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A free-energy stable nodal discontinuous Galerkin approximation with summation-by-parts property for the Cahn-Hilliard equation [article]

Juan Manzanero, Gonzalo Rubio, David A. Kopriva, Esteban Ferrer, Eusebio Valero
<span title="2019-02-21">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We present a nodal Discontinuous Galerkin (DG) scheme for the Cahn-Hilliard equation that satisfies the summation-by-parts simultaneous-approximation-term (SBP-SAT) property.  ...  The latter permits us to show that the discrete free-energy is bounded, and as a result, the scheme is provably stable.  ...  This work was supported by a grant from the Simons Foundation (#426393, David Kopriva).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1902.08089v1">arXiv:1902.08089v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/htlei64z5vdhpa5vhogyyba6ui">fatcat:htlei64z5vdhpa5vhogyyba6ui</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200929165107/https://arxiv.org/pdf/1902.08089v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/65/e4/65e40ae885559c21527a3ddf90491c1897bdc5a1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1902.08089v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

A free-energy stable p-adaptive nodal discontinuous Galerkin for the Cahn-Hilliard equation

Gerasimos Ntoukas, Juan Manzanero, Gonzalo Rubio, Eusebio Valero, Esteban Ferrer
<span title="2020-08-31">2020</span> <i title="Zenodo"> Zenodo </i> &nbsp;
A novel free-energy stable discontinuous Galerkin method is developed for the Cahn-Hilliard equation with non-conforming elements.  ...  use of the summation-by-parts simultaneous-approximation term technique along with Gauss-Lobatto points and the Bassi-Rebay 1 (BR1) scheme.  ...  The DGSEM version of this work uses Gauss-Lobatto (GL) points, which through the Summation-By-Parts Simultaneous-Approximation Term (SBP-SAT) property [15, 16] allow the derivation of free-energy stable  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.5281/zenodo.4008979">doi:10.5281/zenodo.4008979</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/g7mxgoxnvbbuvpfck2c2vetnl4">fatcat:g7mxgoxnvbbuvpfck2c2vetnl4</a> </span>
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A free–energy stable p–adaptive nodal discontinuous Galerkin for the Cahn–Hilliard equation

Gerasimos Ntoukas, Juan Manzanero, Gonzalo Rubio, Eusebio Valero, Esteban Ferrer
<span title="">2021</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/f7kkigxhzjakref5b42jt4uoya" style="color: black;">Journal of Computational Physics</a> </i> &nbsp;
A novel free-energy stable discontinuous Galerkin method is developed for the Cahn-Hilliard equation with non-conforming elements.  ...  use of the summation-by-parts simultaneous-approximation term technique along with Gauss-Lobatto points and the Bassi-Rebay 1 (BR1) scheme.  ...  A free-energy stable p-adaptive nodal discontinuous Galerkin for the Cahn-Hilliard equation Introduction A variety of different approaches and methodologies have been developed throughout the years to  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcp.2021.110409">doi:10.1016/j.jcp.2021.110409</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gv3sfch6zfh2zmjpxqiqfkjos4">fatcat:gv3sfch6zfh2zmjpxqiqfkjos4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210528173822/https://pdf.sciencedirectassets.com/272570/AIP/1-s2.0-S0021999121003041/main.pdf?X-Amz-Security-Token=IQoJb3JpZ2luX2VjELn%2F%2F%2F%2F%2F%2F%2F%2F%2F%2FwEaCXVzLWVhc3QtMSJGMEQCICAS0Rv6Xss22SNw5ccgTsMl0LlQDMDzF2MBilIbhhrxAiBjIlhO0oyNfgpn6iDId%2BKjXlc9d0gAIXobkOqecsJdXyr6AwhiEAQaDDA1OTAwMzU0Njg2NSIM1QVBe%2FKhyobjHZK2KtcDUOqbpzllKCiPdYXsj8s71EvF2je8jlRS0oKx2tPmdnL8nvhd3fBMKwqu1KhunSV709lVg3ws4K8PaI7ZMePl4vdo%2BoVUmIQCu19it6HbOVYhZMsLqEVbffY1w0Iv%2BwOS5e4CQn9WpbCHkDYQIUpzY7%2BJbaixQiAcJIXuHZDiuesZmMLTLlZQnRKMrmwAIcMOtz1LLib84sZA6Z3IFsS3dfpWGMoy%2B62GEvtN3fbTaNs0HU0uXPWUND3Ps4XmtYhYaxNSPh2Rrfx6h%2BiBtQkfIbQ5oyLlsyiayCJW7pSeA9Any9nP%2FVO0ZvNKglxJwvKRWdM%2F0mcsidJqOdnuukgH6qEadhVidFPSNuzo%2F2spWjwe2GEaNMvxlc6MDxLZMMXvlUnq4jnrkFn0hCIM3V4x%2FQEhkisbOzxPRA%2BlM9f%2B1vIVaul4SXmbwAsVzTEt0%2Bp7NX9NjKZ9DI%2BqJWsYZ7RCk70%2FX2%2FQCzbsWI7NKrLXdoq55Q6dNy0jBpLnkGVgrl60ieuPENELOSonopWTmLcg7%2FZWFSinn2zco8YWfan%2Fk2eF8XOW5hYOBzmkHMVeQRY8W9aaPwrggTueSGY135heZ5bnvIJlrG4WCTgrW5tY%2B2aOJIuSy3ufMMK4xIUGOqYBHBo8IbzgVOj3d%2FKx2eKYYgZoOICiSbZqdmzoZcqGlnLanyRiPY5wowBqaYYSL%2FPZoodSejtB38V8GndpfY0T%2F6mES5gGhyFitoiHm1eP%2BvQE0WpfiBC1EFaenzzQ%2BclUUlHv9QcUGhtZ1f1nd63gfCBjHPwUcoHwqkgSclwHa0aXbpzAN%2BLH5wZDCGu28I%2FP1rRjD64xX54DFrRhKQqxMVD7hsm3hw%3D%3D&amp;X-Amz-Algorithm=AWS4-HMAC-SHA256&amp;X-Amz-Date=20210528T173817Z&amp;X-Amz-SignedHeaders=host&amp;X-Amz-Expires=300&amp;X-Amz-Credential=ASIAQ3PHCVTY7SNHXLUI%2F20210528%2Fus-east-1%2Fs3%2Faws4_request&amp;X-Amz-Signature=dd4fda5fef610eb277f5409943f049c8d7833e79ad6ca63bea84d73d8a346c25&amp;hash=787d96b3bd3c122fdcd449c13cf33c60e3db19a195df4d0792a612da98d6ba09&amp;host=68042c943591013ac2b2430a89b270f6af2c76d8dfd086a07176afe7c76c2c61&amp;pii=S0021999121003041&amp;tid=spdf-76049699-86b1-4909-96e8-4fe101b2d9ff&amp;sid=e8971a687adf5045e8087203ab5e740bcee7gxrqa&amp;type=client" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/1a/42/1a4287a36a544d50d415ffea066b6a159d9d011f.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcp.2021.110409"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> elsevier.com </button> </a>

