosity      = quiet
+    set tolerance      = 1e-9
+    set max iterations = 1
+  end
+end
+
+subsection linear solver
+  subsection fluid dynamics
+    set verbosity                             = quiet
+    set method                                = gmres
+    set max iters                             = 100
+    set relative residual                     = 1e-13
+    set minimum residual                      = 1e-14
+    set preconditioner                        = ilu
+    set ilu preconditioner fill               = 0
+    set ilu preconditioner absolute tolerance = 1e-14
+    set ilu preconditioner relative tolerance = 1.00
+  end
+  subsection tracer
+    set verbosity                             = quiet
+    set method                                = gmres
+    set max iters                             = 300
+    set max krylov vectors                    = 300
+    set relative residual                     = 1e-9
+    set minimum residual                      = 1e-9
+    set preconditioner                        = ilu
+    set ilu preconditioner fill               = 0
+    set ilu preconditioner absolute tolerance = 1e-14
+    set ilu preconditioner relative tolerance = 1.00
+  end
+end

applications_tests/lethe-fluid/dg_tracer_circular_advection.mpirun=2.output

@@ -0,0 +1,39 @@
+Running on 2 MPI rank(s)...
+   Number of active cells:       64
+   Number of degrees of freedom: 243
+   Volume of triangulation:      1
+   Number of tracer degrees of freedom: 256
+
+*****************************
+Steady iteration:        1/3
+*****************************
+L2 error velocity : 1.63299
+L2 error tracer : 0.00354869
+
+*****************************
+Steady iteration:        2/3
+*****************************
+   Number of active cells:       256
+   Number of degrees of freedom: 867
+   Volume of triangulation:      1
+   Number of tracer degrees of freedom: 1024
+L2 error velocity : 1.63299
+L2 error tracer : 0.000434047
+
+*****************************
+Steady iteration:        3/3
+*****************************
+   Number of active cells:       1024
+   Number of degrees of freedom: 3267
+   Volume of triangulation:      1
+   Number of tracer degrees of freedom: 4096
+L2 error velocity : 1.63299
+L2 error tracer : 2.77243e-05
+cells   error_velocity    error_pressure  
+   64 1.632993e+00     - 0.000000e+00   - 
+  256 1.632993e+00 0.00 0.000000e+00 nan 
+ 1024 1.632993e+00  0.00 0.000000e+00 nan 
+cells   error_tracer    
+   64 3.548693e-03    - 
+  256 4.340470e-04 3.03 
+ 1024 2.772428e-05 3.97