Add radial DG discretization by jbreue16 · Pull Request #609 · cadet/CADET-Core

jbreue16 · 2026-03-09T09:58:10Z

This PR adds an arbitrary order DG discretization for the radial flow models

Todo

Implementation of radial DG with its own convection dispersion operator, similar to FV
Incorporation of this operator in the ColumnModel1D unit
Incorporation of this operator in the LRM DG unit
Add tests
- Add radial DG EOC tests CADET-Verification#144
- C++ tests in CADET-Core. This will only be done after the python EOC tests
Add documentation

jbreue16 · 2026-03-09T10:00:24Z

Hi Yuvj, now that you have already implemented rLRMP and rGRM as separate units, I think you can first (EOC) test this in pyhton before refactoring into the ColumnModel1D.
Also, there are a couple of unrelated changes.

Yuvraj2710 · 2026-03-30T15:58:59Z

CADET-Verification EOC tests for radial DG: Yuvraj2710/CADET-Verification@radialDG-verification

Tests radial DG convergence (polyDeg 2-5) with constant and variable dispersion (RADIAL_POWER_LAW) using the CADET-Verification framework. All polynomial degrees achieve expected convergence order.

Yuvraj2710 · 2026-03-31T09:19:30Z

Hi @jbreue16, I suppose this impl. of DG radial flow is working, and is ready for a review. I'll remove the rLRMP and rGRM which are as separate units currently, but there's also with ColumnModel1D.

jbreue16

Hi Yuvj, can you show me the convergence results and are they using a FV reference?

Yuvraj2710 · 2026-03-31T11:05:34Z

EOC Convergence Verification — Radial DG Bulk Transport

Ran EOC tests for radial DG (bulk transport only, rLRM no binding) using the CADET-Verification benchmark parameters (r_in=0.01, r_out=0.1, ε=1.0, D=1e-6, v=5e-5, rectangular pulse).

Time integrator tolerances: ABSTOL=1e-12, ALGTOL=1e-12, RELTOL=1e-10.

CADET-Core DG vs FV WENO3 reference (Z=262,144):

P1 (expected order 2):

nElem	nDOFs	L2 error	Linf error	Linf EOC
1	2	7.62e-02	1.65e-01	—
2	4	5.27e-02	1.19e-01	0.47
4	8	2.71e-02	7.41e-02	0.68
8	16	8.94e-03	2.72e-02	1.44
16	32	2.20e-03	7.02e-03	1.96
32	64	5.21e-04	1.68e-03	2.06
64	128	1.26e-04	4.06e-04	2.05
128	256	3.07e-05	9.96e-05	2.03

P2 (expected order 3):

nElem	nDOFs	L2 error	Linf error	Linf EOC
1	3	7.16e-02	1.56e-01	—
2	6	3.66e-02	8.69e-02	0.85
4	12	8.87e-03	2.44e-02	1.83
8	24	7.07e-04	2.28e-03	3.42
16	48	2.77e-05	9.40e-05	4.60
32	96	8.99e-07	3.03e-06	4.95
64	192	2.66e-08	8.90e-08	5.09
128	384	7.15e-10	2.55e-09	5.13

P3 (expected order 4):

nElem	nDOFs	L2 error	Linf error	Linf EOC
1	4	6.29e-02	1.77e-01	—
2	8	2.18e-02	5.66e-02	1.65
4	16	1.61e-03	4.94e-03	3.52
8	32	2.49e-05	8.02e-05	5.95
16	64	3.75e-07	1.18e-06	6.08
32	128	5.94e-09	1.79e-08	6.05
64	256	1.95e-10	4.18e-10	5.42
128	512	9.28e-10	2.57e-09	-2.62

P4 (expected order 5):

nElem	nDOFs	L2 error	Linf error	Linf EOC
1	5	5.31e-02	1.50e-01	—
2	10	1.08e-02	2.99e-02	2.33
4	20	1.83e-04	5.88e-04	5.67
8	40	9.01e-07	3.61e-06	7.35
16	80	4.50e-09	1.45e-08	7.96
32	160	1.06e-10	3.71e-10	5.29
64	320	6.77e-10	1.94e-09	-2.39
128	640	8.12e-10	2.18e-09	-0.16

