ECFD workshop, 6th edition, 2022
Contents
- 1 Description
- 2 Agenda
- 3 Thematics / Mini-workshops
- 4 Projects
- 4.1 Hackathon - G. Staffelbach, CERFACS & P. Begou, LEGI
- 4.2 Mesh adaptation - R. Letournel, Safran & V. Moureau, CORIA
- 4.3 Numerics - S. Mendez, IMAG & M. Bernard, LEGI
- 4.4 Turbulence - P. Benard, CORIA & G. Balarac, LEGI
- 4.5 Two Phase Flow - C. Merlin, Ariane Group & M. Cailler, Safran Tech
- 4.6 Combustion - K. Bioche, CORIA & R. Mercier, Safran Tech
- 4.7 User Experience - J. Leparoux, Safran Tech & A. Pushkarev, GE Renewable Energy
Description
- Event from 23th of January to 3rd of February 2023
- Location: Hôtel Club de la Plage, Merville-Franceville, near Caen (14)
- Two types of sessions:
- common technical presentations: roadmaps, specific points
- mini-workshops. Potential workshops are listed below
- Free of charge
- More than 60 participants from academics, HPC center/experts and industry.
- Objectives
- Bring together experts in high-performance computing, applied mathematics and multi-physics CFDs
- Identify the technological barriers of exaflopic CFD via numerical experiments
- Identify industrial needs and challenges in high-performance computing
- Propose action plans to add to the development roadmaps of the CFD codes
Agenda
Thematics / Mini-workshops
These mini-workshops may change and cover more or less topics. This page will be adapted according to your feedback.
Projects
Hackathon - G. Staffelbach, CERFACS & P. Begou, LEGI
Mesh adaptation - R. Letournel, Safran & V. Moureau, CORIA
- Sub-project 1: Mesh adaptation for vortical flows (MAVERICK) for coupled systems of differential-algebraic equations (L. Bricteux, G. Balarac, S. Zeoli, G. Lartigue)
This project is in the continuation of what has been investigated in the previous ECFD workshops. It aims to develop mesh adaptation strategies for DNS of vortical flows. Turbulent flows are vortical flows. It is thus of primary importance to capture the vorticity dynamics properly if one wants to obtain physically realistic results. As the vorticity field is compact, mesh adaptation allows to refine the mesh only where flow physics happens, in the same way a vortex particle-mesh method would do. The main findings gathered during ECFD6 are: 1/ Gmsh can produce high quality base mesh for AMR with Yales2, yet the proper choice of options is not trivial. 2/ Initial mesh should be as smooth as possible (low hgrad), which is really challenging for wall resolved turbulent wall bounded flows. 3/ Refinement sensor based on vorticity gradients (palenstrophy) seems to works fairly wel.l 4/ two levels strategy provides encouraging results
Numerics - S. Mendez, IMAG & M. Bernard, LEGI
- Sub-project 1: Multi-level domain decomposition method (DDM) for coupled systems of differential-algebraic equations (A. Quirós Rodrígues, V. Le Chenadec)
The numerical approximation of multi-physics problems gives rise to complex linear systems, the solution of which leverages preconditioning techniques such as multi-grid or domain decomposition methods. This project aimed at coupling two Julia packages that being actively developed: a two-dimensional Navier-Stokes solver for free-surface and two-phase flows (Flower.jl) on the other, and a Domain Decomposition package for Cartesian grids (DDM.jl). The decomposed matrix-vector product was optimised to reduce the overhead associated with halo exchanges. The implementation of a deflated Conjugate Gradient as well as one- and two-level Additive Schwartz Method were also completed and shown to significant reduce the number of iterations for inverting monolithic systems (i.e. without resorting to operator splitting), shown to be independent of the number of subdomains for constant property flows. Future work will focus on a further optimisation of the implementation for vectorisation and multi-threading, and extension of the deflation to generalised coarse spaces to support highly discontinuous transport properties (GenEO).
