Naslov
Implicitly coupled finite volume algorithms

Autori
Uroić, Tessa

Vrsta, podvrsta i kategorija rada
Ocjenski radovi, doktorska disertacija

Fakultet
Fakultet strojarstva i brodogradnje

Mjesto
Zagreb

Datum
25.10

Godina
2019

Stranica
242

Mentor
Jasak, Hrvoje

Ključne riječi
Implicit coupling, Block matrix, Pressure–velocity coupling, Algebraic multigrid, Conjugate gradient method

Sažetak
In this thesis a comparison of pressure–velocity coupling algorithms is conducted with special emphasis on the implicit coupling of momentum and pressure equations in a single linear system as an improvement on the conventional segregated methods. The research is done in the scope of the finite volume method, and carried out in foam-extend, a community driven fork of the open source computational fluid dynamics software OpenFOAM. We focus on the equations for steady–state, incompressible, single–phase turbulent flow. To counteract the zero block on the diagonal of the system, the pressure equation is derived as a Schur complement. A description of the OpenFOAM matrix format is given as well as the structure of the finite volume matrices which arise from the computational mesh connectivity. Contributions from finite volume equation discretisation to each term of the implicitly coupled block–matrix are illustrated. The computational effort is directed mostly to solving the pressure Poisson equation, thus it is very important to employ an efficient solver for elliptic equations, which is also effective for the hyperbolic momentum equation. An overview of linear solvers is given: fixed–point methods, algebraic multigrid and some versions of the Krylov subspace solvers are analysed in the context of Finite Volume Method. Two methods for constructing coarse matrices in algebraic multigrid are compared: additive correction method, which is the usual choice for the implicitly coupled pressure–velocity system in recent literature, and the newly implemented selection algebraic multigrid. Incomplete lower– upper factorisation based on Crout’s algorithm is used as an error smoother with the algebraic multigrid method. Parallelisation issues regarding the selection algebraic multigrid are laid out, with additional comments on the possible parallelisation strategies. The performance of both segregated and implicitly coupled pressure–velocity solver is compared for multiple complex test cases including external aerodynamics cases (Formula 1 front wing, bluff body with a diffuser, submarine) and internal flow cases (cooling of an engine jacket, centrifugal pump, Francis turbine) both on structured and unstructured meshes. A comparison of convergence against computation time and number of non–linear iterations is given, both in terms of field residuals as well as integral values. The influence of the linear solver on the convergence of implicitly coupled pressure–velocity solver is investigated, as well as the impact of different settings of selection algebraic multigrid on convergence rate and computation time.

Izvorni jezik
Engleski

Znanstvena područja
Strojarstvo

POVEZANOST RADA