Unstructured Mesh Solution Techniques using the NSU3D Solver. NSU3D is an unstructured mesh Reynolds-averaged Navier-Stokes (RANS) solver designed for aerodynamic flow problems. This paper describes the basic solution techniques implemented and available within NSU3D for both steady-state aerodynamic problems and time-dependent simulations. The base solver consists of a multi-stage point-implicit approach that inverts small block-diagonal matrices at each mesh point. This is generalized to a line-Jacobi method, using lines generated within the unstructured mesh based on the strength of the edge connections between neighboring vertices. The line-Jacobi solver is used as a smoother for an agglomeration multigrid solver which makes use of coarse agglomerated mesh levels to accelerate the convergence of the overall solution procedure based on geometric and algebraic multigrid principles. The multigrid solver, in turn, can be used as a preconditioner for a GMRES algorithm that provides further robustness and convergence efficiency for large difficult cases. Different variants of these solvers are available as both linear and non-linear formulations and are applicable to steady as well as time-dependent cases. The numerical performance and parallel scalability of these solvers are illustrated on two representative steady-state aerodynamic RANS problems, and one unsteady time-implicit problem. The advantages and drawbacks of the various solvers are discussed, and prospects for future solver development are given.

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  1. Alauzet, F.; Frazza, L.: Feature-based and goal-oriented anisotropic mesh adaptation for RANS applications in aeronautics and aerospace (2021)
  2. Mavriplis, Dimitri J.: A residual smoothing strategy for accelerating Newton method continuation (2021)
  3. Nishikawa, Hiroaki: A hyperbolic Poisson solver for wall distance computation on irregular triangular grids (2021)
  4. Ahrabi, Behzad R.; Mavriplis, Dimitri J.: An implicit block ILU smoother for preconditioning of Newton-Krylov solvers with application in high-order stabilized finite-element methods (2020)
  5. Nishikawa, Hiroaki: A hyperbolic Poisson solver for tetrahedral grids (2020)
  6. Roget, Beatrice; Sitaraman, Jay; Lakshminarayan, Vinod; Wissink, Andrew: Prismatic mesh generation using minimum distance fields (2020)
  7. Lakshminarayan, Vinod K.; Sitaraman, Jayanarayanan; Roget, Beatrice; Wissink, Andrew M.: Development and validation of a multi-strand solver for complex aerodynamic flows (2017)
  8. Li, Gaohua; Fu, Xiang; Wang, Fuxin: High-resolution multi-code implementation of unsteady Navier-Stokes flow solver based on paralleled overset adaptive mesh refinement and high-order low-dissipation hybrid schemes (2017)
  9. Nishikawa, Hiroaki; Liu, Yi: Accuracy-preserving source term quadrature for third-order edge-based discretization (2017)
  10. Nishikawa, Hiroaki; Nakashima, Yoshitaka; Watanabe, Norihiko: Effects of high-frequency damping on iterative convergence of implicit viscous solver (2017)
  11. Brazell, Michael J.; Sitaraman, Jayanarayanan; Mavriplis, Dimitri J.: An overset mesh approach for 3D mixed element high-order discretizations (2016)
  12. Economon, Thomas D.; Mudigere, Dheevatsa; Bansal, Gaurav; Heinecke, Alexander; Palacios, Francisco; Park, Jongsoo; Smelyanskiy, Mikhail; Alonso, Juan J.; Dubey, Pradeep: Performance optimizations for scalable implicit RANS calculations with SU2 (2016)
  13. Mishra, Asitav; Mani, Karthik; Mavriplis, Dimitri; Sitaraman, Jay: Time dependent adjoint-based optimization for coupled fluid-structure problems (2015)
  14. Shi, Lei; Wang, Z. J.: Adjoint-based error estimation and mesh adaptation for the correction procedure via reconstruction method (2015)
  15. Jalali, Alireza; Sharbatdar, Mahkame; Ollivier-Gooch, Carl: Accuracy analysis of unstructured finite volume discretization schemes for diffusive fluxes (2014)
  16. Katz, Aaron; Wissink, Andrew M.; Sankaran, Venkateswaran; Meakin, Robert L.; Chan, William M.: Application of strand meshes to complex aerodynamic flow fields (2011)
  17. Ben Haj Ali, Amine; Soulaimani, Azzeddine: An unstructured finite element method for solving the compressible RANS equations and the Spalart-Allmaras turbulence model (2010)
  18. Wong, Peterson; Zingg, David W.: Three-dimensional aerodynamic computations on unstructured grids using a Newton-Krylov approach (2008)