- Sub-project 2: Ghost fluid method (GFM) for Electrodeformation (A. Spadotto , S. Mendez)
According to the Leaky Dielectric Model, red blood cells (RBCs) are subject to a force which is proportional to the jump of the Maxwell tensor. This latter is a quantity scaling as the square of the electric field, which under the quasi-static hypothesis is defined as the gradient of the electrostatic potential. To work out the potential, an elliptic interface problem must be solved, taking into account the presence of the RBC membrane. The aim of the project was implementing the Ghost Fluid Method (GFM) to face the interface problem. Good results were obtained on unstructured meshes. Secondly, a gradient calculation was performed applying the Green-Gauss scheme, modified in the style of the GFM. Future work will focus on interpolation of the gradient field onto the membrane to get an estimation of the effort. Possibly, high-order schemes for the gradient calculation will be explored. In a second time, the effort calculation will be merged into an Immersed Boundary solver for the RBC dynamics.
- Sub-project 3: Optimization of the high order framework (HOF) for Navier-Stokes incompressible (M. Bernard, P. Bégou, G. Lartigue, G. Balarac)
Over the past years, a framework has been developed to improve the spatial accuracy of numerical schemes on distorted meshes. However, even if the solution is more precise, the computational cost of the overall resolution of Navier-Stokes equations is large. As a consequence, HOF becomes profitable only on thin meshes thanks to a better spatial convergence order. The code has been analized with different analysis tools (MAQAO, Gprof, Scalasca). The main time consuming routines have been identified and improved. Moreover, some algorithms have been refactors such that the resolution of Navier-Stokes equations has been speed-up by a factor 2.5.
- Sub-project 4: Force coupling method (FCM) for particulate flows (C. Raveleau, S. Mendez)
The Force Coupling Method (FCM) allows the representation of particles in flows from 0 to finite Reynolds number based on a regularization of the multipole expansion for Stokes flows, providing enough particle resolution to match the exact Stokes flow away from the particle. This is done by using a Gaussian function to spread the singular forces over a domain whose size is derived from physical quantities of interest such as the settling velocity of a particle under gravity in Stokes flow and the particle radius. During the workshop, the first term of the multipole expansion (monopole) and the antisymetric part of the second term (antisymetric dipole) were implemented and validated against test cases from the litterature. The monopole was tested in the case of a particle held fixed against an incoming flow and the dipole was tested by applying a torque on a particle in a still fluid. In both cases, the velocity profiles matched the results from the litterature and approximated well the Stokes solution at a distance of about 1.5 radii from the particle center. It was also compared to the conservative immersed boundary method (CLIB solver) implemented in YALES2 for the monopole test case. Both methods give good results, although the FCM is able to predict the expected solution with a coarser mesh than CLIB. Cases where the particle moves are under investigation.
- Sub-project 5: Breaking limitations of the linearized implicit time advancement (T. Berthelon, G. Lartigue, G. Balarac)
The explicit time advancement classically used in ics solver is limited by CFL constraint. In order to get ride of this constraint, an implicit time advancement method, based on the linearization of the convective term, has been recently developed. However, the method is limited by difficulties to solve linear system, with the BiCGSTAB2 algorithm, during the prediction step. The objective of this project was to understand these limitations. The correction of a bug on the boundary conditions (viscosity imposed at zero) was identified. In addition, the spatial scheme and the presence of a buffer zone at the end of the domain showed a great influence on the convergence of the prediction. The perspectives for a more robust and efficient use of this temporal integration consist in working on the spatial schemes and on the pre-conditioning.
- Sub-project 6: Development of a traction open boundary condition (TOBC) in Yales2 (J.B. Lagaert, G. Balarac)
In simulations, artificial boundaries need to be introduced due to the limited size of computational domains. At these boundaries, flow variables need to be calculated in a way that will not induce any perturbation of the interior solution. During ECFD#6, open traction boundaries (TOBC) has been implemented in Yales2. Instead of enforced pressure value or normal derivative on boundaries, the traction is settled. The traction term gathers the deformation stress and pressure gradient. The implementation has been validated on simple test-case : comparison has been performed between theoritical solutions and numerical solution computed with a Dirichlet TOBC. Future work will add a stabilization term for large backflow and traction models to estimate the values to enforce on outlet boundaries
- Sub-project 7: Development of new spatial differential operators in Yales2 (M. Bernard, G. Lartigue)
It exists different philosophies for computing differential operators on distorted meshes. In a HPC context, the 2 main approaches are the Green-Gauss operators and the Least-Squares operators. During ECFD#6, 2 new types of "non-compact" Hessian operators have been implemented by computing successively the gradient operator, eather with Green-Gauss gradient, or with Least-Squares gradient. Those operators lead to good convergence order, even on distorted mehes. However, their application on low-resolution signals lead to large error magnitude due to their extended stencil. Another pair of gradient & hessian Least-Squares operators have been implemented, leading to 2nd and 1st order accuracy for the gradient and hessian respectively. Those operators have very interesting characteristics as their stencil is restricted to the direct neighbors only and their computational cost remains low.
