| 11. |
- Jansson, Niclas, et al.
(författare)
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Framework For Massively Parallel Adaptive Finite Element Computational Fluid Dynamics On Tetrahedral Meshes
- 2012
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Ingår i: SIAM Journal on Scientific Computing. - : Society for Industrial & Applied Mathematics (SIAM). - 1064-8275 .- 1095-7197. ; 34:1, s. C24-C42
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we describe a general adaptive finite element framework for unstructured tetrahedral meshes without hanging nodes suitable for large scale parallel computations. Our framework is designed to scale linearly to several thousands of processors, using fully distributed and efficient algorithms. The key components of our implementation, local mesh refinement and load balancing algorithms, are described in detail. Finally, we present a theoretical and experimental performance study of our framework, used in a large scale computational fluid dynamics computation, and we compare scaling and complexity of different algorithms on different massively parallel architectures.
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| 12. |
- Jansson, Niclas, 1983-
(författare)
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High Performance Adaptive Finite Element Methods : With Applications in Aerodynamics
- 2013
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The massive computational cost for resolving all scales in a turbulent flow makes a direct numerical simulation of the underlying Navier-Stokes equations impossible in most engineering applications. Recent advances in adaptive finite element methods offer a new powerful tool in Computational Fluid Dynamics (CFD). The computational cost for simulating turbulent flow can be minimized by adaptively resolution of the mesh, based on a posteriori error estimation. Such adaptive methods have previously been implemented for efficient serial computations, but the extension to an efficient parallel solver is a challenging task. This work concerns the development of an adaptive finite element method that enables efficient computation of time resolved approximations of turbulent flow for complex geometries with a posteriori error control. We present efficient data structures and data decomposition methods for distributed unstructured tetrahedral meshes. Our work also concerns an efficient parallelization of local mesh refinement methods such as recursive longest edge bisection, and the development of an a priori predictive dynamic load balancing method, based on a weighted dual graph. We also address the challenges of emerging supercomputer architectures with the development of new hybrid parallel programming models, combining traditional message passing with lightweight one-sided communication. Our implementation has proven to be both general and efficient, scaling up to more than twelve thousands cores.
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| 13. |
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| 14. |
- Compere, Gaetan, et al.
(författare)
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A mesh adaptation framework for dealing with large deforming meshes
- 2010
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Ingår i: International Journal for Numerical Methods in Engineering. - : Wiley. - 0029-5981 .- 1097-0207. ; 82:7, s. 843-867
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Tidskriftsartikel (refereegranskat)abstract
- In this paper. we identify and propose solutions for several issues encountered when designing a mesh adaptation package, such as mesh-to-mesh projections and mesh database design, and we describe an algorithm to integrate a mesh adaptation procedure in a physics solver. The open-source MAdLib package is presented as an example of such a mesh adaptation library. A new technique combining global node repositioning and mesh optimization in order to perform arbitrarily large deformations is also proposed. We then present several test cases to evaluate the performances of the proposed techniques and to show their applicability to fluid-structure interaction problems with arbitrarily large deformations. Copyright (C) 2009 John Wiley & Sons, Ltd.
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| 15. |
- Hoffman, Johan, et al.
(författare)
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Adaptive modeling of turbulent flow with residual based turbulent kinetic energy dissipation
- 2011
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Ingår i: Computer Methods in Applied Mechanics and Engineering. - : Elsevier BV. - 0045-7825 .- 1879-2138. ; 200:37-40, s. 2758-2767
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we first review our recent work on a new framework for adaptive turbulence simulation: we model turbulence by weak solutions to the Navier-Stokes equations that are wellposed with respect to mean value output in the form of functionals, and we use an adaptive finite element method to compute approximations with a posteriori error control based on the error in the functional output. We then derive a local energy estimate for a particular finite element method, which we connect to related work on dissipative weak Euler solutions with kinetic energy dissipation due to lack of local smoothness of the weak solutions. The ideas are illustrated by numerical results, where we observe a law of finite dissipation with respect to a decreasing mesh size.
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| 16. |
- Hoffman, Johan, et al.
(författare)
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Unified Continuum modeling of fluid-structure interaction
- 2011
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Ingår i: Mathematical Models and Methods in Applied Sciences. - : World Scientific. - 0218-2025. ; 21:3, s. 491-513
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, we describe an incompressible Unified Continuum(UC) model in Euler (laboratory) coordinates with a moving mesh for tracking the fluid-structure interface as part of the discretization, allowing simple and general formulation and efficient computation. The model consists of conservation equations for mass and momentum, a phase convection equation and a Cauchy stress and phase variable theta as data for defining material properties and constitutive laws. We target realistic 3D turbulent fluid-structure interaction (FSI) applications, where we show simulation results of a flexible flag mounted in the turbulent wake behind a cube as a qualitative test of the method, and quantitative results for 2D benchmarks, leaving adaptive error control for future work. We compute piecewise linear continuous discrete solutions in space and time by a general Galerkin (G2) finite element method (FEM). We introduce and compensate for mesh motion by defining a local arbitrary Euler-Lagrange (ALE) map on each space-time slab as part of the discretization, allowing a sharp phase interface given by theta on cell facets. The Unicorn implementation is published as part of the FEniCS Free Software system for automation of computational mathematical modeling. Simulation results are given for a 2D stationary convergence test, indicating quadratic convergence of the displacement, a simple 2D Poiseuille test for verifying correct treatment of the fluid-structure interface, showing quadratic convergence to the exact drag value, an established 2D dynamic flag benchmark test, showing a good match to published reference solutions and a 3D turbulent flag test as indicated above.
