Efficient simulations of large-scale convective heat transfer problems

• Autorzy: Goik Damian , Banaś Krzysztof , Bielański Jan , Chłoń Kazimierz

Identyfikatory

DOI

10.7494/csci.2021.22.4.4144

• Języki publikacji: EN

Abstrakty

EN

We describe an approach for efficient solution of large-scale convective heat transfer problems that are formulated as coupled unsteady heat conduction and incompressible fluid-flow equations. The original problem is discretized over 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 (the heat transfer and Navier–Stokes equations) give rise to large sparse systems of linear equations. The systems are solved by using an iterative GMRES solver with suitable preconditioning. For the incompressible flow equations, we employ a special preconditioner that is based on an algebraic multigrid (AMG) technique. This paper presents algorithmic and implementation details of the solution procedure, which is suitably tuned – especially for ill-conditioned systems that arise from discretizations of incompressible Navier–Stokes equations. We describe a parallel implementation of the solver using MPI and elements from the PETSC library. The scalability of the solver is favorably compared with other methods, such as direct solvers and the standard GMRES method with ILU preconditioning.

Słowa kluczowe

EN

convective heat transfer; finite element method; sparse linear equations; algebraic multigrid; Navier–Stokes equations; GMRES; block preconditioning; SUPG stabilization; MPI; PETSc; scalability

• Wydawca: Wydawnictwa AGH
• Czasopismo: Computer Science
• Rocznik: 2021
• Tom: T. 22 (4)
• Strony: 517--538
• Opis fizyczny: Bibliogr. 29 poz., rys., tab.

Twórcy

autor

Goik Damian

• AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Krakow, Poland

autor

Banaś Krzysztof

• AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Krakow, Poland

autor

Bielański Jan

• AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Krakow, Poland

autor

Chłoń Kazimierz

• AGH University of Science and Technology, al. A. Mickiewicza 30, 30-059 Krakow, Poland

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