Max Planck Institute for Dynamics and Self-Organization

A State-of-the-Art DNS code base

original

original

GOLDFISH is a highly scalable and versatile DNS Navier–Stokes solver developed in-house by our
team at the Max Planck Institute for Dynamics and Self-Organization. The code is capable of simulating
turbulent convection problems in both cylindrical and box geometries and it has been benchmarked
against other established DNS codes G. L. Kooij, M. A. Botchev, E. M. Frederix, B. J. Geurts, S. Horn,
D. Lohse, E. P. van der Poel, O. Shishkina, R. J. A. M. Stevens, and R. Verzicco, Comput. Fluids 166,
1 (2018).

Its non-uniform grid clustering permits accurate resolution of the smallest turbulent Kolmogorov
and Batchelor microscales both in the bulk and within boundary layers O. Shishkina, R. J. A. M.
Stevens, S. Grossmann, and D. Lohse, New J. Phys. 12, 075022 (2010). GOLDFISH is built
on a Helmholtz–Hodge decomposition, employs a fourth-order spatial discretization on staggered,
non-uniform grids (clustered near walls and obstacles), and advances in time with a third-order
Runge–Kutta scheme. Its fully conservative, modular design and MPI-based 2D pencil decomposition
(via DECOMP2D N. Li and S. Laizet, Cray User Group 2010 Proceedings, (2010)) enable massive
parallelism and high parallel-I/O performance, (see the figures below).

Goldfish speed-up scaling as a function of the number of CPU-cores used — Goldfish speed-up scaling as a function of the number of CPU-cores used

Goldfish speed-up scaling as a function of the number of CPU-cores used

Goldfish speed-up scaling as a function of the number of CPU-cores used — Goldfish speed-up scaling as a function of the number of CPU-cores used

Goldfish speed-up scaling as a function of the number of CPU-cores used

Presented will be some model systems we are working on in our group.

The Centrifugal Convection (CC) System for Ra = 8.88 × 108, Fr = 6.53, Pr = 4.3left: temperature field in the mid-plane of the horizontal sectionright: streamline analysis of the associated flow field — The Centrifugal Convection (CC) System for Ra = 8.88 × 10⁸, Fr = 6.53, Pr = 4.3 left: temperature field in the mid-plane of the horizontal section right: streamline analysis of the associated flow field

The Centrifugal Convection (CC) System for Ra = 8.88 × 10⁸, Fr = 6.53, Pr = 4.3
left: temperature field in the mid-plane of the horizontal section
right: streamline analysis of the associated flow field

The Centrifugal Convection (CC) System for Ra = 8.88 × 108, Fr = 6.53, Pr = 4.3left: temperature field in the mid-plane of the horizontal sectionright: streamline analysis of the associated flow field — The Centrifugal Convection (CC) System for Ra = 8.88 × 10⁸, Fr = 6.53, Pr = 4.3 left: temperature field in the mid-plane of the horizontal section right: streamline analysis of the associated flow field

The Centrifugal Convection (CC) System for Ra = 8.88 × 10⁸, Fr = 6.53, Pr = 4.3
left: temperature field in the mid-plane of the horizontal section
right: streamline analysis of the associated flow field

Proposed heat transport model in the buoyancy-dominated (pink line) and Lorentz-force-dominated (blue line) regimes in magnetoconvection — Proposed heat transport model in the buoyancy-dominated (pink line) and Lorentz-force-dominated (blue line) regimes in magnetoconvection

Proposed heat transport model in the buoyancy-dominated (pink line) and Lorentz-force-dominated (blue line) regimes in magnetoconvection

Proposed heat transport model in the buoyancy-dominated (pink line) and Lorentz-force-dominated (blue line) regimes in magnetoconvection — Proposed heat transport model in the buoyancy-dominated (pink line) and Lorentz-force-dominated (blue line) regimes in magnetoconvection

Proposed heat transport model in the buoyancy-dominated (pink line) and Lorentz-force-dominated (blue line) regimes in magnetoconvection

Example of a TC flow as obtained in the DNS for Re = 5600, 𝛤 = 2𝜋, 𝜂 = 5/7 with solid top and bottom lids, illustrated by isosurfaces of the axial velocity. Only half of the computational domain is shown. — Example of a TC flow as obtained in the DNS for Re = 5600, 𝛤 = 2𝜋, 𝜂 = 5/7 with solid top and bottom lids, illustrated by isosurfaces of the axial velocity. Only half of the computational domain is shown.

