Open AccessEfficient Simulations of Large Scale Convective Heat Transfer Problems
Author(s) -
Damian Goik,
Krzysztof Banaś,
Jan Bielański,
Kazimierz Chłoń
Publication year - 2021
Publication title -
computer science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.145
H-Index - 5
eISSN - 2300-7036
pISSN - 1508-2806
DOI - 10.7494/csci.2021.22.4.4144
Subject(s) - generalized minimal residual method , preconditioner , multigrid method , solver , computer science , discretization , linear system , mathematics , fluid dynamics , iterative method , mathematical optimization , computational science , partial differential equation , algorithm , mechanics , physics , mathematical analysis , programming language
We describe an approach for efficient solution of large scale convective heat transfer problems, formulated as coupled unsteady heat conduction and incompressible fluid flow equations. The original problem is discretized in time using classical implicit methods, while stabilized finite elements are used for space discretization. The algorithm employed for the discretization of the fluid flow problem uses Picard's iterations to solve the arising nonlinear equations. Both problems, heat transfer and Navier-Stokes quations, give rise to large sparse systems of linear equations. The systems are solved using iterative GMRES solver with suitable preconditioning. For the incompressible flow equations we employ a special preconditioner based on algebraic multigrid (AMG) technique. The paper presents algorithmic and implementation details of the solution procedure, which is suitably tuned, especially for ill conditioned systems arising from discretizations of incompressible Navier-Stokes equations. We describe parallel implementation of the solver using MPI and elements of PETSC library. The scalability of the solver is favourably compared with other methods such as direct solvers and standard GMRES method with ILU preconditioning.