P5 (expected order 6):

nElem	nDOFs	L2 error	Linf error	Linf EOC
1	6	4.29e-02	1.41e-01	—
2	12	4.57e-03	1.33e-02	3.41
4	24	2.35e-05	8.66e-05	7.26
8	48	3.95e-08	1.27e-07	9.42
16	96	1.78e-10	5.47e-10	7.86
32	192	1.78e-10	4.10e-10	0.41
64	384	9.95e-10	2.88e-09	-2.81
128	768	3.07e-10	9.75e-10	1.56

jbreue16 · 2026-03-31T11:30:09Z

Two things that are weird here: EOC is unexpectedly high sometimes, e.g. 8.34 for P4, and convergence stops at around 1e-8.
Did you check that the outlet profile is something meaningful? Otherwise I don't have an idea how the EOC can be that high.

But the most relevant issue is convergence stopping at 1e-8. Can you set time integration tolerances abstol=1e-12 and reltol=1e-10 and use a WENO FV reference with error <= 1e-10 ?

Yuvraj2710 · 2026-03-31T11:45:22Z

Yes I did took tolerances to ABSTOL=1e-12, RELTOL=1e-10. The ~4e-9 (L_2 error) floor is the FV Z=10,000 reference accuracy. I can generate a Z=100k FV reference if needed.

jbreue16 · 2026-03-31T14:16:02Z

radCOL1D_transport_1comp_WENO3_benchmark1_FV_Z262144.zip

I have attached a reference solution with at least 7e-11 accuracy (262.144 cells) which you can use as reference. You can fix cadet/CADET-Verification#110 first and then compute the EOC for DG again

Yuvraj2710 · 2026-04-01T08:24:47Z

radCOL1D_transport_1comp_WENO3_benchmark1_FV_Z262144.zip

I have attached a reference solution with at least 7e-11 accuracy (262.144 cells) which you can use as reference. You can fix cadet/CADET-Verification#110 first and then compute the EOC for DG again

Just updated the EOC results

jbreue16

Im very happy to see the great progress here.
Just reviewing this large PR on GitHub wasn't enough so I went into the code and addressed some issues myself. This PR needs a lot of clean-up and some fixes and needs to be rebased, force pushed. Thus, I made a backup branch: https://github.com/cadet/CADET-Core/tree/back_up/DGRadialFeature
Please read through the changes I made below and tell me if you disagree with any of this

The commits were not separated cleanly, there was stuff all over the place. I think its best to create two big PR's out of this: 1) radial DG incorporated to ColumnModel1D and LumpedRateModelWithoutPoresDG, I think this can be merged fast. 2) adding variable coefficients, Ive seen some implementation issues here so that probably needs further refinement and we shouldn't wait with mergeing the rest, hence a separate PR.
I removed some unwanted changes like increase of default AD directions, PAR_DISC_TYPE was made optional. I suppose there was no clear intent behind those changes and they are artifacts from the long list of changes made.
I updated how the integration mode is handled, making this part more modular for the seamless use of another convDispOp: #644
#646 fix of input group for filmDiff parDep in LRMP_FV as independent PR, added fixed docs and test for surfDiff

jbreue16 · 2026-04-07T11:22:37Z

Hi @Yuvraj2710 please don't force push with squashes unless we agree to clean things up, such froce-pushes once I've started reviewing make it impossible for me to review. The final squash into one commit will happen at the very end, probably through the GitHub interface, not from a force push.

Ive kept the changes you force pushed in 5bb4f16 and 01ee54d, except for 1) the changes made to the ConvDispOp, which reintroduced an ambiguous interface that I removed and 2) the changes which falsely incorporated the rLRM into the ColumnModel1D. The rLRM should become part of the LRM_DG unit operation which is defined in LumpedRateModelWithoutPoresDG. We decided against the unification of this unit since it is structurally very different. The code you added would not work that way.

Copilot

Pull request overview

This PR adds an arbitrary-order discontinuous Galerkin (DG) spatial discretization for CADET’s radial-flow column models by introducing a dedicated radial DG convection–dispersion operator, wiring it into radial unit operations, and extending tests and documentation to cover the new discretization.

