Stochastic Backscatter Model for Grey Area Mitigation in Hybrid RANS-LES Simulations by AngPass · Pull Request #2572 · su2code/SU2

AngPass · 2025-09-16T10:34:22Z

Proposed Changes

Hybrid RANS-LES methods aim to leverage the strengths of both Reynolds-Averaged Navier-Stokes (RANS) approaches and Large Eddy Simulation (LES), applying RANS near solid walls for computational efficiency and LES in outer flow regions for improved fidelity. A persistent challenge in these techniques is the appearance of the so-called grey area—the transitional region between RANS and LES zones—which is characterized by the absence of resolved turbulence. This leads to degraded accuracy in capturing free shear layers. The Stochastic Backscatter Model (Kok, 2017) aims to mitigate this issue. The model introduces stochastic forcing terms into the momentum and total energy equations that emulate the backscatter of energy from unresolved (subgrid) scales to resolved scales. The random forcing is formulated as the curl of a stochastic vector potential, say $\underline\xi$. The latter must be constructed using a three-step procedure:

A vector of three mutually-uncorrelated normally-distributed random variables is generated at each node.
A Laplacian smoothing in space (Passariello, 2025) is performed on each component of this vector.
The smoothed fields are used as source terms in three stochastic differential equations (also known as Langevin equations). The latter are solved for the components of the vector potential $\underline\xi$.
The curl of $\underline\xi$ is added to the momentum and total energy equations as source term. This can be done modifying the definition of the modeled stress tensor.

References:

Kok, J. C. (2017). A stochastic backscatter model for grey-area mitigation in detached eddy simulations. Flow, Turbulence and Combustion, 99(1), 119-150.
Passariello, A. (2025). Stochastic Backscatter Model for Unstructured Solvers. arXiv preprint arXiv:2508.17958.

Roadmap

Modifying the definition of the modeled stress tensor using a stochastic contribution. As preliminary step, the vector of uncorrelated variables (point 1 in the procedure above) is employed.
Performing a smoothing on the uncorrelated variables. This requires the solution of a Laplace equation at the beginning of each step.
Implementing three additional equations for the components of the stochastic vector potential. These equations require the use of symmetry-preserving central scheme for the discretization of the convective terms (Kok, 2017).

Related Work

None.

PR Checklist

I am submitting my contribution to the develop branch.
My contribution generates no new compiler warnings (try with --warnlevel=3 when using meson).
My contribution is commented and consistent with SU2 style (https://su2code.github.io/docs_v7/Style-Guide/).
I used the pre-commit hook to prevent dirty commits and used pre-commit run --all to format old commits.
I have added a test case that demonstrates my contribution, if necessary.
I have updated appropriate documentation (Tutorials, Docs Page, config_template.cpp), if necessary.

The Reynolds stress tensor definition is modified to include a random contribution, which is expressed as the curl of a normally-distributed stochastic vector potential.

SU2_CFD/include/numerics/CNumerics.hpp

Add Langevin equations to Spalart-Allmaras solver (uncorrelated random source term) + add stochastic contribution to Reynolds stress tensor (using conservative variables from Langevin equations).

SU2_CFD/include/numerics/CNumerics.hpp

SU2_CFD/src/solvers/CTurbSASolver.cpp

SU2_CFD/src/variables/CTurbSAVariable.cpp

Fix sanitizer warnings and regression test failures - Address issues reported by clang sanitizers. - Adjust implementation to ensure regression tests pass.

- Enhance readability. - Ensure consistent declaration types.

- Extend implementation to 2D configurations. - Improve robustness.

Enforce boundary conditions in Langevin equations.

- Implement a skew-symmetric scheme for the discretization of the convective terms in the Langevin equations. - Fix the seed for the generation of the random source terms at the beginning of the simulation.

- Add the flag for the simulation of the Decaying Isotropic Homogeneous Turbulence. - Generate the initial velocity field matching the experimental data by Comte-Bellot & Corrsin. - Include a preliminary test case.