- Sub-project 8: DOROTHY optimization (M. Roperch, H. Mulakaloori, G. Pinon, P. Bénard, G. Lartigue)
DOROTHY is three-dimensional unsteady Lagrangian Vortex Particles Methods code. Because of the number of particles that increases during the numerical simulation, some routines begin to be very expensive. During this workshop, MAQAO has been used to identify the most time consuming routines and why. They have been factorized, merged and vectorized. At the end, these routines have been speed up by a factor 4 and the global program by a factor 2.8.
- Sub-project 9: Anamika, a tool to improve programming productivity (K. Mohana Muraly, G. Staffelbach)
Turbulence - P. Benard, CORIA & G. Balarac, LEGI
- Sub-project 1: Explore hybrid RANS/LES strategies (T. Berthelon, G. Balarac)
For complex industrial applications, LES can still lead to a too long restitution time. In other hand, statistical approaches can lead too a lack of accuracy. In this project, the potentiality of hybrid approaches combining both have been explored. Conventional hybrid RANS/LES approaches consider a unique solution field, with an unique transport equation and a clusre terme modeled using RANS or LES models depending of the regions. The main idea is to evaluate a strategy based on a separation between mean fields and fluctuations with distinct coupled transport equations. First elements of validation using YALES2 code are shown that it was possible to correct the prediction of a RANS models, by performing LES of the fluctuations. Next steps should be to consider disctinct meshes, or even computational domains for RANS and LES with this strategy.
- Sub-project 2: Flow Instabilities over Rotating curved Surfaces (S. Sawaf, M. Shadloo, A. Hadjadj, S. Moreau, S. Poncet)
For evaluating the effect of the clearance between the blade tip and the casing of axial ducted fans on noise emissions, LES offers excellent tool to capture the consitricted flow around the blade tip especially for small clearances where RANS fails because of unsteady flow conditions. LES simulation of the aerodynamics is the first step toward extracting accoustics data that helps to improve the design of axial ducted fans so they comply with the noise emission regulations in admistrative buildings. noise emmisions are estimated using analytical aeroacoustic models informed by data that are extracted from the LES simulations.
- Sub-project 3: Automatic statistical convergence metric (C. Papagiannis, G. Balarac, O. Le Maitre, P. Congedo)
Statistics accumulation can be an important part of the restitution time in unsteady simulations (DNS/LES). In this project, the goal was to estimate uncertainties on the "finite time statistics". For time correlated data, it can be shown that the variance of the mean estimator (i.e. the fluctuation of the estimation of the mean) is dependent of the correlation time. Modeling this correlation time based on the integral time scale of the turbulence appears as a first way to define a practical metric to evaluate the statistic convergence on-fly during simulations. Next step should be to explore procedures to accelerate the statistics accumulation step.
- Sub-project 4: Aerodynamics of floating wind turbines (R. Amaral, F. Houtin-Mongrolle, E. Muller)
Floating wind turbines have the potential to unlock up to 80% of the wind energy located offshore making it a very strong candidate to mediate the energy transition. For this reason, many projects will soon come online with plenty of others entering the project phase. However, since now the foundation will experience translational and rotational movements, the rotor will experience changes in its local and global velocity fields whose effect is not well understood. This project intends to shed light on this matter, by making use of the high-fidelity large-eddy simulations (LES) and the actuator-line model (ALM) that are available in the YALES2 framework. This project will first cover floating wind turbines under user-prescribed motion to identify how the different degrees-of-freedom of the platform affect the rotor aerodynamics and in which proportion and will later move to more realistic conditions with sea-states described by a spectrum, turbulent wind and elastic turbine. During the ECFD workshop, we focused on finalizing some details of the prescribed motion implementation on the actuator-line model of YALES2 and well as preparing the implementation to be merged with the master branch.