Changes:

Implement radial DG transport support (including rho-weighted mass matrices and variable-coefficient handling) and expose it through the existing DG operator framework.
Generalize ColumnModel1D and LumpedRateModelWithoutPoresDG to support axial vs radial DG via templated convection–dispersion operators, and update model selection/registration accordingly.
Add radial DG regression/reference tests, helper utilities, and JSON benchmark models; update radial-flow documentation to include DG configuration options.

Reviewed changes

Copilot reviewed 29 out of 37 changed files in this pull request and generated 6 comments.

Show a summary per file

File	Description
test/RadialLumpedRateModelWithPores.cpp	Adds extensive radial LRMP_DG CI test coverage (benchmarks, Jacobians, sensitivity, CI comparisons vs FV references).
test/RadialLumpedRateModelWithoutPores.cpp	Adds radial LRM_DG CI test coverage analogous to existing FV tests plus DG-vs-FV reference checks.
test/RadialGeneralRateModel.cpp	Adds radial GRM_DG CI tests, including parameter-dependence Jacobian checks and DG-vs-FV reference benchmark.
test/ParticleHelper.hpp	Extends arrowhead Jacobian helper API to accept a spatial method argument.
test/ParticleHelper.cpp	Implements the new spatial-method-aware arrowhead Jacobian helper.
test/JsonTestModels.cpp	Updates JSON model factories to correctly detect GRM/LRMP behavior for radial unit type strings and fixes frustum/radial parameter placement.
test/data/model_radLRMP_dynLin_1comp_sensbenchmark1.json	Updates LRMP benchmark model to use DG discretization settings.
test/data/model_radLRMP_DG_noBnd_1comp_eocbenchmark.json	Adds new DG model for EOC/benchmark comparisons (no binding).
test/data/model_radLRMP_DG_linBnd_1comp_eocbenchmark.json	Adds new DG model for EOC/benchmark comparisons (linear binding).
test/data/model_radLRM_dynLin_1comp_sensbenchmark1.json	Updates LRM benchmark model to use DG discretization settings.
test/data/model_radLRM_DG_noBnd_1comp_eocbenchmark.json	Adds new radial LRM DG model for EOC/benchmark comparisons (no binding).
test/data/model_radLRM_DG_linBnd_1comp_eocbenchmark.json	Adds new radial LRM DG model for EOC/benchmark comparisons (linear binding).
test/data/model_radGRM_dynLin_1comp_sensbenchmark1.json	Refactors GRM benchmark JSON structure and preserves FV settings while aligning with updated unit-type detection.
test/data/model_radGRM_DG_noBnd_1comp_eocbenchmark.json	Adds new radial GRM DG model for EOC/benchmark comparisons (no binding).
test/ColumnTests.hpp	Declares new radial DG benchmark/convergence helper test APIs.
test/ColumnTests.cpp	Implements radial DG vs FV reference comparison and self-convergence EOC helper.
test/ColumnModel1D.cpp	Adds radial ColumnModel1D DG test matrix (Jacobian, sensitivities, particle-type coverage, variable coefficient checks).
src/libcadet/model/parts/DGToolbox.hpp	Adds quadrature/node utilities (Chebyshev + Gauss) and radial DG helper declarations (weighted mass, radial dispersion matrix, basis derivative).
src/libcadet/model/parts/DGToolbox.cpp	Implements new quadrature/node utilities and radial dispersion matrix integration helper.
src/libcadet/model/parts/ConvectionDispersionOperatorDG.hpp	Introduces `RadialConvectionDispersionOperatorBaseDG` with radial DG residual/Jacobian scaffolding and flux handling.
src/libcadet/model/LumpedRateModelWithoutPoresDG.hpp	Templates the DG LRM unit on the convection–dispersion operator and adds a radial DG identifier.
src/libcadet/model/LumpedRateModelWithoutPoresDG.cpp	Refactors implementation to template form and explicitly instantiates axial + radial DG variants.
src/libcadet/model/ColumnModelBuilder.cpp	Enables radial DG unit selection and registers axial/radial DG models under appropriate identifiers.
src/libcadet/model/ColumnModel1D.hpp	Templates ColumnModel1D on the convection–dispersion operator, adds radial identifier mapping, and adds explicit extern template declarations.
src/libcadet/model/ColumnModel1D.cpp	Refactors ColumnModel1D implementation to template form and explicitly instantiates axial + radial DG variants.
src/libcadet/model/ColumnModel1D-LinearSolver.cpp	Updates linear solver methods to template form for the generalized ColumnModel1D.
src/libcadet/model/ColumnModel1D-InitialConditions.cpp	Updates initial-condition and sensitivity initialization code to template form for the generalized ColumnModel1D.
doc/interface/unit_operations/radial_flow_column_1D_config.rst	Documents DG as an available radial discretization method and adds DG-specific parameters and notes.

