On time integration in the XFEM

Fries, Thomas‐Peter; Zilian, Andreas

doi:10.1002/nme.2558

Cited by 52 publications

(66 citation statements)

References 31 publications

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“…The Neumann boundary condition has been omitted for the sake of clarity. Using a backward Euler scheme for the time derivative of v in (15) gives the system of equations Fries and Zilian (2009):…”

Section: Stokes Problemmentioning

confidence: 99%

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Modelling of Phase Change With Non-Constant Density Using Xfem and a Lagrange Multiplier

Martin¹,

Chaouki²,

Robert³

et al. 2017

Frontiers in Heat and Mass Transfer

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A two phase model for two-dimensional solidification problems with variable densities was developed by coupling the Stefan problem with the Stokes problem and applying a mass conserving velocity condition on the phase change interface. The extended finite element method (XFEM) was used to capture the strong discontinuity of the velocity and pressure as well as the jump in heat flux at the i nterface. The melting temperature and velocity condition were imposed on the interface using a Lagrange multiplier and the penalization method, respectively. The resulting formulations were then coupled using a fixed point iteration a lgorithm. Three examples were investigated and the results were compared to numerical results coming from a commercial software using ALE techniques to track the solid/liquid interface. The model was able to reproduce the benchmark simulations while maintaining a sharp phase change interface and conserving mass.

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Section: Stokes Problemmentioning

confidence: 99%

“…The integration scheme for the mass matrix (equations (13c) and (17d)) must take both intersections into account when generating the integration subelements to obtain optimal convergence Fries and Zilian (2009). This can be difficult and can significantly increases the number of subelements required to fit the geometry.…”

Section: Numerical Integrationmentioning

confidence: 99%

Modelling of Phase Change With Non-Constant Density Using Xfem and a Lagrange Multiplier

Martin¹,

Chaouki²,

Robert³

et al. 2017

Frontiers in Heat and Mass Transfer

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show abstract

“…This is the approach recently taken in the context of XFEM [Fries and Zilian, 2009] and immersed boundary methods [Ilinca and Hetu, 2011B]. For example, using such an approach to assemble the Galerkin residual contribution for the time derivative for a scalar field, , the integral over the entire domain is split into subdomains …”

Section: Dynamic Discretization Via Subdomain Integrationmentioning

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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“…It is noted that for moving high gradients, the enrichment functions are time-dependent which effects the time discretization. Time-stepping schemes are then to be used with care as discussed in [21,22]. Consequently, for all subsequent test-cases with moving high gradients we employ the discontinuous Galerkin method in time (i.e.…”

Section: Numerical Examples With High Gradients Inside the Domainmentioning

confidence: 99%

“…Due to the movement of the interface, we prefer to employ the discontinuous Galerkin method in time so that the variational weak form (3.9) is relevant. The movement of the high gradient is then captured naturally [21,22].…”

Section: Advection-diffusion Equation With Moving High Gradient (Posimentioning

confidence: 99%

The XFEM for high‐gradient solutions in convection‐dominated problems

Abbas

Alizada

Fries

2009

Numerical Meth Engineering

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SUMMARYConvection-dominated problems typically involve solutions with high gradients near the domain boundaries (boundary layers) or inside the domain (shocks). The approximation of such solutions by means of the standard finite element method requires stabilization in order to avoid spurious oscillations. However, accurate results may still require a mesh refinement near the high gradients. Herein, we investigate the extended finite element method (XFEM) with a new enrichment scheme that enables highly accurate results without stabilization or mesh refinement. A set of regularized Heaviside functions is used for the enrichment in the vicinity of the high gradients. Different linear and non-linear problems in one and two dimensions are considered and show the ability of the proposed enrichment to capture arbitrary high gradients in the solutions.

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On time integration in the XFEM

Cited by 52 publications

References 31 publications

Modelling of Phase Change With Non-Constant Density Using Xfem and a Lagrange Multiplier

Modelling of Phase Change With Non-Constant Density Using Xfem and a Lagrange Multiplier

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

The XFEM for high‐gradient solutions in convection‐dominated problems

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