- Sub-project 5: Implementation of the Risoe dynamic stall model for YALES2 (V. Maronnier, E. Muller, B. Duboc)
Dynamic loads must be predicted accurately to estimate the fatigue life of wind turbines operating in turbulent wind conditions. Dynamic stall has a huge impact on these loads. A semi-empirical Beddoes-Leishman type model is formulated to represent the unsteady lift, drag, and pitching moment. The so called RISOE dynamic stall model follows the initial formulation presented in (Hansen et al. 2004) with improvements described in (Pirrung et al. 2018). This model considers impulsive and circulatory terms in attached flow, and trailing edge separation in stall regions while in the Oye model only the lift coefficient was corrected in detached flow. This model will be implemented in the actuator line model in YALES2 and will be validated against experimental wind tunnel data for single airfoils (FFA-W3-241 and NACA0015). Simulations for a real wind turbine will be performed to estimate the impact of this model on loads into the coupling with the aeroelastic code BHawC.
Hansen, M.H., M. Gaunaa, and H.A. Madsen. “A Beddoes-Leishman Type Dynamic Stall Model in Sate-Space and Indicial Formulations.” Risoe, 2004 Pirrung, G. R., and M. Gaunaa. “Dynamic Stall Model Modifications to Improve the Modeling of Vertical Axis Wind Turbines.” DTU Wind Energy, June 2018
- Sub-project 6: YALES2-OpenFAST coupling (A. Parinam, A. Viré, D. Von Terzi, B. Duboc, F. Houtin-Mongrolle, P. Bénard)
- Sub-project 7: Wall law for Immersed Boundaries & Rough surfaces (M. Cailler, A. Cuffaro, P. Benez, S. Meynet)
Conservative Lagrangian Immersed Boundaries (CLIB) are now a useful way to take into account complex geometries in YALES2. During the workshop, a brand-new data-structure for modular and generic immersed-body has been developed. This data-structure paves the way for various new capabilities for IB methods: penalization mask shape optimization for improved velocity imposition, better control of near wall discretization based on a reliable evaluation of wall units, wall-modeling, etc... For this purpose the periodic hill test case has been considered. Simulations of this configuration has been performed by using body-fitted meshes, and CLIB for both smooth and rough surfaces. This will allow to assess the accuracy of the IB methods, and will constitute a database for IB models improvement, and the development of wall-modeling strategies.
- Sub-project 8: Atmospheric flow (U. Vigny, L. Voivenel, P. Benard, S. Zeoli)
Atmospheric flow such as Atmospheric Boundary Layer (ABL) and thermal stratification have an impact on wind turbines aerodynamic and wakes. Mostly at a wind farm scale, the change of wind turbine wake size and recovery can modify the global power production. During the workshop, the Coriolis force implementation has been validated through neutral case (where no thermal stratification i.e. no temperature gradient). It also allowed to validate the pressure forcing term, needed to drive the flow in a periodic box. YALES2 results showed a good agreement with other numerical and experimental results. Afterwards, the stable case (i.e. temperature gradient downwards) has been studied. A surface temperature as boundary condition has been developed. Yet, results are not as expected and further investigation is needed.
Two Phase Flow - C. Merlin, Ariane Group & M. Cailler, Safran Tech
- Sub-project 1: Convergent computation of interface curvature (G. Ghigliotti, M. Benard, G. Balarac, J. Carmona, R. Mercier, G. Lartigue)
Though Level-set distance evaluation through GPMM (Janodet et al., 2022) converges at order 2, the interface curvature convergence is as best 0 using the non-compact Goldman formulation. Following progresses obtained during ECFD5, a strategy based on parabolic fit of the interface has been explored during the workshhop. This method aims at fitting a parabola through least squares using the interface markers stored in the interface vicinity. First the method was applied on a 2-D perfectly spherical droplet with exact projection of the marker on the circle. This results in a first order convergent curvature. Without projection of the markers, the fiting strategy allows a slight decrease of the error but no improve on the curvature convergence order in comparison with the standard non-compact formulation. As a persective, these results will be validated on dynamic and 3-D cases (MMG3D meshes). Also, the sensitivity on the number of markers and their redundancy will be investigated.
- Sub-project 2: Phase Change Solver : towards pressurization & moving bodies (F. Pecquery, C. Merlin, V. Moureau, I. El Yamani)
Main objective of this sub-project was to extend the capabilities of the Phase Change Solver towards pressurization and coupling with the immersed-boundary method. During the workshop, the new and generalized data structure, proposed by F. Pecquery, allowing the treatment of n-phases whose properties are described by an equation of state has been validated by setting-up an aqat (mph_data_registration). Moreover, a new age Phase Change Solver based on this data-structure was implemented by adapting all numerical ingredients of the temporal loop : going from boundary treatment to velocity, phase indicator, data-set advancement and pressure evaluation. Perspectives of this work include extension towards multi-species treatment and derivation of n-velocities momentum conserving framework.
