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Stencil scaling for vector-valued PDEs on hybrid grids with applications to generalized Newtonian fluids [article]

Daniel Drzisga, Ulrich Rüde, Barbara Wohlmuth
2020 arXiv   pre-print
The final example considers a non-linear shear-thinning generalized Newtonian fluid.  ...  Here, we show that they are also competitive with respect to the run time in the low order case if combined with suitable stencil scaling techniques.  ...  The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V.  ... 
arXiv:1908.08666v2 fatcat:46xqoynaa5cafiohyookgtcpwy

ExaStencils: Advanced Multigrid Solver Generation [chapter]

Christian Lengauer, Sven Apel, Matthias Bolten, Shigeru Chiba, Ulrich Rüde, Jürgen Teich, Armin Größlinger, Frank Hannig, Harald Köstler, Lisa Claus, Alexander Grebhahn, Stefan Groth (+5 others)
2020 Lecture Notes in Computational Science and Engineering  
Present-day stencil codes are implemented in general-purpose programming languages, such as Fortran, C, or Java, Python or derivates thereof, and harnesses for parallelism, such as OpenMP, OpenCL or MPI  ...  At every layer, the corresponding language expresses not only computational directives but also domain knowledge of the problem and platform to be leveraged for optimization.  ...  We are grateful to Rochus Schmid for letting us have the RSDFT code for the molecular dynamics simulation.  ... 
doi:10.1007/978-3-030-47956-5_14 fatcat:xhbxnt45ynhilgh6vv2ui2n76i

Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme [article]

Aditya A. Ghodgaonkar, Ivan C. Christov
2019 arXiv   pre-print
Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape h(x,t).  ...  We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined  ...  I.C.C. acknowledges a very productive trip to Tallinn in September of 2014 (on invitation of Prof. Andrus Salupere) and fondly recalls meeting and interacting with Prof.  ... 
arXiv:1903.07568v2 fatcat:2ncslwkhwfgkjdh244xwj4snuu

The Curvature-Augmented Closest Point method with vesicle inextensibility application

Christopher J. Vogl
2017 Journal of Computational Physics  
Surface quantities are embedded into the surrounding domain by assigning each value at a given spatial location to the corresponding value at the closest point on the surface.  ...  This embedding allows for surface derivatives to be replaced by their Cartesian counterparts (e.g. ∇_s = ∇).  ...  The author acknowledges the valuable input from the reviewers that led to an improvement in the implementation of the CACP method, as well as funding support from the National Science Foundation [DMS-1304081  ... 
doi:10.1016/ fatcat:mkcs5235djf4fbffwi6kakydia

Using analog computers in today's largest computational challenges [article]

Sven Köppel, Bernd Ulmann, Lars Heimann, Dirk Killat
2021 arXiv   pre-print
Computational fluid dynamics are discussed as an example of large scale scientific computing applications.  ...  General statements are made about the solution of ordinary and partial differential equations.  ...  We thank our anonymous referees for helpful comments and corrections. We further thank Dr. Chris Giles for many corrections and suggestions which improved the text considerably.  ... 
arXiv:2102.07268v2 fatcat:2umpc3vmrvfgxmif6tlrlbby7m

lbmpy: Automatic code generation for efficient parallel lattice Boltzmann methods [article]

Martin Bauer, Harald Köstler, Ulrich Rüde
2020 arXiv   pre-print
Extensions are available to simulate multi-phase, multi-component, turbulent, or non-Newtonian flows.  ...  Lattice Boltzmann methods are a popular mesoscopic alternative to macroscopic computational fluid dynamics solvers.  ...  Additionally we are grateful to the Regionales Rechenzentrum Erlangen, the Leibniz-Rechenzentrum in Garching and the Swiss National Supercomputing Centre in Lugano for providing compute time on their HPC  ... 
arXiv:2001.11806v2 fatcat:k6ttxc2mvbczdbypw244gpcfay

Real-Time Fluid Effects on Surfaces using the Closest Point Method

S. Auer, C. B. Macdonald, M. Treib, J. Schneider, R. Westermann
2012 Computer graphics forum (Print)  
For rendering the surface (and the PDE solution) directly from the closest point representation without the need to reconstruct a triangulated surface, we present a GPU ray-casting method that works on  ...  The CPM uses a closest point representation of the surface, to solve the unmodified Cartesian version of a surface PDE in a 3D volume embedding, using simple and well-understood techniques.  ...  Incompressible Navier-Stokes equations An incompressible, Newtonian fluid with constant temperature can be described by two continuity equations: One for momentum ∂u ∂t = − (u · ∇ S ) u − 1 ρ ∇ S p + ν  ... 
doi:10.1111/j.1467-8659.2012.03071.x fatcat:irzdz44oubhqfofyb6iulhmpdm

Using analog computers in today's largest computational challenges

Sven Köppel, Bernd Ulmann, Lars Heimann, Dirk Killat
2021 Advances in Radio Science  
Computational fluid dynamics are discussed as an example of large scale scientific computing applications.  ...  General statements are made about the solution of ordinary and partial differential equations.  ...  We thank our anonymous referees for helpful comments and corrections. We further thank Chris Giles for many corrections and suggestions which improved the text considerably. Review statement.  ... 
doi:10.5194/ars-19-105-2021 fatcat:js3ubsxkpraojcit7fg7tkrzfi

High order ADER schemes for a unified first order hyperbolic formulation of continuum mechanics: Viscous heat-conducting fluids and elastic solids

