High-Order CFD Solver Developed at LIFSE 

The LIFSE laboratory develops a high-order finite volume CFD solver for unstructured meshes based on a Moving Least Squares reconstruction. This compressible flow solver, extensively validated through numerous international publications, is designed for the accurate simulation of complex steady and unsteady flows over a wide range of Mach numbers.

The code features very high-order spatial discretizations, a posteriori adaptive strategies for automatic numerical dissipation control, and advanced models for turbulence (implicit LES), aeroacoustics, compressible multiphase flows, phase change, and Navier–Stokes–Korteweg formulations. It supports fixed and moving meshes.

Successfully applied to problems in aerodynamics, aeroacoustics, turbomachinery, and multiphase flows, this solver currently serves as a reference research platform at LIFSE. Although presently an in-house code, it is intended for future open-source release in order to foster academic and industrial collaborations.

Some illustrative results obtained with CFDkit

5th order calculation of water shock air shock interaction

Solver using Homogeneous relaxation model (HRM) with Nobel Abel Stiffened Gas equation of state. 

 

Left: Initial setup, Centrer: density gradient, Right: MOOD activation for a-posteriori order reduction with blue cell highlighted with non physical solution detected and red cells with numerical oscillations with unlimited reconstruction

 

 

 

List of selected publications :

 

