Conservative Remapping and Region Overlays by Intersecting Arbitrary Polyhedra

Grandy, J.

doi:10.1006/jcph.1998.6125

Cited by 88 publications

(68 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…L 2 projection or interpolation of the solution between the source and target meshes may cause non-negligible spatial error [41]. In order to minimize the spatial coupling error due to the data transfer between the different physics defined on non overlapping meshes, several techniques have been developed [42]. Jiao and Heath [43] have derived rigorous cost estimates for different remapping methods along with the solution costs.…”

Section: Spatial Coupling Error In Multi-mesh Approachesmentioning

confidence: 99%

“…Hence, the numerical integration over a cell is carried out on the real geometry (the actual cell itself), and not on its mapped reference element. Here, high order quadrature rules for each physics are employed along with inverse mapping of the meshes in different It is also important to note that, making use of available degrees of freedom, certain quantities such as total mass and energy need to be conserved through these projections [42]. This needs special attention while devising schemes to project these variables on a different mesh to be coupled with another physics.…”

mentioning

confidence: 99%

“…Let 41) and, by recursion after simplification, this yields the modified non-linear 'temporal' residual equation defined by 42) where …”

mentioning

confidence: 99%

See 2 more Smart Citations

Neutronic/Thermalhydraulic Coupling Technigues for Sodium Cooled Fast Reactor Simulations

Ragusa¹,

Siegel²,

Ruggieri³

2010

View full text Add to dashboard Cite

Executive SummaryThe objective of this project was to test new coupling algorithms and enable efficient and scalable multi-physics simulations of advanced nuclear reactors, with considerations regarding the implementation of such algorithms in massively parallel environments. Numerical tests were carried out to verify the proposed approach and the examples included some reactor transients. The project was directly related to the Sodium Fast Reactor program element of the Generation IV Nuclear Energy Systems Initiative and the Advanced Fuel cycle Initiative, and, supported the requirement of high-fidelity simulation as a mean of achieving the goals of the presidential Global Nuclear Energy Partnership (GNEP) vision.For decades, the modeling of nuclear cores has been divided into several distinct domains of physics: neutronics, hydraulics, heat transfer, … Yet, these physical models describe physical processes that are tightly intertwined and rely heavily on the solution field of one another. In the last decade or so, various existing mono-disciplinary codes have been coupled together in a naive "black-box" fashion, where the output of one code serves as the input of another code, producing nonlinearly inconsistent multiphysics solutions. Such schemes, which are still the main coupling paradigm today for solving nonlinear nuclear reactor physics equations, are based on a linearization of the coupling terms that is never resolved and that can lead to a loss of accuracy and stability in the solution procedure. In order to address the inconsistencies of traditional coupling strategies, a 3-D test-bed code based on reduced physical models has been developed. It includes several physic components, namely, multigroup neutron diffusion, monophasic fluid conservation laws (mass, momentum, energy), nonlinear heat conduction. This test-bed code was used to demonstrate the loss of accuracy order due to traditional operator-split techniques used in conventional coupling schemes; to implement Jacobian-free full resolution coupling schemes; to develop adaptive preconditioning techniques; and to investigate high-order time discretizations and adaptive time stepping strategies. The test-bed code employs state-of-the-art algorithms and libraries, namely the Jacobian0free Newton-Krylov technique to solve consistently fully implicit tightly coupled simulations and the ANL's PETSc library of linear and nonlinear solvers for scalability. We have demonstrated that the multiphysics solution procedure yields highly accurate solutions in space and time and is amenable for space/time adaptivity. This portion of the work is discussed in Part A of this report.It is widely agreed that high fidelity simulations is an utmost important tool for the conception, design and validation of complex physical systems such as nuclear reactors. Examples of such thrust can be seen in the ASCI program and the SciDAC program. GNEP strongly advocates the development of the next-generation simulation software with a far wider range of applicability than conven...

show abstract

Section: Spatial Coupling Error In Multi-mesh Approachesmentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Neutronic/Thermalhydraulic Coupling Technigues for Sodium Cooled Fast Reactor Simulations

