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Added homogeneous and heterogeneous first order reactions for tracer (chaos-polymtl#1411)
Description The tracer physics needed one new assembler and two new reaction constant models to take into account simple reactions where only one reactive species is considered. This PR adds this feature, with documentation and application tests of homogeneous and heterogeneous first order reactions. Testing 3 new tests are added, that test the features both with and without solid, and with the discontinuous Galerkin formulation as well. [lethe-fluid/tracer_first_order_reaction_homogeneous] [lethe-fluid/tracer_first_order_reaction_homogeneous_dg] [lethe-fluid-sharp/tracer_first_order_reaction_heterogeneous] Documentation The new parameters are documented. Co-authored-by: Bruno Blais <[email protected]> Co-authored-by: mivaia <[email protected]> Co-authored-by: hepap <[email protected]>
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‎CHANGELOG.md‎

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All notable changes to the Lethe project will be documented in this file.
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The format is based on [Keep a Changelog](http://keepachangelog.com/).
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## [Master] - 2025-02-22
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### Added
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- MINOR In the tracer physics, a new feature is added that allows to take into account single species reaction of arbitrary reaction constant and order. This feature works in CG or DG, with or without immersed solids. [#1411](https://github.com/chaos-polymtl/lethe/pull/1411)
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## [Master] - 2025-02-20
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### Added

‎applications_tests/lethe-fluid-sharp/mms_tracer_reaction_heterogeneous.output‎

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Running on 1 MPI rank(s)...
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Number of active cells: 1024
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Number of degrees of freedom: 3267
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Volume of triangulation: 1
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Number of tracer degrees of freedom: 1089
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*****************************
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Steady iteration: 1/3
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*****************************
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div u : 3.22831e-09
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error at the weak BC : 0.000732218
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L2 error velocity : 0.00107872 L2 error pressure: 0.0119908
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L2 error tracer: 2.46686e-06
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*****************************
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Steady iteration: 2/3
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*****************************
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Number of active cells: 4096
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Number of degrees of freedom: 12675
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Volume of triangulation: 1
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Number of tracer degrees of freedom: 4225
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div u : -3.03625e-08
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error at the weak BC : 0.000187088
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L2 error velocity : 0.000275274 L2 error pressure: 0.00423168
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L2 error tracer: 4.47348e-07
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*****************************
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Steady iteration: 3/3
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*****************************
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Number of active cells: 16384
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Number of degrees of freedom: 49923
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Volume of triangulation: 1
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Number of tracer degrees of freedom: 16641
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div u : 2.93362e-10
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error at the weak BC : 4.74152e-05
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L2 error velocity : 7.0998e-05 L2 error pressure: 0.00140056
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L2 error tracer: 9.70565e-08
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cells error_velocity error_pressure
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1024 1.078724e-03 - 1.199081e-02 -
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4096 2.752737e-04 1.97 4.231680e-03 1.50
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16384 7.099801e-05 1.96 1.400565e-03 1.60
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cells error_tracer
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1024 2.466861e-06 -
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4096 4.473484e-07 2.46
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16384 9.705649e-08 2.20

