Galatea-I (CFD solver)

Galatea-I is a parallelized Computational Flow Dynamics (CFD) solver for the numerical simulation of 3D incompressible (steady and unsteady) viscous flows in hybrid unstructured grids, developed in Fortran by members of the Turbomachines & Fluid Dynamics Laboratory (TurboLab-TUC). The Galatea-I solver is based on the 3-dimensional Reynolds-Averaged Navier–Stokes (RANS) equations, modified appropriately by the artificial compressibility method to account for incompressible flow phenomena. For turbulence modeling and subsequently computation of the values of turbulent dynamic viscosity and turbulent kinetic energy, the SST two-equations model has been incorporated. Additionally, Galatea-I has been enhanced with four Sub-Grid Scale (SSG) LES (Large Eddy Simulation) models, so that more accurate numerical simulations of unsteady turbulent incompressible fluid flows can be obtained: (a) the Smagorinsky, (b) the WALE, (c) the dynamic Germano-Lilly, and (d) the dynamic kinetic energy model.

A node-centered Finite-Volume (FV) method is implemented for the discretization of the computational field in 3D hybrid unstructured grids; the median-dual control volume of a node is constructed by connecting lines defined by edge midpoints, barycenters of faces, and barycenters of elements, sharing this node.  For the calculation of the convective fluxes, the Roe or the HLLC (Harten-Lax-van Leer-Contact) approximate Riemann solvers are implemented. An edge-based data structure is employed to reduce the required computational effort and memory storage. In addition, a second-order accurate spatial scheme, based on the MUSCL (Monotone Upwind Scheme for Conservation Laws) method, is applied to increase the accuracy of the final steady-state solution.

As far as the diffusive fluxes are concerned, the gradients of the velocity components and temperature have to be computed at the middle of each edge of the grid; for this calculation, two alternative methods have been incorporated in Galatea-I, an element-based and a nodal-averaging one. For steady-state solutions, the PDEs are iteratively approximated by employing an explicit scheme with a four-stage Runge–Kutta method and local time stepping. The Galatea-I solver can be also used against unsteady or transient problems via the incorporated dual-time-stepping method; according to this scheme, an additional derivative of the variable vector over real time t is added to the flow and turbulence model equations. The parallelization strategy in Galatea-I solver is based on the domain decomposition approach along with the message passing interface (MPI) communication protocol.

Galatea-I includes a parallel agglomeration multigrid method, based on the solution of the flow problem on successively coarser grids, derived from the initial finest one through the fusion of the adjacent control volumes. The agglomeration of the neighboring control cells is performed on a topology-preserving framework resembling the advancing front technique, limited though by predefined rules concerning the boundary nodes and the ghost nodes. Depending on the type of the examined flow (inviscid or viscous) and consequently on the type of the initial finest grid (tetrahedral or hybrid) either an isotropic agglomeration or a directional (semi- or full-coarsening) one can be performed.

[Galatea was a Nereid who was loved by the Cyclops Polyphemus (in Greek mythology). Nereids (sea Nymphs of Greek mythology) were the daughters of the sea god Nereus and of Doris, daughter of Oceanus]. 

References:

S.S. Sarakinos, G.N. Lygidakis, I.K. Nikolos, "Evaluation of a Parallel Agglomeration Multigrid Finite-Volume Algorithm, Named Galatea-I, for the Simulation of Incompressible Flows on 3D Hybrid Unstructured Grids", Proceedings of the ASME 2014 International Mechanical Engineering Conference & Exposition, IMECE2014, Nov. 14-20, Montreal, Quebec, Canada, Paper No. IMECE2014-39759. https://doi.org/10.1115/IMECE2014-39759

S.S. Sarakinos, G.N. Lygidakis, I.K. Nikolos, "Acceleration Strategies for Simulating Compressible and Incompressible Flows", in P. Iványi, B.H.V. Topping, (Editors), Proceedings of the Fourth International Conference on Parallel, Distributed, Grid and Cloud Computing for Engineering, Civil-Comp Press, Stirlingshire, UK, Paper 47, 2015. doi:10.4203/ccp.107.47

S.S. Sarakinos, G.N. Lygidakis, I.K. Nikolos, "Simulating unsteady incompressible flows using Galatea-I, a parallel multigrid finite volume solver", Proceedings 8th GRACM International Conference on Computational Mechanics, 12-15 July, 2015, Volos, Greece.

S.S. Sarakinos, G.N. Lygidakis, I.K. Nikolos, "Assessment of the academic CFD code GALATEA-I with the DARPA SUBOFF test case", Proceedings of the ASME 2015 International Mechanical Engineering Conference & Exposition, IMECE2015, Nov. 13-19, Houston, Texas, USA, Paper No. IMECE2015-50980. https://doi.org/10.1115/IMECE2015-50980

G.N. Lygidakis, S.S. Sarakinos, I.K. Nikolos, "Comparison of different agglomeration multigrid schemes for compressible and incompressible flow simulations", Advances in Engineering Software, 101, pp. 77-97, 2016. https://doi.org/10.1016/j.advengsoft.2015.12.004

S.S. Sarakinos, On the simulation of steady and unsteady incompressible flows using the finite volume approach and artificial compressibility concept on hybrid unstructured grids, Ph.D. Thesis, School of Production Engineering & Management, Technical University of Crete, 16/4/2016.

G.N. Lygidakis, S.S. Sarakinos, I.K. Nikolos, "Simulation of the flow over the CAARC standard tall building using different LES turbulence models", Proceedings of the ASME 2016 International Mechanical Engineering Conference & Exposition, IMECE2016, Nov. 11-17, Phoenix, Arizona, USA, Paper No. IMECE2016-66399. https://doi.org/10.1115/IMECE2016-66399

S.S. Sarakinos, G.N. Lygidakis, I.K. Nikolos, "Assessment of the academic CFD code Galatea-I with the DLR-F11 model in high lift configuration", Proceedings of the ASME 2016 International Mechanical Engineering Conference & Exposition, IMECE2016, Nov. 11-17, Phoenix, Arizona, USA, Paper No. IMECE2016-66405. https://doi.org/10.1115/IMECE2016-66405

S.S. Sarakinos, G.N. Lygidakis, I.K. Nikolos, "Flow Analysis of the DLR-F11 High Lift Model Using the Galatea-I Code", AIAA Journal of Aircraft, 55(1), pp. 355-372, 2018. https://doi.org/10.2514/1.C034289

Numerical Applications and Simulations