Ragusa¹,

Siegel²,

Ruggieri³

2010

View full text Add to dashboard Cite

show abstract

“…In this method, the value of a target element is the weighted average of the values of the source elements in contact, where the weights are the areas of the intersections between the source and target elements. This method is sometimes called conservative rezoning (remapping) [13][14][15]. For the discretization of conservative rezoning, integrations are usually evaluated over the intersections of the source and target elements, or sometimes converted to boundary integration.…”

Section: Area-weighted Averagingmentioning

confidence: 99%

Common‐refinement‐based data transfer between non‐matching meshes in multiphysics simulations

Jiao

Heath

2004

Numerical Meth Engineering

156

130

View full text Add to dashboard Cite

SUMMARYIn multiphysics simulations using a partitioned approach, each physics component solves on its own mesh, and the interfaces between these meshes are in general non-matching. Simulation data (e.g. jump conditions) must be exchanged across the interface meshes between physics components. It is highly desirable for such data transfers to be both numerically accurate and physically conservative. This paper presents accurate, conservative, and efficient data transfer algorithms utilizing a common refinement of two non-matching surface meshes. Our methods minimize errors in a certain norm while achieving strict conservation. Some traditional methods for data transfer and related problems are also reviewed and compared with our methods. Numerical results demonstrate significant advantages of common-refinement based methods, especially for repeated transfers. While the comparisons are performed with matching geometries, this paper also addresses additional complexities associated with non-matching surface meshes and presents some experimental results from 3-D simulations using our methods.

show abstract

“…The use of mesh intersection for conservative interpolation seems natural for unconnected meshes and has already been alluded in [10] or applied in [11] for order 1 reconstruction. The locality is inherent for efficiency and robustness.…”

Section: Introductionmentioning

confidence: 99%

A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes

Alauzet

2016

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

This document presents an interpolation operator on unstructured tetrahedral meshes that satisfies the properties of mass conservation, P 1 -exactness (order 2) and maximum principle. Interpolation operators are important for many applications in scientific computing. For instance, in the context of anisotropic mesh adaptation for time-dependent problems, the interpolation stage becomes crucial as the error due to solution transfer accumulates throughout the simulation. This error can eventually spoil the overall solution accuracy. When dealing with conservation laws in CFD, solution accuracy requires enforcement of mass preservation throughout the computation, in particular in long time scale computations. In the proposed approach, the conservation property is achieved by local mesh intersection and quadrature formulae. Derivatives reconstruction is used to obtain a second order method. Algorithmically, our goal is to design a method which is robust and efficient. The robustness is mandatory to obtain a reliable method on real-life applications and to apply the operator to highly anisotropic meshes. The efficiency is achieved by designing a matrix-free operator which is highly parallel. A multi-thread parallelization is given in this work. Several numerical examples are presented to illustrate the efficiency of the proposed approach.Key-words: Solution interpolation, matrix-free conservative interpolation, parallel interpolation, unstructured mesh, mesh adaptation, conservation laws * INRIA, Équipe-projet Gamma3, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France. email: frederic.alauzet@inria.fr A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes Résumé : Ce document présente un opérateur d'interpolation sur des maillages tétraé-driques non-structurés qui satisfait les propriétés de conservation de la masse, P 1 -exactitude (ordre 2) et principe du maximum.Mots-clés : Interpolation de solution, interpolation conservative sans matrice, interpolation parallèle, maillage non-structuré, adaptation de maillage, adaptation de maillage, loi de conservation A parallel matrix-free conservative solution interpolation on tetrahedral meshes 3

show abstract

Conservative Remapping and Region Overlays by Intersecting Arbitrary Polyhedra

Cited by 88 publications

References 12 publications

Neutronic/Thermalhydraulic Coupling Technigues for Sodium Cooled Fast Reactor Simulations

Neutronic/Thermalhydraulic Coupling Technigues for Sodium Cooled Fast Reactor Simulations

Common‐refinement‐based data transfer between non‐matching meshes in multiphysics simulations

A parallel matrix-free conservative solution interpolation on unstructured tetrahedral meshes

Contact Info

Product

Resources

About