‎applications_tests/lethe-fluid-sharp/mms_tracer_reaction_heterogeneous.prm‎

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# SPDX-FileCopyrightText: Copyright (c) 2025 The Lethe Authors
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# SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception OR LGPL-2.1-or-later
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# This MMS tests a 1.5-order heterogeneous reaction across a disk.
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set dimension = 2
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subsection simulation control
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set method = steady
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set output frequency = 0
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set number mesh adapt = 2
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end
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subsection multiphysics
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set fluid dynamics = true
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set tracer = true
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end
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subsection FEM
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set velocity order = 1
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set pressure order = 1
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set tracer order = 1
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end
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subsection mesh
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set type = dealii
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set grid type = subdivided_hyper_rectangle
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set grid arguments = 1, 1: 0, 0: 1, 1 : true
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set initial refinement = 5
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end
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subsection mesh adaptation
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set type = uniform
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end
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subsection boundary conditions
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set number = 4
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subsection bc 0
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set id = 0
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set type = function weak
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end
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subsection bc 1
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set id = 1
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set type = function weak
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end
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subsection bc 2
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set id = 2
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set type = function weak
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end
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subsection bc 3
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set id = 3
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set type = function weak
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end
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end
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subsection boundary conditions tracer
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set number = 4
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set time dependent = false
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subsection bc 0
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set id = 0
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set type = dirichlet
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subsection dirichlet
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set Function expression = (sin(pi*x)*cos(pi*y) + 1)*(0.5*tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0) + 0.5)/2
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end
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end
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subsection bc 1
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set id = 1
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set type = dirichlet
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subsection dirichlet
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set Function expression = (sin(pi*x)*cos(pi*y) + 1)*(0.5*tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0) + 0.5)/2
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end
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end
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subsection bc 2
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set id = 2
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set type = dirichlet
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subsection dirichlet
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set Function expression = (sin(pi*x)*cos(pi*y) + 1)*(0.5*tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0) + 0.5)/2
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end
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end
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subsection bc 3
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set id = 3
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set type = dirichlet
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subsection dirichlet
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set Function expression = (sin(pi*x)*cos(pi*y) + 1)*(0.5*tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0) + 0.5)/2
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end
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end
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end
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subsection initial conditions
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set type = nodal
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subsection uvwp
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set Function expression = (((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*x)^2*sin(pi*y)*cos(pi*y); -(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*x)*sin(pi*y)^2*cos(pi*x); sin(pi*x) + sin(pi*y)
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end
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subsection tracer
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set Function expression = (sin(pi*x)*cos(pi*y) + 1)*(0.5*tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0) + 0.5)/2
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end
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end
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subsection particles
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set assemble Navier-Stokes inside particles = true
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set number of particles = 1
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subsection particle info 0
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set type = sphere
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set shape arguments = 0.1
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subsection position
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set Function expression = 0.5; 0.5
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end
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end
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end
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subsection physical properties
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set number of fluids = 1
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subsection fluid 0
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set tracer diffusivity model = immersed solid tanh
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set tracer reaction constant model = immersed solid tanh
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set tracer reaction order = 1.5
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subsection immersed solid tanh
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set tracer diffusivity inside = 1
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set tracer diffusivity outside = 1
