Gal2D (CFD solver)

Gal2D is a Computational Flow Dynamics (CFD) solver for the numerical simulation of 2D (& 2D axisymmetric) steady or unsteady, compressible viscous flows in hybrid unstructured grids, developed in Fortran by members of the Turbomachines & Fluid Dynamics Laboratory (TurboLab-TUC). It actually serves as a test-bed, used for testing of new ideas in CFD, before their incorporation in 3D solvers. The flow governing equations are the non-dimensional (or dimensional) Reynolds-Averaged Navier-Stokes (RANS) ones. For turbulence modeling and subsequently computation of the values of turbulent dynamic viscosity and turbulent kinetic energy, the SST two-equation model has been incorporated. The interaction between flow and turbulence model equations is achieved mainly via the turbulent dynamic viscosity, while wall boundary conditions are based on the low Reynolds approach.

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 [a cell-centered and a centroid-dual Finite-Volume versions of the code have been also developed and tested].  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. A second-order accurate spatial scheme, based on the MUSCL (Monotone Upwind Scheme for Conservation Laws) method is applied, along with various slope limiters (Van Leer-Van Albada; MinMod; Supper Bee; MC; Van Leer). Higher-order schemes have been also tested. Gradients calculation is performed using either a Green-Gauss (edge dual) or a Least-Squares approach. The PDEs are iteratively approximated by employing an explicit scheme with a five-stage, fourth-order Runge–Kutta method (Strong Stability Preserving Runge-Kutta - SSPRK). Local time stepping is used for steady-state simulations.

Gal2D includes an 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.

The h-refinement method has been also incorporated in Gal2D, adding more Degrees-Of-Freedom (DOF) to the examined grid in regions where high flow gradients are observed. In that way increased accuracy at user-defined or automatically-defined areas is obtained and significant computational savings can be achieved, as the generation of a new mesh from scratch is avoided.

In order to allow for the simulation of rarefied gas flows, slip velocity and temperature jump boundary conditions have been incorporated in Gal2D; improved accuracy at the solid wall surfaces is obtained with the second-order slip scheme of Beskok and Karniadakis. The normalization scheme of Ferras et al. was adopted to alleviate any excessive residual oscillations, which are derived from the Dirichlet-type of the slip/jump boundary conditions, especially during the initial steps of an explicit iterative solution procedure.

References:

A. Antoniou, I.K. Nikolos, A.I. Delis, "Solution reconstruction and limiting for the 2D Euler equations in centroid-dual unstructured finite volumes", Proceedings of the 10th HSTAM International Congress on Mechanics, Chania, Crete, Greece, 25-27 May, 2013.

D. Angelopoulos, Validation of a High-Order Numerical Discretization Scheme for the Solution of the 3-D Euler Equations, M.Sc. Thesis, School of Production Engineering & Management, Technical University of Crete, 14/5/2019.

D.P. Angelopoulos G.N. Lygidakis, I.K. Nikolos, "Validation of a High-order Numerical Discretization Scheme for the Solution of the 2-D Euler Equations", Proceedings of Global Power and Propulsion Society, ISSN-Nr: 2504-4400, GPPS Chania20, Chania, Greece, 7 – 9 September, 2020. Paper No.: GPPS-CH-2020-0039. DOI: 10.33737/gpps20-tc-39