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+						std::vector<StateType> c_star(_nElem + 1);
+						std::vector<StateType> g_star(_nElem + 1);
+						std::vector<double> d_rad_i(_nElem + 1);
+
+						computeNumericalFluxesRadial<StateType, ParamType>(yBulk, d_rad, c_star, g_star, d_rad_i);


+				 *      b. Scale g by (2/Δρ)
+				 *      c. Compute numerical fluxes c*, g*
+				 *      d. Compute main equation Dc via surface + volume integrals


+				refValues.push_back(ref_outlet[i]);
+			}
+		}
+


- Add RadialLumpedRateModelWithoutPoresDG, RadialLumpedRateModelWithPoresDG, RadialGeneralRateModelDG with full residual, analytic Jacobian, and parameter sensitivity support - Extend ConvectionDispersionOperatorDG and DGToolbox for radial geometry - Register radial DG models in ColumnModelBuilder - Add EOC convergence tests for rLRM DG polyDeg 1-5 (all pass) - Add testRadialDGConvergence helper and reference benchmark infrastructure Co-authored-by: Jan Breuer <74359367+jbreue16@users.noreply.github.com>

…cibility

jbreue16 added feature request numerics labels Mar 9, 2026

github-project-automation Bot added this to CADET Repositories Mar 9, 2026

github-project-automation Bot moved this to Todo in CADET Repositories Mar 9, 2026

Yuvraj2710 force-pushed the DGRadialFeature branch from 2470a36 to 756efad Compare March 9, 2026 15:29

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Yuvraj2710 force-pushed the DGRadialFeature branch 2 times, most recently from eb9c111 to fe88c77 Compare March 16, 2026 16:37

jbreue16 mentioned this pull request Mar 17, 2026

Improve spatial numerical method for radial flow models #296

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Yuvraj2710 force-pushed the DGRadialFeature branch from d0c96f7 to 03f4cb7 Compare March 24, 2026 16:30

Yuvraj2710 marked this pull request as ready for review March 31, 2026 07:25

jbreue16 commented Mar 31, 2026

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jbreue16 mentioned this pull request Apr 1, 2026

Add radial DG EOC tests cadet/CADET-Verification#112

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Yuvraj2710 force-pushed the DGRadialFeature branch from d7b7177 to a8504a1 Compare April 7, 2026 10:14

jbreue16 force-pushed the DGRadialFeature branch from a8504a1 to 01ee54d Compare April 7, 2026 11:18

jbreue16 mentioned this pull request Apr 7, 2026

Bump version to 6.0.0a3 #656

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jbreue16 mentioned this pull request Jun 29, 2026

Add radial DG EOC tests cadet/CADET-Verification#144

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Yuvraj2710 and others added 20 commits June 29, 2026 15:47

Update integration mode, jacInlet handling

d5526e6

revert AD directions increase

c86bfb5

remove separate radial units

b98b643

remove unused operators (might become part of parDep PR)

261592c

fixup! remove jacInlet function again

1136656

3/2 rule for quadrature

c55972c

tests: work in progress

c0f37cf

LRM DG unit

acb9d59

Add radial DG reference data and align test tolerances with axial DG

b0724d6

Refine radial DG consistent-init tests to select binding/AD modes

2de5792

Relax radial DG numerical benchmark absTol for cross-platform reprodu…

4c7feee

…cibility

Add radial DG tests to CI

6b6a8ce

add smoothness indicator functions to radialConvDispOpDG

dfab64a

fix documentation

7138f89

update model builder

b0df607

wip improve testing

8ad4092

fixup! modelbuilder

0593fc5

wip tests

f8c1b9d

wip tests

0113e1d

jbreue16 force-pushed the DGRadialFeature branch from 27ef6af to 0113e1d Compare June 29, 2026 13:48

remove unnecessary stuff

e4a0dcd

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EOC Convergence Verification — Radial DG Bulk Transport

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