- Implement flag to enforce LES in the whole domain. - Add option to set the LES filter width to a user-specified value. - Add velocity divergence to volume outputs. - Remove internal generation of initial velocity field for simulating the Decaying Isotropic Homogeneous Turbulence (DIHT).

- Add consistent evaluation of the turbulent kinetic energy in the random source term appearing in the momentum equations. - Add backscatter intensity coefficient in the configuration file. - Add random initialization of the Langevin variables.

- Add Laplacian smoothing of source terms in Langevin equations. Remark: pseudo-time integration is employed (residuals are printed on screen with fixed frequency, the maximum number of time iterations can be defined by the user).

- Fix redundancy in virtual member definition.

- Add stochastic source term to Spalart-Allmaras turbulence model equation (to ensure exchange of modeled and resolved kinetic energy).

- Replace dual-time integration with Successive Over-Relaxation for Laplacian smoothing. - Initialize stochastic vector potential as equal to the stochastic source terms in Langevin equations. - Add random source term to main balance equations in LES zones exclusively. - Blend RANS and LES turbulence timescales using the LES sensor.

- Scale source terms in Langevin equations using Bessel functions to preserve the variance. - Compute Bessel integral at the beginning of the simulation for optimization. - Add variance monitoring to screen output.

- Add the option to apply the backscatter model only in a bounded box. - Add the option to enforce backscatter where shielding function exceeds user-defined value. - Correct bug in LD2 implementation. - Make style consistent and update configuration template.

- Modify the scaling of the stochastic forcing to include the modeled viscosity. - Fix the computation of the stochastic tensor. - Add the MPI communication of the DES lengthscale.

Remove outdated configuration file.

- Add the stochastic variables (from Langevin equations) to the restart file. - Optimize the definition of the points lying inside the box where the backscatter model is active. - Limit the turbulence time scale in RANS regions (Langevin equations). - Add test case: spatially-developing mixing layer.

AngPass · 2026-03-10T09:48:55Z

@pcarruscag I added the cfg file of a test case (i.e., the spatially-developing mixing layer). Should I open a separate pull request under Test Cases to upload the grid, or is it fine to include everything here?

pcarruscag · 2026-03-10T13:44:27Z

Large files in testcases please.

AngPass · 2026-03-16T15:15:23Z

Large files in testcases please.

@pcarruscag I uploaded the grid for the proposed test case (i.e., the backward-facing step). I had to compress it. The reference pull request in the TestCases repo is su2code/TestCases#187.

The code is now ready for review.

pcarruscag · 2026-03-16T15:43:30Z

Add a regression test to parallel_regression.py, you'll probably need to do something custom to decompress the file.
It would be good to make it a bit smaller if possible too.

Common/include/toolboxes/random_toolbox.hpp

pcarruscag · 2026-03-17T02:39:17Z

SU2_CFD/src/solvers/CTurbSASolver.cpp

+         su2double Res_Wall[MAXNVAR] = {0.0};
+         Res_Wall[0] = coeff*RoughWallBC*Area;
+         LinSysRes.SubtractBlock(iPoint, Res_Wall);


Revert and use LinSysRes(iPoint, 0) -= Res_Wall;

pcarruscag · 2026-03-17T02:39:48Z

SU2_CFD/src/solvers/CTurbSASolver.cpp

-         su2double Jacobian_i = (laminar_viscosity /density *Area)/(0.03*Roughness_Height*sigma);
-         Jacobian_i += 2.0*RoughWallBC*Area/sigma;
-         if (implicit) Jacobian.AddVal2Diag(iPoint, -Jacobian_i);
+         Jacobian_i[0][0] = (laminar_viscosity /density *Area)/(0.03*Roughness_Height*sigma);
+         Jacobian_i[0][0] += 2.0*RoughWallBC*Area/sigma;


revert, just your last change to this part is enough to make it compatible right?