- Sub-project 3: Towards unity ratio between particle size & grid size (I. El Yamani, M. Helal, N. Gasnier, M. Cailler, V. Moureau)
In a two-way coupled Eulerian-Lagrangian framework, dedidated numerical treatment is necessary as soon as the ratio between the particle size and the cell size is greater than unity. In this configuration, in the best case the evaluation of the undisturbed velocity and drag force is inacurate, and in the worst situation the high local Eulerian source-term may lead to gas velocity divergence. During the workshop, a gaussian-based regularization of the Eulerian source term was implemented and tested on various test cases. Use of this regularization shows improvement on the particle trajectory description, but still some errors are obtained for low particle Reynolds numbers. To improve the accuracy of the strategy the model for undisturbed gas velocity prediction proposed by (Balachandar, 2019) was tested. Unfortunately some difficulties were encoutered regarding its numerical implementation. Next steps will include a thorough validation of the method on isolated and interacting particles test cases and identification of model parameter for the gaussian-filter size.
Combustion - K. Bioche, CORIA & R. Mercier, Safran Tech
- Sub-project 1: Multi-regime F-TACLES (S. Dillon, R. Mercier, B. Fiorina)
Filtered tabulated chemistry for large eddy simulations is currently a common tool to model premixed flames or diffusion flames. Tabulation using 1D counterflow flames, as a function of the mixture fraction and progress variable, was previously tested on laminar and turbulent cases. It resulted in difficulties to describe the outer mixing zone and yield a very stiff evolution of SGS source terms in the phase space. The model was modified to include the mixture fraction scalar dissipation rate as a table dimension. This solves previous limitations, but using 1D counterflow flames yields empty table zones, making the method numerically infeasible. Tabulation using both 1D counterflow flames and 1D partially premixed flames gives well-built tables, and was tested on 1D flames for various strain rates.
- Sub-project 2: Limiter model for turbulence combustion interaction in MILD combustion (E. Stendardo, L. Bricteux, K. Bioche)
MILD combustion yields intense turbulence and widespread reaction zones, requiring expensive mesh refinement over large areas. Practical mesh won’t be fine enough, leading to sub-grid heterogeneousness and effects of sub-grid turbulent fluctuations. A generic limiter type combustion model was implemented to solve for turbulence combustion interaction. This family of models includes Partially Stirred Reactor, Quasi Laminar Finite Rate and Laminar Finite Rate models. In these models, the source term is multiplied by a limiter factor and the residence time in inner cell reactive structure can be modelled. This implementation will permit testing the various limiter formulations in the future.
- Sub-project 3: Evaluate spatial discretization schemes on scalar transport (K. Bioche, Y. Bechane, R. Mercier, G. Lartigue, V. Moureau, J. Carmona, M. Bernard, L. Voivenel)
Common practice in combustion solvers is to use centred spatial schemes. Such low-dissipation schemes can prove unstable when applied to under-resolved scalar transport in presence of strong gradients. This is typically the case for H2/air combustion. Initial low-resolution simulations require thus adapted numerical schemes. Various spatial schemes were evaluated on the scalar transport problem, including: 4th order, 3rd order, 2nd order, WENO3, high order schemes, MUSCL schemes with various limiters (overbee, superbee, sweby, van leer, minmod). Their application to various configurations was discussed to emphasize on their robustness and accuracy. Tests cases include: 1D scalar convection Jiang Shu test case, 2D scalar bump convection for convergence analysis, a 2D reactive Bunsen burner and finally the 3D Preccinsta burner.
- Sub-project 4: Phenomenological plasma model for reacting systems (S. Wang, Y. Bechane, B. Fiorina)
Plasma assisted combustion consists in stabilizing flames in near extinction conditions thanks to electric discharges. Stabilization of lean premixed flames with Nanosecond Repetitively Pulsed electric Discharges is a strategy to reduce NOx emissions. Full 3D simulations of plasma assisted combustion are extremely expensive, so that the use of a semi-empirical strategy to model NRPD is preferred in CFD solvers. During the workshop, Castela’s model was implemented in a variable density solver. This model was extended to an explicit compressible solver. The model of Blanchard was also implemented in both frameworks. A 2D pin-to-pin configuration was successfully simulated with both models and frameworks.
