A Newton–Raphson Pseudo-Solid Domain Mapping Technique for Free and Moving Boundary Problems: A Finite Element Implementation

Sackinger, P.A.; Schunk, Peter Randall; Rao, Rekha R.

doi:10.1006/jcph.1996.0081

Cited by 166 publications

(132 citation statements)

References 30 publications

(44 reference statements)

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“…The mesh deformation is dealt based on the sizes of the elements. Following the work in [15] and [17] we want smaller elements to be stiffer than larger ones. In regions where the mesh would undergo large distortions (e.g.…”

Section: Strong Formulationmentioning

confidence: 99%

Multigrid Solver With Domain Decomposition Smoothing for Steady-State Incompressible Fsi Problems

Aulisa¹,

Bnà²,

Bornia³

2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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Abstract. In this paper we investigate the numerical performance of a monolithic Newtonmultigrid solver with domain decomposition smoothers for the solution of a class of stationary incompressible FSI problems. The physics of the problem is described using a monolithic approach, where mass continuity and stress balance are automatically satisfied across the fluidsolid interface. The deformation of the fluid domain is taken into account within the nonlinear Newton iterations according to an Arbitrary Lagrangian Eulerian (ALE) scheme. Due to the complexity and variety of the operators, the implementation of the Jacobian matrix in the nonlinear iterations is not a trivial task. To this purpose, we make use of automatic differentiation tools for an exact computation of the Jacobian matrix. The numerical solution of steady-state problems is particularly challenging, due to the ill-conditioning of the induced stiffness matrix. Moreover, the enforcement of the incompressibility condition calls for the use of incompressible solvers either of mixed or segregated type. At each nonlinear outer iteration the resulting linearized system is solved with a geometric multigrid solver. We consider a GMRES smoother preconditioned by an Additive Schwarz Method (ASM). The domain decomposition of the preconditioner is driven by the natural splitting between fluid and solid domain. The numerical results of some benchmark tests for steady-state cases show agreement with the literature and an increased robustness with our choice of smoothers with respect to standard ones.

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Section: Strong Formulationmentioning

confidence: 99%

Multigrid Solver With Domain Decomposition Smoothing for Steady-State Incompressible Fsi Problems

Aulisa¹,

Bnà²,

Bornia³

2015

Proceedings of the 5th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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“…This leads to the most common update rule and has, for example, been used in [12,18,26]. However, there the update is performed in the normal direction rather than the radial direction which might lead to a degeneration of the domain.…”

Section: First Order Update Rulementioning

confidence: 99%

“…The level set method for Bernoulli's problem has been used in [6,7,18], enjoying the property of allowing topology changes. In all these papers, however, only the Laplace equation and constant Dirichlet and Neumann data have been considered which corresponds to the original Bernoulli free boundary problem.…”

mentioning

confidence: 99%

Improved trial methods for a class of generalized Bernoulli problems

Harbrecht

Mitrou

2014

Journal of Mathematical Analysis and Applications

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The aim of this article is to develop improved trial methods for the solution of a generalized exterior Bernoulli free boundary problem. At the free boundary, we prescribe the Neumann boundary condition and update the free boundary with the help of the remaining Dirichlet boundary condition. Appropriate update rules are obtained by expanding the state's Dirichlet data at the actual boundary via a Taylor expansion of first and second order. The resulting trial methods converge linearly for both cases, although the trial method based on the second order Taylor expansion is much more robust. Nevertheless, via results of shape sensitivity analysis, we are able to modify the update rules such that their convergence is improved. The feasibility of the proposed trial methods and their performance is demonstrated by numerical results.

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“…Elsewhere, the mesh moves in an arbitrary manner. An example of an ALE implementation can be found in [Sackinger, Schunk and Rao, 1996] for 2D and extended to 3D by [Cairncross et al, 2000]. This nodal mesh velocity is defined by differentiating the position of the nodes with respect to time.…”

Section: Dynamic Discretization Via Moving Meshmentioning

confidence: 99%

Multiscale models of nuclear waste reprocessing : from the mesoscale to the plant-scale.

Rao¹,

Brotherton²,

Domino³

et al. 2012

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Nuclear waste reprocessing and nonproliferation models are needed to support the renaissance in nuclear energy. This report summarizes an LDRD project to develop predictive capabilities to aid the next-generation nuclear fuel reprocessing, in SIERRA Mechanics, Sandia's high performance computing multiphysics code suite and Cantera, an open source software product for thermodynamics and kinetic modeling.Much of the focus of the project has been to develop a moving conformal decomposition finite element method (CDFEM) method applicable to mass transport at the water/oil droplet interface that occurs in the turbulent emulsion of droplets within the contactor. Contactor-scale models were developed using SIERRA Mechanics turbulence modeling capability. Unit operations occur at the column-scale where many contactors are connected in series. Population balance models 4 were developed to investigate placements and coupling of contactors at this scale. Thermodynamics models of the separation were developed in Cantera to allow for the prediction of distribution coefficients for various concentrations of surfactant and acid. Droplet-scale modeling was conducted in a microfluidic device and for verification of the algorithm. Extensive validation and discovery experiments were performed at the droplet and contactor-scales for both fluid dynamics and mass transport. 5 AcknowledgmentsThe authors would like to thank our mission specialist Veena Tikare for helping us develop the project, our reprocessing material balance expert Ben Cipiti for explaining the details of the reprocessing plant., Roger Pawlowski and Rich Schiek helped with the idea of a scalable network model, but were unable to continue with the project, though were very helpful in the first year of the work. We believe this type of work should be continued at Sandia. Paul Galambos and John Pflug supported our microfluidic experiments. Reviewers Randy Schunk and Lisa Mondy provided helpful feedback. Randy Schunk also helped with our droplet-scale modeling in a moving reference frame. The Aria Product Owners past and present, Amalia Black, Sheldon Tieszen, and Kim Mish, have been invaluable for keeping the project going despite the many other directions of Sierra Mechanics. We would like to thank the "Enabling Predictive Simulations" investment area of the LDRD program for funding this work. We would like to express our gratitude to the LDRD office for the extension given for receiving the final report due to the illness of the PI.6

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A Newton–Raphson Pseudo-Solid Domain Mapping Technique for Free and Moving Boundary Problems: A Finite Element Implementation

Cited by 166 publications

References 30 publications

Multigrid Solver With Domain Decomposition Smoothing for Steady-State Incompressible Fsi Problems

Multigrid Solver With Domain Decomposition Smoothing for Steady-State Incompressible Fsi Problems

Improved trial methods for a class of generalized Bernoulli problems

Multiscale models of nuclear waste reprocessing : from the mesoscale to the plant-scale.

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