SU2_CFD/src/solvers/CTurbSASolver.cpp

pcarruscag · 2026-03-17T02:47:07Z

SU2_CFD/src/solvers/CTurbSASolver.cpp

+        su2double mean_check_new = 0.0;
+        su2double var_check_notSmoothed = 0.0;
+        su2double mean_check_notSmoothed = 0.0;
+        for (unsigned long iPoint = 0; iPoint < nPointDomain; iPoint++) {


There is some OpenMP stuff missing; I can help with that later.

pcarruscag · 2026-03-17T02:47:46Z

Post some results you obtained with this implementation please.

Co-authored-by: Pedro Gomes <38071223+pcarruscag@users.noreply.github.com>

AngPass and others added 2 commits September 15, 2025 18:26

Preliminary implementation: uncorrelated stochastic variables

36b6f7a

The Reynolds stress tensor definition is modified to include a random contribution, which is expressed as the curl of a normally-distributed stochastic vector potential.

Merge branch 'su2code:develop' into develop

d6d6e39

pcarruscag reviewed Sep 18, 2025

View reviewed changes

SU2_CFD/include/numerics/CNumerics.hpp Outdated Show resolved Hide resolved

AngPass and others added 2 commits September 23, 2025 10:12

Add solution of Langevin equations

cfa0cd8

Add Langevin equations to Spalart-Allmaras solver (uncorrelated random source term) + add stochastic contribution to Reynolds stress tensor (using conservative variables from Langevin equations).

Merge branch 'develop' into develop

fd800d3

pcarruscag changed the title ~~Stochastic Backscatter Model for Grey Area Mitigation in Hybrid RANS-LES Simulations~~ [WIP] Stochastic Backscatter Model for Grey Area Mitigation in Hybrid RANS-LES Simulations Sep 23, 2025

bigfooted added the changelog:feature label Sep 23, 2025

github-advanced-security bot found potential problems Sep 23, 2025

View reviewed changes

SU2_CFD/include/numerics/CNumerics.hpp Fixed Show fixed Hide fixed

SU2_CFD/include/numerics/CNumerics.hpp Fixed Show fixed Hide fixed

SU2_CFD/src/solvers/CTurbSASolver.cpp Fixed Show fixed Hide fixed

SU2_CFD/src/variables/CTurbSAVariable.cpp Fixed Show fixed Hide fixed

AngPass and others added 22 commits September 24, 2025 11:05

Fix sanitizer warnings and regression failures

34f676f

Fix sanitizer warnings and regression test failures - Address issues reported by clang sanitizers. - Adjust implementation to ensure regression tests pass.

Minor fixes

66293fd

- Enhance readability. - Ensure consistent declaration types.

Merge branch 'develop' into develop

4a11c8b

Ensure consistency with DES

3481df3

- Extend implementation to 2D configurations. - Improve robustness.

Merge branch 'develop' into develop

26bcfda

Boundary conditions for Langevin equations

85b8aac

Enforce boundary conditions in Langevin equations.

Use symmetry-preserving scheme for Langevin equations

6293042

- Implement a skew-symmetric scheme for the discretization of the convective terms in the Langevin equations. - Fix the seed for the generation of the random source terms at the beginning of the simulation.

Merge branch 'develop' into develop

b03f630

Add option for simulating DIHT

1e8e4e1

- Add the flag for the simulation of the Decaying Isotropic Homogeneous Turbulence. - Generate the initial velocity field matching the experimental data by Comte-Bellot & Corrsin. - Include a preliminary test case.

Merge branch 'develop' into develop

25a32f7

Merge branch 'develop' into develop

e1181d3

Add Laplacian smoothing (Langevin equations)

968d8f9

- Add Laplacian smoothing of source terms in Langevin equations. Remark: pseudo-time integration is employed (residuals are printed on screen with fixed frequency, the maximum number of time iterations can be defined by the user).