- Sub-project 5: Development and assessment of combustion in an explicit compressible solver (Y. Bechane, L. Voivenel, R. Mercier, K. Bioche)
The implementation of reactive physics in the Explicit Compressible Solver (ECS) of the YALES2 platform was undertaken. To this aim, reactive gases thermochemical functions were implemented. Specific schemes were developed to increase the temperature and species diffusion schemes from 2nd to 4th order. Finally, a 2D methane-air Bunsen flame was simulated with low order numerical schemes (RK1 and SLAU2).
- Sub-project 6: Clustering for finite rate chemistry using PCA (R. Mercier, A. Stock)
To reduce the cost of species source terms computation, a clustering method was adopted. It consists in detecting nodes with similar properties and compute chemical source terms only once for these. Still, considering each species in this process creates a high dimensional cluster, while replacing species by a user-set progress variable may not well describe species. The strategy adopted here relies on the application of a PCA on species. It can be viewed as an automated “progress variable” creation. The use of such strategy was shown to reduce the simulation cost of source term computation by a factor 6 on a simple 2D flame ball case.
User Experience - J. Leparoux, Safran Tech & A. Pushkarev, GE Renewable Energy
- Sub-project 1: External coupling with CWIPI (R. Letournel, V. Moureau, C. Merlin, M. Cailler, P. Bégou, S. Meynet)
The coupling between different YALES2 solvers but also between YALES2 and an external code has been generalized. It relies on the CWIPI coupling library, which allows to interpolate the data exchanged on any mesh. By introducing a new dedicated data structure, several simultaneous couplings can be performed, on different boundaries or on volume domains. Keywords also allow to pre-process the data to be sent, by a spatial filtering or a temporal average in case of temporal desynchronization of the solvers (asynchronous coupling). Dedicated test cases have been added to the distribution.
- Sub-project 2: Automated Grid Convergence refactoring (J. Leparoux, M. Cailler, R. Letournel)
Several grid convergence algorithms (Grenouilloux et al. (2022), Puggelli et al. (2022)) have been recently proposed but no one was fully embeded in the YALES2 solver which made the use of automatic mesh convergence tedious for users. A new data structure was introduced allowing to perform more easily grid convergence without to modify the fortran file of the YALES2 case. To go further, data structures state, event and action have been refactored allowing now to instantiate easily a new object (state, event or action) without previous user declaration. The next step will use these structures to propose an agile sequence that can be easily adapted. Dedicated test cases have been updated or added to the distribution.
- Sub-project 3: Advanced Liquid spray post-processing (J. Carmona, J. Leparoux, N. Gasnier, C. Brunet, I. El Yamani)
- Sub-project 4: YALES2 as industrial solver for GE design optimization tools (A. Pushkarev, H. Lam, G. Balarac)
A Graphical User Interface (GUI) exists at GE Hydro, which provide a rapid and user-friendly solution to run Ansys CFD Tools for typical hydroelectric simulations from geometry files. We started develop an interface for Yales2 code, so that any user would only need a few clicks on a laptop to launch the simulation on a cluster with Yales2 solver instead of Ansys solutions. This required to (i) Create a mesh file from a geometry files. We were stuck at the export of the file in a *.msh format because Ansys does not support it in batch mode. (ii) Launching Yales2 solver from the GUI interfaced by y2_workflow. This was done successfully. (iii) Typical post-processing done at GE Hydro should be reproduced for the Yales2 code. We implemented the calculation of the evolution of losses along the streamlines direction. Future works should find a way to export a mesh file in batch mode and further develop post processing and inlet conditions in Yales2
- Sub-project 5: YALES2 History and Geography (T. Marzlin, A. Dauptain, P. Bénard)
- Sub-project 6: Improve the HT solver: refactoring of linear solver operators & Robin BC (C. Merlin, V. Moureau, R. Letournel)
First some linear solver functions were refactored with the introduction of a yales2 pointer to store C pointer and the use of function pointer. A Robin condition was also implemented in Heat Transfer Solver (HTS) to take into account convective flux. A first 2D test case was used to validate the implementation versus an analytical solution.