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set tracer reaction constant inside = 9.86960440109
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set tracer reaction constant outside = 0
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set thickness = 0.1
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end
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end
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end
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subsection analytical solution
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set enable = true
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set verbosity = verbose
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subsection uvwp
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set Function expression = (((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*x)^2*sin(pi*y)*cos(pi*y); -(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*x)*sin(pi*y)^2*cos(pi*x); sin(pi*x) + sin(pi*y)
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end
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subsection tracer
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set Function expression = (sin(pi*x)*cos(pi*y) + 1)*(0.5*tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0) + 0.5)/2
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end
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end
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subsection source term
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subsection tracer
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set Function expression = 0.353553390593274*((sin(pi*x)*cos(pi*y) + 1)*(0.5*tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0) + 0.5))^1.5*(-pi^2*(0.5*tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0) + 0.5) + pi^2) + (2.5*(1 - tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0)^2)*(1.0*x - 0.5)*(sin(pi*x)*cos(pi*y) + 1)/((x - 0.5)^2 + (y - 0.5)^2)^0.5 + pi*(0.5*tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0) + 0.5)*cos(pi*x)*cos(pi*y)/2)*(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*x)^2*sin(pi*y)*cos(pi*y) - (2.5*(1 - tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0)^2)*(1.0*y - 0.5)*(sin(pi*x)*cos(pi*y) + 1)/((x - 0.5)^2 + (y - 0.5)^2)^0.5 - pi*(0.5*tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0) + 0.5)*sin(pi*x)*sin(pi*y)/2)*(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*x)*sin(pi*y)^2*cos(pi*x) - (-10.0*pi*(1.0*x - 0.5)*(tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0)^2 - 1)*cos(pi*x)*cos(pi*y)/((x - 0.5)^2 + (y - 0.5)^2)^0.5 + (sin(pi*x)*cos(pi*y) + 1)*(tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0)^2 - 1)*(5.0*(1.0*x - 0.5)^2/((x - 0.5)^2 + (y - 0.5)^2)^1.5 + 100.0*(1.0*x - 0.5)^2*tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0)/((x - 0.5)^2 + (y - 0.5)^2)^1.0 - 5.0/((x - 0.5)^2 + (y - 0.5)^2)^0.5) - 0.5*pi^2*(tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0) + 1)*sin(pi*x)*cos(pi*y))/2 - (10.0*pi*(1.0*y - 0.5)*(tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0)^2 - 1)*sin(pi*x)*sin(pi*y)/((x - 0.5)^2 + (y - 0.5)^2)^0.5 + (sin(pi*x)*cos(pi*y) + 1)*(tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0)^2 - 1)*(5.0*(1.0*y - 0.5)^2/((x - 0.5)^2 + (y - 0.5)^2)^1.5 + 100.0*(1.0*y - 0.5)^2*tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0)/((x - 0.5)^2 + (y - 0.5)^2)^1.0 - 5.0/((x - 0.5)^2 + (y - 0.5)^2)^0.5) - 0.5*pi^2*(tanh(10.0*((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 1.0) + 1)*sin(pi*x)*cos(pi*y))/2
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end
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subsection fluid dynamics
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set Function expression = ((1.0*x - 0.5)*sin(pi*x)^2*sin(pi*y)*cos(pi*y)/((x - 0.5)^2 + (y - 0.5)^2)^0.5 + 2*pi*(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*x)*sin(pi*y)*cos(pi*x)*cos(pi*y))*(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*x)^2*sin(pi*y)*cos(pi*y) - (((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*((1.0*y - 0.5)*sin(pi*x)^2*sin(pi*y)*cos(pi*y)/((x - 0.5)^2 + (y - 0.5)^2)^0.5 - pi*(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*x)^2*sin(pi*y)^2 + pi*(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*x)^2*cos(pi*y)^2)*sin(pi*x)*sin(pi*y)^2*cos(pi*x) - (4*pi*(1.0*x - 0.5)*sin(pi*x)*cos(pi*x)/((x - 0.5)^2 + (y - 0.5)^2)^0.5 - ((1.0*x - 0.5)^2/((x - 0.5)^2 + (y - 0.5)^2)^1.5 - 1.0/((x - 0.5)^2 + (y - 0.5)^2)^0.5)*sin(pi*x)^2 - 2*pi^2*(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*(sin(pi*x)^2 - cos(pi*x)^2))*sin(pi*y)*cos(pi*y) - (-2*pi*(1.0*y - 0.5)*sin(pi*y)^2/((x - 0.5)^2 + (y - 0.5)^2)^0.5 + 2*pi*(1.0*y - 0.5)*cos(pi*y)^2/((x - 0.5)^2 + (y - 0.5)^2)^0.5 - ((1.0*y - 0.5)^2/((x - 0.5)^2 + (y - 0.5)^2)^1.5 - 1.0/((x - 0.5)^2 + (y - 0.5)^2)^0.5)*sin(pi*y)*cos(pi*y) - 4*pi^2*(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*y)*cos(pi*y))*sin(pi*x)^2 + pi*cos(pi*x); -(-(1.0*y - 0.5)*sin(pi*x)*sin(pi*y)^2*cos(pi*x)/((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 2*pi*(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*x)*sin(pi*y)*cos(pi*x)*cos(pi*y))*(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*x)*sin(pi*y)^2*cos(pi*x) + (((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*(-(1.0*x - 0.5)*sin(pi*x)*sin(pi*y)^2*cos(pi*x)/((x - 0.5)^2 + (y - 0.5)^2)^0.5 + pi*(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*x)^2*sin(pi*y)^2 - pi*(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*y)^2*cos(pi*x)^2)*sin(pi*x)^2*sin(pi*y)*cos(pi*y) - (-4*pi*(1.0*y - 0.5)*sin(pi*y)*cos(pi*y)/((x - 0.5)^2 + (y - 0.5)^2)^0.5 + ((1.0*y - 0.5)^2/((x - 0.5)^2 + (y - 0.5)^2)^1.5 - 1.0/((x - 0.5)^2 + (y - 0.5)^2)^0.5)*sin(pi*y)^2 + 2*pi^2*(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*(sin(pi*y)^2 - cos(pi*y)^2))*sin(pi*x)*cos(pi*x) - (2*pi*(1.0*x - 0.5)*sin(pi*x)^2/((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 2*pi*(1.0*x - 0.5)*cos(pi*x)^2/((x - 0.5)^2 + (y - 0.5)^2)^0.5 + ((1.0*x - 0.5)^2/((x - 0.5)^2 + (y - 0.5)^2)^1.5 - 1.0/((x - 0.5)^2 + (y - 0.5)^2)^0.5)*sin(pi*x)*cos(pi*x) + 4*pi^2*(((x - 0.5)^2 + (y - 0.5)^2)^0.5 - 0.1)*sin(pi*x)*cos(pi*x))*sin(pi*y)^2 + pi*cos(pi*y); (1.0*x - 0.5)*sin(pi*x)^2*sin(pi*y)*cos(pi*y)/((x - 0.5)^2 + (y - 0.5)^2)^0.5 - (1.0*y - 0.5)*sin(pi*x)*sin(pi*y)^2*cos(pi*x)/((x - 0.5)^2 + (y - 0.5)^2)^0.5
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end
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end
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subsection non-linear solver
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subsection fluid dynamics
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set verbosity = quiet
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set tolerance = 1e-6
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set max iterations = 10
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end
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subsection tracer
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set verbosity = quiet
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set tolerance = 1e-6
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set max iterations = 10
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end
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end
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subsection linear solver
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subsection fluid dynamics
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set verbosity = quiet
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set method = gmres
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set relative residual = 1e-3
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set minimum residual = 1e-10
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set max krylov vectors = 200
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end
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subsection tracer
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set verbosity = quiet
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set method = gmres
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set relative residual = 1e-6
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set minimum residual = 1e-10
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end
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end