Fix redundancy in CTurbSAVariable.hpp

2f8245e

- Fix redundancy in virtual member definition.

Add stochastic source to turbulence model equation

bdbfa05

- Add stochastic source term to Spalart-Allmaras turbulence model equation (to ensure exchange of modeled and resolved kinetic energy).

Merge branch 'develop' into develop

7457d95

Merge branch 'su2code:develop' into develop

ddb99bf

Correct scaling of stochastic source terms in Langevin eqs.

15dbff3

- Scale source terms in Langevin equations using Bessel functions to preserve the variance. - Compute Bessel integral at the beginning of the simulation for optimization. - Add variance monitoring to screen output.

Merge branch 'su2code:develop' into develop

4dd0f90

Merge branch 'su2code:develop' into develop

d93ed49

paan882 and others added 6 commits February 13, 2026 17:25

Add new features

dc5189d

- Add the option to apply the backscatter model only in a bounded box. - Add the option to enforce backscatter where shielding function exceeds user-defined value. - Correct bug in LD2 implementation. - Make style consistent and update configuration template.

Merge branch 'develop' into develop

6598226

Merge branch 'develop' into develop

6515a53

Merge branch 'develop' into develop

0a0f348

Redefine scaling of stochastic source term

cb91b8e

- Modify the scaling of the stochastic forcing to include the modeled viscosity. - Fix the computation of the stochastic tensor. - Add the MPI communication of the DES lengthscale.

Update config template

190a1cc

AngPass marked this pull request as ready for review March 2, 2026 11:03

AngPass marked this pull request as draft March 2, 2026 11:04

AngPass and others added 3 commits March 4, 2026 15:21

Delete TestCases/backscatter/DIHT directory

e6b9937

Remove outdated configuration file.

Merge branch 'develop' into develop

af37287

AngPass and others added 2 commits March 16, 2026 15:36

Merge branch 'develop' into develop

692e87a

Change proposed test case

3e49b9b

AngPass mentioned this pull request Mar 16, 2026

Test Case for Stochastic Backscatter Model su2code/TestCases#187

Open

pcarruscag marked this pull request as ready for review March 16, 2026 15:41

pcarruscag changed the title ~~[WIP] Stochastic Backscatter Model for Grey Area Mitigation in Hybrid RANS-LES Simulations~~ Stochastic Backscatter Model for Grey Area Mitigation in Hybrid RANS-LES Simulations Mar 16, 2026

pcarruscag reviewed Mar 17, 2026

View reviewed changes

AngPass and others added 8 commits March 27, 2026 17:39

Merge branch 'develop' into develop

3d4bcb4

Update Common/include/toolboxes/random_toolbox.hpp

fcbca34

Co-authored-by: Pedro Gomes <38071223+pcarruscag@users.noreply.github.com>

Update Common/include/toolboxes/random_toolbox.hpp

d3e8e31

Co-authored-by: Pedro Gomes <38071223+pcarruscag@users.noreply.github.com>

Update SU2_CFD/src/solvers/CTurbSASolver.cpp

6500ddd

Co-authored-by: Pedro Gomes <38071223+pcarruscag@users.noreply.github.com>

Update SU2_CFD/src/solvers/CTurbSASolver.cpp

5459137

Co-authored-by: Pedro Gomes <38071223+pcarruscag@users.noreply.github.com>

Update SU2_CFD/include/numerics/turbulent/turb_sources.hpp

f633f7b

Co-authored-by: Pedro Gomes <38071223+pcarruscag@users.noreply.github.com>

Update SU2_CFD/src/numerics/flow/convection/centered.cpp

5203d3f

Co-authored-by: Pedro Gomes <38071223+pcarruscag@users.noreply.github.com>

Update SU2_CFD/src/solvers/CTurbSASolver.cpp

f4b2fa1

Co-authored-by: Pedro Gomes <38071223+pcarruscag@users.noreply.github.com>

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AngPass commented Sep 16, 2025 •

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