Parallel finite element simulations of incompressible viscous fluid flow by domain decomposition with Lagrange multipliers

Rivera, Christian; Heniche, Mourad; Glowinski, Roland; Tanguy, Philippe A.

doi:10.1016/j.jcp.2010.03.028

Cited by 13 publications

(7 citation statements)

References 47 publications

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“…Typical examples are hierarchical interface decomposition (HID) [42] and heuristics for nodal or block multi-coloring [13][14][15]. These techniques and other related methods have been used in various application domains, such as CFD, computational electromagnetics, and structure analyses [16,17,[43][44][45].…”

Section: Performance Comparisonmentioning

confidence: 99%

Algebraic Block Multi-Color Ordering Method for Parallel Multi-Threaded Sparse Triangular Solver in ICCG Method

Iwashita

Nakashima

Takahashi

2012

2012 IEEE 26th International Parallel and Distributed Processing Symposium

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In this paper, we propose a new parallel ordering method to vectorize and parallelize the sparse triangular solver, which is called hierarchical block multi-color ordering. In this method, the parallel forward and backward substitutions can be vectorized while preserving the advantages of block multi-color ordering, that is, fast convergence and fewer thread synchronizations. To evaluate the proposed method in a parallel ICCG (Incomplete Cholesky Conjugate Gradient) solver, numerical tests were conducted using five test matrices on three types of computational nodes. The numerical results indicate that the proposed method outperforms the conventional block and nodal multi-color ordering methods in 13 out of 15 test cases, which confirms the effectiveness of the method.

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Section: Performance Comparisonmentioning

confidence: 99%

Algebraic Block Multi-Color Ordering Method for Parallel Multi-Threaded Sparse Triangular Solver in ICCG Method

Iwashita

Nakashima

Takahashi

2012

2012 IEEE 26th International Parallel and Distributed Processing Symposium

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“…In solving the Navier-Stokes equations, ordering of the degrees of freedom is essential for the convergence [32]. For parallel computations at hand, the variables were reordered in blocks, depending on if the equations correspond to internal, interface, pressure or Lagrange multipliers as illustrated in the following equation:…”

Section: Parallel Implementationmentioning

confidence: 99%

A parallel finite element sliding mesh technique for the simulation of viscous flows in agitated tanks

Rivera

Heniche

Bertrand

et al. 2011

Numerical Methods in Fluids

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SUMMARY A parallel sliding mesh algorithm for the finite element simulation of viscous fluid flows in agitated tanks is presented. Lagrange multipliers are used at the sliding interfaces to enforce the continuity between the fixed and moving subdomains. The novelty of the method consists of the coupled solution of the resulting velocity–pressure‐Lagrange multipliers system of equations by an ILU(0)‐QMR solver. A penalty parameter is introduced for both the interface and the incompressibility constraints to avoid pivoting problems in the ILU(0) algorithm. To handle the convective term, both the Newton–Raphson scheme and the semi‐implicit linearization are tested. A penalty parameter is introduced for both the interface and the incompressibility constraints to avoid the failure of the ILU(0) algorithm due to the lack of pivoting. Furthermore, this approach is versatile enough so that it allows partitioning of sliding and fixed subdomains if parallelization is required. Although the sliding mesh technique is fairly common in CFD, the main advantage of the proposed approach is its low computational cost due to the inexpensive and parallelizable calculations that involve preconditioned sparse iterative solvers. The method is validated for Couette and coaxial stirred tanks. Copyright © 2011 John Wiley & Sons, Ltd.

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“…The enriched tetrahedral nine‐node P 1 + − P 0 element (first introduced by Bertrand et al 20) solves velocity and pressure using a Lagrange multiplier that connects the continuity and momentum equations 17, 21, 22. This element is based on the classical linear tetrahedron P 1 + − P 0 , comprises 24 velocity degrees of freedom and 1 pressure degree of freedom at the element centroid and uses the Uzawa algorithm to approximate the velocity with a linear polynomial considering a constant pressure inside each element.…”

Section: Numerical Investigationmentioning

confidence: 99%

“…At this stage, let us mention that in the transition regime the advection term ( v ·grad v ) in the Navier–Stokes equations cannot be neglected and poses convergence issues. One way to cure the problem consists in introducing the well‐known SUPG technique to help stabilize the Newton–Raphson iterations procedure 22…”

Section: Numerical Investigationmentioning

confidence: 99%

CFD investigation of new helical ribbon mixers bottom shapes to improve pumping

Sanjuan-Galindo

Heniche

Ascanio

et al. 2011

Asia-Pacific J Chem Eng

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It is well known that helical ribbon (HR) impellers exhibit poor bottom pumping properties. Three different HR impeller geometries, varying in their bottom design, are compared in terms of their mixing performance. Particular emphasis is given to the improvement of pumping capabilities. The selected bottom geometries were a standard bottom termination, an anchor-type termination and a paddle-type termination. The investigation was based on the use of 3D finite-element simulation to assess the hydrodynamics and mixing performance using various distributive and dispersive criteria. Analysis of Poincaré maps showed that an HR with a paddle-type termination operating in a down-pumping mode offered the best performance. 

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Parallel finite element simulations of incompressible viscous fluid flow by domain decomposition with Lagrange multipliers

Cited by 13 publications

References 47 publications

Algebraic Block Multi-Color Ordering Method for Parallel Multi-Threaded Sparse Triangular Solver in ICCG Method

Algebraic Block Multi-Color Ordering Method for Parallel Multi-Threaded Sparse Triangular Solver in ICCG Method

A parallel finite element sliding mesh technique for the simulation of viscous flows in agitated tanks

CFD investigation of new helical ribbon mixers bottom shapes to improve pumping

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