  1.  M. Deligant, C.-J. Romero-Casado, X. Nogueira, L. Ramírez, M. Specklin, F. Bakir, S. Khelladi. Very high order finite volume solver for multi component two-phase flow with phase change using a posteriori Multi-dimensional Optimal Order Detection. (2025) Computers and Fluids, 288, art. no. 106509. DOI: 10.1016/j.compfluid.2024.106509. 
  2. X. Nogueira, L. Ramos, S. Seijo, I. Couceiro, S. Khelladi, L. Ramírez, "Data-Driven Riemann Solvers: A Neural Network Approach and a Hybrid solver", Physics of Fluids, 37, 096142 (2025), https://doi.org/10.1063/5.0288995
  3. M. Deligant, C. Romero, X. Nogueira, L. Ramirez, M. Specklin, F. Bakir, S. Khelladi, "Very high order finite volume solver for multi component two-phase flow with phase change using a posteriori Multi-dimensional Optimal Order Detection", Computers and Fluids, vol. 288, 2025, https://doi.org/10.1016/j.compfluid.2024.106509
  4. T. Ait-Ali, S. Khelladi, F. Bakir, N. Hannoun, X. Nogueira, L. Ramirez, "A Diffuse Interface Model for Cavitation Taking into Account Capillary Forces", International Journal for Numerical Methods in Fluids, 2024, https://doi.org/10.1002/fld.5350
  5. L. Ramírez, J.            Fernández-Fidalgo, J. París, M. Deligant, S. Khelladi, X.        Nogueira. A very fast high-order flux reconstruction for Finite         Volume schemes for Computational Aeroacoustics. Engineering with   Computers, 2024, https://doi.org/10.1007/s00366-024-02039-2
  6. Ch. Foulquié, S. Khelladi, M. Deligant, L. Ramirez, X. Nogueira, J. Mardjono: "Numerical Assessment of Fan Blades Screen Effect onFan/OGV Interaction Tonal Noise", Journal of Sound and Vibration, Vol. 481, 115428, 2020     
  7. Nogueira X., Ramirez L., Fernández-Fidalgo J., Deligant M., Khelladi S., Chassaing J.-C., Navarrina F. : "An a posteriori-implicit turbulent model with automatic dissipation adjustment for Large Eddy Simulation of compressible flows", Computers and Fluids, Vol.197, 104371, 2020
  8. A. Martínez, L. Ramirez, X. Nogueira, S. Khelladi, F. Navarrina : "A high-order finite volume method with improved isotherms reconstruction for the computation of multiphase flows using the Navier-Stokes-Korteweg equations", Computers & Mathematics with Applications, Volume 79, Issue 3, pp. 673-696, 2020
  9. L. Ramirez, X. Nogueira, S. Khelladi, A. Krimi, I. Colominas:A very accurate Arbitrary Lagrangian-Eulerian meshless method for Computational Aeroacoustics. Computer Methods in Applied Mechanics and Engineering , Vol. 342, pp 116-141, 2018 (DOI:10.1016/j.cma.2018.07.036)
  10. L. Ramírez, X. Nogueira, P. Ouro, · F. Navarrina, S. Khelladi, I. Colominas:A Higher-Order Chimera Method for Finite Volume Schemes. Archives of Computational Methods in Engineering,  Vol. 25, Issue 3, pp 691–706, 2018 (DOI:10.1007/s11831-017-9213-8)
  11. X. Nogueira, L. Ramirez, S. Khelladi, J.-C. Chassaing, I. Colominas:A high-order density-based finite volume method for the computation of all-speed flows. Computer Methods in Applied Mechanics and Engineering, vol. 298, pp 229–251, 2016 (DOI:10.1016/j.cma.2015.10.004)
  12. L. Ramirez, C. Foulquié, X. Nogueira, S. Khelladi, J.-C. Chassaing, I. Colominas:New High-Resolution-Preserving Sliding mesh Techniques for Higher-order Finite Volume Schemes. Computers & Fluids, vol. 118, pp. 114–130, 2015 (DOI:10.1016/j.compfluid.2015.06.008)
  13. M. Deligant, M. Specklin, S. Khelladi:A Naturally Anti-Diffusive Compressible Two-Phase Kapila Model with Boundedness Preservation Coupled to a High Order Finite Volume Solver. Computers & Fluids, Vol. 114, Pages 265–273, 2015 (DOI:10.1016/j.compfluid.2015.03.004)
  14. L. Ramírez, X. Nogueira, S. Khelladi, J.-C. Chassaing, I. Colominas:A new higher-order finite volume method based on Moving Least Squares for the resolution of the incompressible Navier–Stokes equations on unstructured grids. Computer Methods in Applied Mechanics and Engineering, vol. 278, pp. 883–901, 2014 (DOI:10.1016/j.cma.2014.06.028)
  15. R. Ata, S. Pavan, S. Khelladi, E. F. Toro:A Weighted Average Flux (WAF) scheme applied to shallow water equations for real-life applications. Advances in Water Resources, Vol. 62, Part A, pp. 155–172, 2013 (DOI:10.1016/j.advwatres.2013.09.019)
  16. J.-C. Chassaing, S. Khelladi, X. Nogueira:Accuracy assessment of a high-order moving least squares finite volume method for compressible flows. Computers & Fluids, vol. 71, pp. 41-53, 2013 (DOI:10.1016/j.compfluid.2012.09.021)
  17. J.-C. Chassaing, X. Nogueira, S. Khelladi:Moving Kriging reconstruction for high order finite volume computations of compressible Flows. Computer Methods in Applied Mechanics and Engineering, vol. 253, pp. 463-478, 2013 (DOI:10.1016/j.cma.2012.08.016)
  18. X. Nogueira, S. Khelladi, I. Colominas, L. Cueto-Felgueroso, José París, Héctor Gómez:High-Resolution Finite Volume Methods on Unstructured Grids for Turbulence and Aeroacoustics. Archives of Computational Methods in Engineering, vol. 18/3, pp 315-340, 2011 (DOI:10.1007/s11831-011-9062-9)
  19. S. Khelladi, X. Nogueira, I. Colominas, F. Bakir:Toward a Higher Order Unsteady Finite Volume Solver Based on Reproducing Kernel Methods. Computer Methods in Applied Mechanics and Engineering, vol. 200, pp. 2348-2362, 2011 (DOI:10.1016/j.cma.2011.04.001)
  20. X. Nogueira, I. Colominas, L. Cueto-Felgueroso, S. Khelladi, F. Navarrina, M. Casteleiro:Resolution of computational aeroacoustics problems on unstructured grids with a higher-order finite volume scheme. Journal of Computational and Applied Mathematics, vol. 234/7, pp.2089-2097, 2010 (online since 2009) ( DOI:10.1016/j.cam.2009.08.067)
  21. X. Nogueira, S. Khelladi, L. Cueto-Felgueroso, F. Bakir, I. Colominas, Héctor Gómez:Implicit Large-Eddy Simulation with a Moving Least Squares-based finite volume method. IOP Conference Series Materials Science and Engineering, vol. 10/ 012235, 2010 (DOI:10.1088/1757-899X/10/1/012235)
  22. X. Nogueira, I. Colominas, L. Cueto-Felgueroso, S. Khelladi:On the simulation of wave propagation with a higher-order finite volume scheme based on Reproducing Kernel Methods. Computer Methods in Applied Mechanics and Engineering, vol. 199, pp. 1471-1490, 2010 ( DOI:10.1016/j.cma.2009.12.015)