‎applications_tests/lethe-fluid/mms_tracer_reaction_homogeneous.output‎

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Running on 1 MPI rank(s)...
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Number of active cells: 256
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Number of degrees of freedom: 867
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Volume of triangulation: 1
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Number of tracer degrees of freedom: 289
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*****************************
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Steady iteration: 1/3
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*****************************
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L2 error velocity: 0.00380898
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L2 error tracer: 1.57375e-06
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*****************************
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Steady iteration: 2/3
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*****************************
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Number of active cells: 1024
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Number of degrees of freedom: 3267
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Volume of triangulation: 1
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Number of tracer degrees of freedom: 1089
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L2 error velocity: 0.000962316
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L2 error tracer: 9.81605e-08
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*****************************
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Steady iteration: 3/3
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*****************************
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Number of active cells: 4096
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Number of degrees of freedom: 12675
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Volume of triangulation: 1
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Number of tracer degrees of freedom: 4225
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L2 error velocity: 0.000241505
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L2 error tracer: 6.13192e-09
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cells error_velocity error_pressure
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256 3.808975e-03 - 1.772614e-02 -
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1024 9.623156e-04 1.98 5.122861e-03 1.79
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4096 2.415048e-04 1.99 1.490588e-03 1.78
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cells error_tracer
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256 1.573750e-06 -
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1024 9.816048e-08 4.00
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4096 6.131918e-09 4.00

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