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| 17. |
- Jansson, Johan, 1978-, et al.
(författare)
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Adaptive error control in finite element methods using the error representation as error indicator
- 2013
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we present a new a posteriori adaptive finite elementmethod (FEM) directly using the error representation as a local errorindicator, and representing the primal and dual solutions in the samefinite element space (here piecewise continuous linear functions onthe same mesh). Since this approach gives a global a posteriori errorestimate that is zero (due to the Galerkin orthogonality), the errorrepresentation has historically been thought to contain no informationabout the error. However, we show the opposite, that locally, theorthogonal error representation behaves very similar to thenon-orthogonal error representation using a quadratic approximation ofthe dual. We present evidence of this both in the form of an a prioriestimate for the local error indicator and a detailed computationalinvestigation showing that the two methods exhibit very similarbehavior and performance, and thus confirming the theoreticalprediction. We also present a stabilized version of the method fornon-elliptic partial differential equations (PDE) where the errorrepresentation is no longer orthogonal, and where both the local errorindicator and global error estimate behave similar to the errorrepresentation using a quadratic approximation of the dual.
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| 18. |
- Jansson, Johan, et al.
(författare)
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Adaptive stabilized finite element framework for simulation of vocal fold turbulent fluid-structure interaction
- 2013
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Ingår i: Proceedings of Meetings on Acoustics. - : Acoustical Society of America (ASA). ; , s. 1-9
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Konferensbidrag (refereegranskat)abstract
- As a step toward building a more complete model of voice production mechanics, we assess the feasibility of a fluid-structure simulation of the vocal fold mechanics in the Unicorn incompressible Unified Continuum framework. The Unicorn framework consists of conservation equations for mass and momentum, a phase function selecting solid or fluid constitutive laws, a convection equation for the phase function and moving mesh methods for tracking the interface, and discretization through an adaptive stabilized finite element method. The framework has been validated for turbulent flow for both low and high Reynolds numbers and has the following features: implicit turbulence modeling (turbulent dissipation only occurs through numerical stabilization), goal-oriented mesh adaptivity, strong, implicit fluid-structure coupling and good scaling on massively parallel computers. We have applied the framework for turbulent fluid-structure interaction simulation of vocal folds, and present initial results. Acoustic quantities have been extracted from the framework in the setting of an investigation of a configuration approximating an exhaust system with turbulent flow around a flexible triangular steel plate in a circular duct. We present some results of the investigation as well as results of the framework applied to other problems.
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| 19. |
- Jansson, Johan, 1978-, et al.
(författare)
-
Automated adaptive error control in finite element methods using the error representation as error indicator
- 2014
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we present a new adaptive finite element method directly using the a posteriori error representation as a local error indicator, and representing the primal and dual solutions in the same finite element space (here piecewise continuous linear functions on the same mesh). Since this approach gives a global a posteriori error estimate that is zero (due to Galerkin orthogonality), the error representation has traditionally been thought to contain no information about the error. However, we show the opposite, that locally, the orthogonal error representation behaves very similar to the non-orthogonal error representation using a higher order approximation of the dual, which is a standard approach to overcome the problem of a zero error estimate. We present evidence of this both in the form of an a priori estimate for the local error indicator for an elliptic model problem and a detailed computational investigation showing that the two methods exhibit very similar behavior and performance, and thus confirming the theoretical prediction. We also present computational results using a stabilized version of the method for non-elliptic partial differential equations where the error representation is no longer orthogonal, and where both the local error indicator and global error estimate behave similar to the error representation using a higher order approximation of the dual. The benefits of this adaptive method are generality and simplicity in formulation, sharpness, and efficiency since high order approximation of the dual and computation of additional constructs such as jump terms over interior facets or local problems are avoided.
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| 20. |
- Jansson, Johan, 1978-, et al.
(författare)
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Automated error control in finite element methods withapplications in fluid flow
- 2014
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper we present a new adaptive finite element method for thesolution of linear and non-linear partial differential equationsdirectly using the a posteriori error representation as a local errorindicator, with the primal and dual solutions approximated in the samefinite element space, here piecewise continuous linear functions onthe same mesh. Since this approach gives a global a posteriori errorrepresentation that is zero due to Galerkin orthogonality, the errorrepresentation has traditionally been thought to contain noinformation about the error. However, for elliptic andconvection-diffusion model problems we show the opposite, that locallythe orthogonal error representation behaves very similar to thenon-orthogonal error representation using a higher order approximationof the dual. We have previously proved an a priori estimate of thelocal error indicator for elliptic problems, and in this paper weextend the proof to convection-reaction problems. We also present aversion of the method for non-elliptic and non-linear problems using astabilized finite element method where the a posteriori errorrepresentation is no longer orthogonal. We apply this method to thestationary incompressible Navier-Stokes equation and perform detailednumerical experiments which show that the a posteriori error estimateis within a factor 2 of the error based on a reference value on a finemesh, except in a few data points on very coarse meshes for anon-smooth test case where it is within a factor 3.
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