Michael Dumbser, Ilya Peshkov, Evgeniy Romenski, Olindo Zanotti
2016 Journal of Computational Physics  
A very important key feature of the model is its ability to describe at the same time the behavior of inviscid and viscous compressible Newtonian and non-Newtonian fluids with heat conduction, as well  ...  To show the universality of the model, the paper is rounded-off with an application to wave propagation in elastic solids.  ...  Last but not least, we would like to thank the two anonymous referees for their constructive comments that helped to improve the clarity and the quality of this paper.  ... 
doi:10.1016/ fatcat:f7mjfzdvsnhcxpoddyu45oywku

Numerical simulation of geodynamic processes with the Portable Extensible Toolkit for Scientific Computation

R.F. Katz, M.G. Knepley, B. Smith, M. Spiegelman, E.T. Coon
2007 Physics of the Earth and Planetary Interiors  
that conform to stencil indexing (i.e., u(i, j, k)) instead of vector (i.e., u(I)) indexing.  ...  stencil.  ...  The spreading ridge is parallel to the y-axis, transform faults, and the spreading rate vector parallel to the x-axis. 55 List of  ... 
doi:10.1016/j.pepi.2007.04.016 fatcat:nu5w4t4x55aqdm2dfcptxxdqkq

Universal Differential Equations for Scientific Machine Learning [article]

Christopher Rackauckas, Yingbo Ma, Julius Martensen, Collin Warner, Kirill Zubov, Rohit Supekar, Dominic Skinner, Ali Ramadhan, Alan Edelman
2021 arXiv   pre-print
We demonstrate the generality of the software tooling to handle stochasticity, delays, and implicit constraints.  ...  This funnels the wide variety of SciML applications into a core set of training mechanisms which are highly optimized, stabilized for stiff equations, and compatible with distributed parallelism and GPU  ...  just applicable to large-scale dynamical systems like PDEs but also can be effectively employed to accelerate small scale systems.  ... 
arXiv:2001.04385v4 fatcat:megacwjw2fbwxkwcnxw7wploia

High-Order Unstructured Lagrangian One-Step WENO Finite Volume Schemes for Non-Conservative Hyperbolic Systems: Applications to Compressible Multi-Phase Flows [article]

Michael Dumbser, Walter Boscheri
2013 arXiv   pre-print
Finally, the proposed method is also applied to a reduced version of the compressible Baer-Nunziato model for the simulation of free surface water waves in moving domains.  ...  In this article we present the first better than second order accurate unstructured Lagrangian-type one-step WENO finite volume scheme for the solution of hyperbolic partial differential equations with  ...  The full seven-equation Baer-Nunziato model with inter-phase drag and pressure relaxation is given by the following non-conservative system of partial  ... 
arXiv:1304.4816v1 fatcat:ane5sqy7hnazbmiee3pf4qujvi

Simulation results and applications of an advection bounded scheme to practical flows

Valdemir G Ferreira, Rafael A.B de Queiroz, Miguel A. Caro Candezano, Giseli A.B Lima, Laís Corrêa, Cassio M Oishi, Fernando L.P Santos
2012 Computational and Applied Mathemathics  
This paper reports experiments on the use of a recently introduced advection bounded upwinding scheme, namely TOPUS (Computers & Fluids 57 (2012) 208-224), for flows of practical interest.  ...  It is concluded that the TOPUS scheme is a competent, powerful and generic scheme for complex flow phenomena. Mathematical subject classification: Primary: 06B10; Secondary: 06D05.  ...  The results and applications presented in the next section were generated by using the free parameter α equal to 2, since for this value of α the scheme has guaranteed to be oscillation-free and has provided  ... 
doi:10.1590/s1807-03022012000300009 fatcat:sv7d4dkdcfcgbm6lgoa6ymnsbm

TerraNeo—Mantle Convection Beyond a Trillion Degrees of Freedom [chapter]

Simon Bauer, Hans-Peter Bunge, Daniel Drzisga, Siavash Ghelichkhan, Markus Huber, Nils Kohl, Marcus Mohr, Ulrich Rüde, Dominik Thönnes, Barbara Wohlmuth
2020 Lecture Notes in Computational Science and Engineering  
Simulation of mantle convection on planetary scales is considered a grand-challenge application even in the exascale era.  ...  In TerraNeo the hierarchical hybrid grids paradigm was employed to demonstrate that scalability can be achieved when solving the Stokes system with more than ten trillion (1.1 · 10 13 ) degrees of freedom  ...  Stencil Scaling for Vector-Valued PDEs with Applications to Generalized Newtonian Fluids Our target problem is vector-valued, thus, we expanded the scalar stencil scaling idea from Sect. 3.6.2 and developed  ... 
doi:10.1007/978-3-030-47956-5_19 fatcat:4jhueyv5qrhfdkmpfxxv5lsmqa

On direct Arbitrary-Lagrangian-Eulerian ADER-WENO finite volume schemes for the HPR model of nonlinear hyperelasticity [article]

Walter Boscheri and Michael Dumbser and Raphaël Loubère
2016 arXiv   pre-print
relaxation to determine the mesh motion, and a path-conservative technique of Castro & Par\'es for the treatment of non-conservative products.  ...  elasto-plastic solids can be simulated in the framework of nonlinear hyperelasticity with the same system of governing PDE.  ...  Romenski for the design of proper boundary conditions and the computation of the relaxation time τ 1 for the HPR model in the case of elasto-plastic solids. We also would like to thank S.  ... 
arXiv:1602.06869v1 fatcat:x4ezkbcvkjgszbpl6lwiifkjqe
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