In the world of computational fluid dynamics (CFD), solving the governing equations of incompressible, turbulent, single-phase fluid flow still represents the basis of many industrial and academic applications. The im...
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In the world of computational fluid dynamics (CFD), solving the governing equations of incompressible, turbulent, single-phase fluid flow still represents the basis of many industrial and academic applications. The implicitly coupled (monolithic) solution approach is still being developed and investigated for industrial-size applications. A parallel selection algebraic multigrid algorithm (AMG) based on the domain decomposition method is presented, applied for the solution of the linearised implicitly coupled pressure-velocity system discretised by the finite volume method, implemented in OpenFOAM. Since the setup phase of the selection AMG, i.e. sorting the equations into coarse and fine subsets is inherently sequential, it was decided to perform the setup phase locally on each processing unit. The prolongation matrix for transferring the correction from coarse to fine level and restriction matrix for transferring the residual from fine to coarse level are assembled locally as well. Parallel communication is necessary only for the calculation of the coarse level matrix, i.e. the matrix elements which describe the cross-coupling of equations located on different processing units. A localised version of the ILU factorisation based on Crout's algorithm is used as a smoother in the multigrid cycle. A detailed analysis of the coarse level matrix complexity is conducted in the context of the finite volume method in domain decomposition mode. The performance and scaling of our parallel implementation is investigated for two test cases and the possible drawbacks of the method are given. (C) 2020 Elsevier B.V. All rights reserved.
The fully coupled pressure-based algorithm is widely recognised for its superior convergence and robustness in solving incompressible flow problems. However, the increased scale of equations and the difficulty in solv...
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The fully coupled pressure-based algorithm is widely recognised for its superior convergence and robustness in solving incompressible flow problems. However, the increased scale of equations and the difficulty in solving linear systems have limited the widespread use of this algorithm in large-scale simulations. This paper presents an optimised block selective algebraic multigrid method significantly reducing computational complexity. Our approach employs a parallel modified independent set algorithm, allowing each process to perform matrix coarsening individually. Furthermore, an aggressive coarsening strategy is introduced to reduce complexity and enable the solution of larger-scale problems. Numerical experiments demonstrate that the solution time is shortened by 14% to 49% compared to the latest existing methods and outperforms the segregated algorithm. By addressing the computational challenges associated with the selective algebraic multigrid solver, this work unleashes the superior convergence properties of the fully coupled method.
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