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We are currently developing a variety of solvers, including a compressible Navier-Stokes DG solver, with local adaptation/multigrid, and also an incompressible solver for multiphase flows, etc. More information is available in this link: Horses3D
Our high order CFD software is open source!
You can find our paper about Horses3D here: https://www.sciencedirect.com/science/article/pii/S0010465523000450
and the code here: https://github.com/loganoz/horses3d
HORSES3D capabilities include:
- DGSEM formulation for efficiency,
- Compressible & incompressible flows,
- Turbulent regimes can be simulated by means of DNS, LES and RANS,
- Parallelised with MPI and OPENMP,
- Energy/Entropy stable formulations for robustness,
- h/p local adaptation (hanging nodes and polynomial adaptation),
- Explicit/Implicit and multigrid time marching,
- High order curved boundary conditions,
- Immersed Boundaries (mesh free),
- Actuator lines to simulate wind turbines
- Multiphase flows
- Aeroacoustics (FWH, APE)
Additionally, during my doctorate, I developed and implemented an unsteady unstructured incompressible high order (order ≥ 3) Discontinuous Galerkin - Fourier solver. Linearised and adjoint linearised versions of the code for flow instability analysis have been developed.
The solver main capabilities include:
- Flow described using primitive variables (velocity and pressure),
- Triangular and quadrilateral elements,
- High order curved boundary conditions,
- A sliding mesh capability that enables high order solutions of rotating geometries,
- 2D and 3D versions, the latter being an extension of the 2D-DG with Fourier series,
- Laminar and turbulent regimes can be simulated by means of DNS or LES closure models,
- Parallelised for distributed memory clusters using a a combination of MPI and OPENMP paradigms.
Static and rotating geometries
Fig 1: DG snapshots of the rotating NACA0015 foil with 21 velocity magnitude contours [0:1.3] for polynomial order k = 5 and rotational speed Lω/U = 0.05 for (a) geometric AOA = 17.2◦ and (b) geometric AOA = 28.6◦.
Fig 2: DG solution: Vorticity contours −1 ≤ ωz ≤ 1 for the square cylinder with the unstructured triangular mesh overlaid in the figure for Re = 100 and k = 7.
Fig 3: DG flow field snapshots of velocity magnitude for λ = 2; (a) one bladed turbine, (b) three bladed turbine and (c) ducted three bladed turbine.
Numerical examples and verification
Fig 4: Approximation of sinusoïdal initial condition using high order discontiuous polynomials of various degrees.
Fig 5: Spectral convergence of the DG solver for the Taylor vortex problem in 2D and various mesh topologies.
Turbulent flows
Fig 6: ILES-DG SVV-Fourier solution for a circular cylinder at Re =3900 showing iso-surfaces of velocity magnitude (grey |u| = 0.3 m/s, red |u| = 0.8 m/s and blue |u| = 1.2 m/s). Overlaid in the main figure are streamlines showing the flow trajectory. Inset figure shows details of the flow structures near the circular cylinder (velocity magnitude iso-surface |u| = 0.3 m/s).
Fig 7: 3D ILES-DG SVV-Fourier flow field snapshot for the NACA0012 at Re =10000 with 4 Fourier planes and Lz/c = 0.2 for AOA = 20 ◦, k = 5. Pressure field is shown at the plane z = 0. Overlaid are streamlines showing flow trajectory and an iso-surface of velocity magnitude with iso-values |u| = 0.3 m/s.
Fig 8: 3D ILES-DG SVV-Fourier flow field snapshot for a rotaing NACA0015 at Re =10000 with 64 Fourier planes and Lz/c = 0.5, k = 3. Showing 4 iso-surface of velocity magnitude.
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