Example of a TC flow as obtained in the DNS for Re = 5600, 𝛤 = 2𝜋, 𝜂 = 5/7 with solid top and bottom lids, illustrated by isosurfaces of the axial velocity. Only half of the computational domain is shown.

Example of a TC flow as obtained in the DNS for Re = 5600, 𝛤 = 2𝜋, 𝜂 = 5/7 with solid top and bottom lids, illustrated by isosurfaces of the axial velocity. Only half of the computational domain is shown. — Example of a TC flow as obtained in the DNS for Re = 5600, 𝛤 = 2𝜋, 𝜂 = 5/7 with solid top and bottom lids, illustrated by isosurfaces of the axial velocity. Only half of the computational domain is shown.

Example of a TC flow as obtained in the DNS for Re = 5600, 𝛤 = 2𝜋, 𝜂 = 5/7 with solid top and bottom lids, illustrated by isosurfaces of the axial velocity. Only half of the computational domain is shown.

Natural convection in cylindrical containers with isothermal ring-shaped obstacles for Ra = 108 and h/H = 0.06 — Natural convection in cylindrical containers with isothermal ring-shaped obstacles for Ra = 10⁸ and h/H = 0.06

Natural convection in cylindrical containers with isothermal ring-shaped obstacles for Ra = 10⁸ and h/H = 0.06

Natural convection in cylindrical containers with isothermal ring-shaped obstacles for Ra = 108 and h/H = 0.06 — Natural convection in cylindrical containers with isothermal ring-shaped obstacles for Ra = 10⁸ and h/H = 0.06

Natural convection in cylindrical containers with isothermal ring-shaped obstacles for Ra = 10⁸ and h/H = 0.06

References

• R. E. Ecke and O. Shishkina, Annu. Rev. Fluid Mech. 55, 603 (2023)
• R. E. Ecke, X. Zhang, and O. Shishkina, Phys. Rev. Fluids 7, L011501 (2022)
• X. Zhang, P. Reiter, O. Shishkina and R. E. Ecke, Phys. Rev. Fluids 9, 053501 (2024)
• J. Song, O. Shishkina and X. Zhu, J. Fluid Mech. 989, A3 (2024)
• J. Song, V. Kannan, O. Shishkina and X. Zhu, Int. J. Heat Mass Transfer 232, 125971 (2024)
• Z. Yao, M. S. Emran, A. Teimurazov, and O. Shishkina, Int. J. Heat Mass Transfer 236, 126314 (2025)
• G. Ahlers, E. Bodenschatz, R. Hartmann, X. He, D. Lohse, P. Reiter, R. J. A. M. Stevens, R. Verzicco, M. Wedi, S. Weiss, X. Zhang, L. Zwirner, and O. Shishkina, Phys. Rev. Lett. 128, 084501 (2022)
• O. Shishkina and D. Lohse, Phys. Rev. Lett. 133, 144001 (2024)
• S. Weiss, M. S. Emran, and O. Shishkina, J. Fluid Mech. 986, R2 (2024)
• R. E. Ecke, X. Zhang, and O. Shishkina, Phys. Rev. Fluids 7, L011501 (2022)
• X. Zhang, P. Reiter, O. Shishkina and R. E. Ecke, Phys. Rev. Fluids 9, 053501 (2024)
• J. Song, C. Xu, and O. Shishkina, J. Comput. Phys. 525, 113732 (2025)
• C. Xu, C. Zhang, L. Brandt, J. Song and O. Shishkina, J. Fluid Mech. 1014, A22 (2025)
• A. Teimurazov, M. McCormack, M. Linkmann and O. Shishkina, J. Fluid Mech. 980, R3 (2024)
• L. Zwirner, M. S. Emran, F. Schindler, S. Singh, S. Eckert, T. Vogt, and O. Shishkina, J. Fluid Mech. 932, A9 (2022)
• A. Teimurazov, S. Singh, S. Su, S. Eckert, O. Shishkina and T. Vogt, J. Fluid Mech. 977, A16 (2023)
• S. Weiss, M.S. Emran, O. Shishkina, J. Fluid Mech., 986, R2 (2024)
• G. L. Kooij, M. A. Botchev, E. M. Frederix, B. J. Geurts, S. Horn, D. Lohse, E. P. van der Poel, O. Shishkina, R. J. A. M. Stevens, and R. Verzicco, Comput. Fluids 166, 1 (2018)
• O. Shishkina, R. J. A. M. Stevens, S. Grossmann, and D. Lohse, New J. Phys. 12, 075022 (2010)
• N. Li and S. Laizet, (Cray User Group 2010 Proceedings, (2010))