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Unified Formulation for High-Order Streamline Tracing on Two-Dimensional Unstructured Grids

Ruben Juanes, Sébastien F. Matringe
2008 Journal of Scientific Computing  
In this paper we present a unified formulation for the development of high-order accurate streamline tracing algorithms on unstructured triangular and quadrilateral grids.  ...  Therefore, we provide a sound theoretical justification for the low-order algorithms currently in use, and we show how to achieve higher-order accuracy both in the streamline tracing and the travel time  ...  Conclusions We have presented a unified formulation for streamline tracing on unstructured grids.  ... 
doi:10.1007/s10915-008-9228-2 fatcat:52gma44gb5crhplizia7mku3hi

Robust streamline tracing for the simulation of porous media flow on general triangular and quadrilateral grids

Sébastien F. Matringe, Ruben Juanes, Hamdi A. Tchelepi
2006 Journal of Computational Physics  
We identify and implement two classes of velocity spaces: the lowest-order Raviart-Thomas space (low-order tracing) and the Brezzi-Douglas-Marini space of order one (high-order tracing), both on triangles  ...  We conclude that, for the same computational cost, high-order tracing is more accurate (smaller error in the time-of-flight) and robust (less sensitive to grid distortion) than low-order tracing.  ...  Acknowledgments We gratefully acknowledge financial support from the industrial affiliates of the Stanford University Petroleum Research Institute for Reservoir Simulation (SUPRI-B).  ... 
doi:10.1016/ fatcat:njkmscv6nrhgbjn6q5tgfvzvcq

fenicsR13: A Tensorial Mixed Finite Element Solver for the Linear R13 Equations Using the FEniCS Computing Platform [article]

Lambert Theisen, Manuel Torrilhon
2020 arXiv   pre-print
The presented solver serves as an example for implementing tensorial variational formulations in FEniCS, for which the documentation and literature seem to be very sparse.  ...  We describe a new tensorial approach utilizing the extension capabilities of FEniCS's Unified Form Language (UFL) to define required differential operators for tensors above second degree.  ...  The authors acknowledge the anonymous reviewers for their helpful comments.  ... 
arXiv:2007.05944v2 fatcat:ba6kewlcwvcpndnlbahtpnujuu

Flux Correction Tools for Finite Elements

D. Kuzmin, S. Turek
2002 Journal of Computational Physics  
Criteria for positivity of the numerical solution are formulated, and the low-order transport operator is constructed from the discrete high-order operator by adding modulated dissipation so as to eliminate  ...  Thereby essentially one-dimensional flux correction tools can be readily applied to multidimensional problems involving unstructured meshes.  ...  Many popular schemes are limited to one-dimensional problems or Cartesian grids with directional splitting.  ... 
doi:10.1006/jcph.2001.6955 fatcat:jevbzxidarhupnzosrlv4pjipe

A pressure-based semi-implicit space–time discontinuous Galerkin method on staggered unstructured meshes for the solution of the compressible Navier–Stokes equations at all Mach numbers

Maurizio Tavelli, Michael Dumbser
2017 Journal of Computational Physics  
We propose a new arbitrary high order accurate semi-implicit space-time discontinuous Galerkin (DG) method for the solution of the two and three dimensional compressible Euler and Navier-Stokes equations  ...  on staggered unstructured curved meshes.  ...  to the Su-perMUC supercomputer, as well as the support of the HLRS in Stuttgart, Germany, for awarding access to the Hazel Hen supercomputer.  ... 
doi:10.1016/ fatcat:wrj45xa4gbcubilpirq5cvzboq

Simulation of all-scale atmospheric dynamics on unstructured meshes

Piotr K. Smolarkiewicz, Joanna Szmelter, Feng Xiao
2016 Journal of Computational Physics  
The outlined approach exploits the synergy of two specific ingredients: the MPDATA methods for the simulation of fluid flows based on the sign-preserving properties of upstream differencing; and the flexible  ...  This has improved resolution of weather systems and enhanced the accuracy of forecasts, while setting the trend for development of unified all-scale atmospheric models.  ...  The quest for unified CFD models can be traced back to implicit continuousfluid Eulerian (ICE) method [51, 52] applicable to all speed flows, from incompressible to hypersonic regime, in multidimensional  ... 
doi:10.1016/ fatcat:v4bieeupdbb7jobm5q7p6gczjm

Multivalued Geodesic Ray-Tracing for Computing Brain Connections Using Diffusion Tensor Imaging

N. Sepasian, J. H. M. ten Thije Boonkkamp, B. M. Ter Haar Romeny, A. Vilanova
2012 SIAM Journal of Imaging Sciences  
In [49] Sepasian et al. focused on the mathematical and numerical model for analytic and synthetic fields in two-dimensional domains.  ...  Furthermore, streamline methods are based on local characteristics and therefore sensitive to noise.  ...  The authors would like to thank Olof Runborg for permission to use Figure 1 .  ... 
doi:10.1137/110824395 fatcat:awnezmtkzjdvtgikdoc7qfihju

Spectral semi-implicit and space–time discontinuous Galerkin methods for the incompressible Navier–Stokes equations on staggered Cartesian grids

Francesco Fambri, Michael Dumbser
2016 Applied Numerical Mathematics  
In this paper two new families of arbitrary high order accurate spectral DG finite element methods are derived on staggered Cartesian grids for the solution of the inc.NS equations in two and three space  ...  While the pressure is defined on the control volumes of the main grid, the velocity components are defined on a spatially staggered mesh.  ...  Acknowledgments The authors would like to thank Maurizio Tavelli and Vincenzo Casulli for the inspiring discussions on the topic.  ... 
doi:10.1016/j.apnum.2016.07.014 fatcat:24fixulyxze6vongm6lkvcyxti

