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On the simulation of steady and unsteady incompressible flows using the finite volume approach and artificial compressibility concept on hybrid unstructured grids

Sarakinos Sotirios

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Summary

In this study the development and evaluation of a Computational Fluid Dynamics (CFD) code for the simulation of incompressible flows is reported. The code, named Galatea-I after the sea-nymph of ancient Greek mythology, utilizes the Navier-Stokes equations, augmented with the artificial compressibility method – which is considered superior to pressure-based methods such as SIMPLE, especially in case of steady state flows – for the simulation of inviscid, laminar and turbulent viscous incompressible flows, of steady or unsteady nature. For the simulation of turbulence the Reynolds Averaged form of the Navier-Stokes (RANS) is used, where the stress tensor in the viscous fluxes vector is analyzed with the Boussinesq assumption in a laminar and a turbulent part. For the evaluation of the turbulent kinematic energy and the turbulent kinematic viscosity the SST turbulence model has been incorporated in the Galatea-I solver. The flow model, as well as the turbulence model equations are discretized in space over three dimensional hybrid unstructured grids with a node-centered, Finite Volume (FV) scheme. For the evaluation of inviscid fluxes Roe’s approximate Riemann solver is used, while for the calculation of the velocity gradients, which are required for the evaluation of the viscous fluxes, either an element based approach, or a nodal averaging method is used. Free-slip or no-slip conditions are imposed on solid boundaries, while at the inlet or outlet boundaries a characteristics based boundary conditions scheme has been incorporated. Time integration in pseudo-time is performed with an explicit four-stage Runge-Kutta (RK(4)) scheme, while for the time-accurate evaluation of unsteady flows a dual time-stepping scheme is adopted. Two acceleration techniques have been applied in the Galatea-I solver. Firstly, via parallel processing with the domain decomposition approach, where the initial computational grid is divided into smaller sub-domains, each attributed to a single computer core and treated as an autonomous grid with inner boundaries, where information from adjacent grids is passed via the Message Passing Interface (MPI). Secondly, with an agglomeration multigrid method, where a number of consecutively coarser meshes are generated by fusing adjacent control volumes of the finer meshes and evaluation of the governing equations is performed successively on all generated and initial meshes, thus enhancing the convergence rate of the iterative procedures. The performance of the Galatea-I solver was assessed with a number of steady and unsteady test cases, demonstrating the capabilities of the proposed methodologies in accuracy and efficiency. While many of the utilized test cases can be characterized as standard for the evaluation of incompressible flow solvers, the proposed code was used against more complex ones, such as the DARPA SUBOFF model and the DLR-F11 aircraft model in high lift configuration. As far as the latter test case is concerned, although it constitutes a test case where traditionally compressible flow solvers with preconditioning matrices are evaluated, the Galatea-I solver has generated excellent results.

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