Solver Technology

Our team is using a variety of solvers to match the numerical problem including finite volume,
and finite element (continuous & discontinuous Galerkin).


Finite Volume Solver

NSU3D (Navier-Stokes Unstructured 3D) is a state-of-the-art Reynolds-Averaged Navier Stokes code based on unstructured meshes.
The solution algorithms in NSU3D have been in continuous development and validation for more than 20 years, providing accurate, reliable, and repeatable results over a wide range of flow regimes. Fully unstructured mess support with automatic hybridization of tetrahedral meshes greatly reduces meshing overhead while automatic agglomeration multigrid and line implicit solution in the near all regions provide rapid results on large models.
Capabilities
  • High speed compressible flow analysis
  • Viscous turbulent flow analysis
  • Inviscid flow analysis
  • Inviscid with Interactive Boundary Layer (IBL) analysis
  • Design optimization based on adjoint technology
  • Steady and unsteady flows with moving meshes
Features
  • Multigrid acceleration for fast solutions
  • Implicit line solver for highly stretched meshes
  • Hybrid MPI-OMP programming paradigm
  • Benchmarked on over 4000 cpus with good scalability



Continuous Galerkin Solver

HOMA(High-Order Multilevel Adaptive) solver is a continuous finite-element framework for the solution of RANS equations on unstructured grids. High-order discretizations, scalable preconditioning techniques, and multigrid capabilities are important features of this flow solver.

For parallelization, it uses MPI. In this solver, the time integration is fully implicit, and automatic differentiation is used for the exact linearization. For non-linear advancements, two principle algorithms are used: (1) a Newton-Krylov method based on the Pseudo-Transient Continuation (PTC), and (2) a spectral multigrid algorithm based on the full approximation scheme (FAS). For preconditioning of the linear systems, implicit line relaxation, incomplete factorization, and additive Schwarz method (ASM) have been built into the code. Also, the PETSc library has been integrated into the code, through which, external packages such as BoomerAMG and Trilinios are accessible for algebraic multigrid (AMG) preconditioning.



Discontinuous Galerkin Solver

Achieving higher accuracy and fidelity in aerodynamic simulations using higher-order methods has received significant attention over the last decade. High-order methods are attractive because they provide higher accuracy with fewer degrees of freedom and at the same time relieve the burden of generating very fine meshes. Discontinuous Galerkin (DG) methods have received particular attention for aerodynamic problems; these methods combine the ideas of finite element and finite volume methods allowing for high- order approximations and geometric flexibility.

DG3D

  • Tensor Product
  • Explicit
  • Supports hybrid, mixed-element, unstructured meshes
  • Element types: tetrahedra, prisms, pyramids, and hexahedra
  • p-enrichment and h-refinement capabilities using non-conforming elements (hanging nodes)
  • Solves compressible Navier-Stokes equations
  • PDE-based artificial viscosity equation
  • Spalart-Allmaras turbulence model (negative-SA variant)
  • The advective fluxes are calculated using a Riemann solver.
  • Riemann solvers include: Lax-Friedrichs, Roe, and artificially upstream flux vector splitting scheme (AUFS)
  • Time derivative is approximated using the explicit scheme RK4 or an implicit BDF2 scheme
  • Linearized to obtain the full Jacobian, solved using a flexible-GMRES
  • Preconditioners include: Jacobi relaxation, Gauss-Seidel relaxation, line implicit Jacobi, and ILU(0)

CartDG

  • Tensor product
  • Cartesian structured meshes
  • Supports dynamic AMR using P4est
  • Parallel scalability up to 1,048,576 MPI ranks on 524,288 cores on ANL Mira