Assessment of surgical effects on patients with obstructive sleep apnea syndrome using computational fluid dynamics simulations

Gary C. Cheng, Roy P. Koomullil, Yasushi Ito, Alan M. Shih, Somsak Sittitavornwong, Peter D. Waite
2014 Mathematics and Computers in Simulation  
the pressure effort required for normal breathing using a high-fidelity, 3-D numerical model.  ...  Obstructive sleep apnea syndrome is one of the most common sleep disorders.  ...  To enable such assessment and prediction with high accuracy, high-fidelity imaging techniques are necessary for acquiring the three-dimensional (3-D) detailed upper airway geometry of patients before and  ... 
doi:10.1016/j.matcom.2012.11.008 pmid:25530663 pmcid:PMC4269252 fatcat:fwk4ow6gxzewxbwcvkaa3nwp74

Multidimensional FEM-FCT schemes for arbitrary time stepping

D. Kuzmin, M. Möller, S. Turek
2003 International Journal for Numerical Methods in Fluids  
Zalesak's multidimensional limiter is employed to switch between linear discretizations of high and low order. A rigorous proof of positivity is provided.  ...  The flux-corrected-transport paradigm is generalized to finite element schemes based on arbitrary time-stepping.  ...  Encouraging results obtained for a number of one-and two-dimensional test problems demonstrate the potential of the implicit formulation.  ... 
doi:10.1002/fld.493 fatcat:bext45itgrboxboa74f4coqm4a

Blending isogeometric analysis and local maximum entropy meshfree approximants

A. Rosolen, M. Arroyo
2013 Computer Methods in Applied Mechanics and Engineering  
Indeed, it preserves the high fidelity boundary representation (exact CAD geometry) of isogeometric analysis, out of reach for bare meshfree methods, and easily handles volume discretization and unstructured  ...  The ability of the proposed method to impose directly essential boundary conditions in non convex domains, and to deal with unstructured grids and local refinement in domains of complex geometry and topology  ...  Acknowledgements We gratefully acknowledge Hennadiy Netuzhylov and David Modesto for their technical support and invaluable discussions about isogeometric analysis and NEFEM methods, respectively.  ... 
doi:10.1016/j.cma.2013.05.015 fatcat:ijfmidyrhvb7lmrn52b7jufqwi

Meshless techniques for anisotropic diffusion

Annamaria Mazzia, Giorgio Pini, Flavio Sartoretto
2014 Applied Mathematics and Computation  
Moreover, it would be good for the methods to be of high order accuracy.  ...  A good numerical method would be locally mass conservative, produce no or minimal over/under-shoots, produce minimal numerical diffusion, and require no CFL time-step limit for stability.  ...  Alfio Grillo MS5 High Order One-Step Pnpm Schemes on Unstructured Meshes for Hyperbolic Balance Laws In this talk we present a new unified approach of general PN PM schemes on unstructured meshes in  ... 
doi:10.1016/j.amc.2014.03.032 fatcat:c527226gyfgbffnq4p67qxd7wi

The Visual Haptic Workbench [chapter]

2005 Visualization Handbook  
We thank Robert MacLeod for suggesting the heart visualization example and Hope M.F. Eksten for her help with various construction and fabrication projects.  ...  Support for this research was provided by NSF grant ACI-9978063, ARO DURIP grant DAAG-559710065, and the DOE Advanced Visualization Technology Center (AVTC).  ...  Since haptic rendering is a local process, like particle advection, point-location algorithms for vector-field visualization on curvilinear and unstructured grids are readily applied [49] .  ... 
doi:10.1016/b978-012387582-2/50024-1 fatcat:2qzkmb4o5jf5dgo7imca7ikt3y

Visualization for the Physical Sciences [article]

Dan R. Lipsa, Robert S. Laramee, Simon J. Cox, Jonathan C. Roberts, Rick Walker
2011 Eurographics State of the Art Reports  
survey of its kind that provides a comprehensive view on existing work on visualization for the physical sciences.  ...  We introduce a novel classification scheme based on application area, data dimensionality and main challenge addressed and apply this classification scheme to each contribution from the literature.  ...  This is used for defect detection in an unstructured grid of liquid crystals, a previously unsolved problem. The phenomena being studies is 3D, static on a unstructured grid.  ... 
doi:10.2312/eg2011/stars/049-073 fatcat:5osoymuysfbwjav6kkbgmlls34

A Review of Element-Based Galerkin Methods for Numerical Weather Prediction: Finite Elements, Spectral Elements, and Discontinuous Galerkin

Simone Marras, James F. Kelly, Margarida Moragues, Andreas Müller, Michal A. Kopera, Mariano Vázquez, Francis X. Giraldo, Guillaume Houzeaux, Oriol Jorba
2015 Archives of Computational Methods in Engineering  
The new dynamical cores at the heart of these unified models are designed to scale e ciently on clusters with hundreds of thousands or even millions of CPU cores and GPUs.  ...  One decade after the review of numerical methods for atmospheric modeling by Steppeler et al. (2003) [Review of numerical methods for nonhydrostatic weather prediction models Meteorol. Atmos.  ...  115] for a unified treatment of high-order continuous and discontinuous Galerkin methods.  ... 
doi:10.1007/s11831-015-9152-1 fatcat:tmjzwcxorfgt5fdcrlf6kb24ny
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