Entropy-stable discontinuous Galerkin approximation with summation-by-parts property for the incompressible Navier-Stokes/Cahn-Hilliard system [article]

Juan Manzanero, Gonzalo Rubio, David A. Kopriva, Esteban Ferrer, Eusebio Valero
<span title="2019-10-25">2019</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
We develop an entropy stable two-phase incompressible Navier--Stokes/Cahn--Hilliard discontinuous Galerkin (DG) flow solver method.  ...  The model poses the Cahn-Hilliard equation as the phase field method, a skew-symmetric form of the momentum equation, and an artificial compressibility method to compute the pressure.  ...  This work was supported by a grant from the Simons Foundation (#426393, David Kopriva).  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.11252v2">arXiv:1910.11252v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bsrtdnouojgcxduw6t3l2z6a34">fatcat:bsrtdnouojgcxduw6t3l2z6a34</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200903085853/https://arxiv.org/pdf/1910.11252v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/38/35/3835d79ab030e3f6ae5eee96cb21576043e8f901.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1910.11252v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations [article]

Andrew R. Winters and David A. Kopriva and Gregor J. Gassner and Florian Hindenlang
<span title="2020-05-05">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric  ...  This chapter takes a constructive approach to introduce a modern incarnation of the DG spectral element method for the compressible Navier-Stokes equations in a three-dimensional curvilinear context.  ...  Prologue The discontinuous Galerkin (DG) method dates back to the work of Nitsche (1971) for the solution of elliptic problems and to the work of Reed and Hill (1973) for the solution of linear hyperbolic  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2005.02317v1">arXiv:2005.02317v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/wb3wxummhfgzviauonjb3xee7y">fatcat:wb3wxummhfgzviauonjb3xee7y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200528234735/https://arxiv.org/pdf/2005.02317v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2005.02317v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

A Novel Robust Strategy for Discontinuous Galerkin Methods in Computational Fluid Mechanics: Why? When? What? Where?

Gregor J. Gassner, Andrew R. Winters
<span title="2021-01-29">2021</span> <i title="Frontiers Media SA"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/im246jdlofanriyhr3bpyw2cwy" style="color: black;">Frontiers in Physics</a> </i> &nbsp;
by Maxwell's equations, incompressible and compressible fluid and plasma dynamics governed by the Navier-Stokes and the Magnetohydrodynamics equations, or as a solver for ordinary differential equations  ...  In this paper we will review a recent emerging paradigm shift in the construction and analysis of high order Discontinuous Galerkin methods applied to approximate solutions of hyperbolic or mixed hyperbolic-parabolic  ...  for the corresponding functions u and v E u dv dx dx + E du dx v dx [u v] 1 −1 , (44) hence the name summation-by-parts.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3389/fphy.2020.500690">doi:10.3389/fphy.2020.500690</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/3iywvhxpxrgufienlxmhwtxhbq">fatcat:3iywvhxpxrgufienlxmhwtxhbq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210201212917/https://fjfsdata01prod.blob.core.windows.net/articles/files/500690/pubmed-zip/.versions/1/.package-entries/fphy-08-500690.pdf?sv=2018-03-28&amp;sr=b&amp;sig=sxLfOsHWtZZYEx0cn9bvgMCGF%2BCkJY9hw06TYNUE4eU%3D&amp;se=2021-02-01T21%3A29%3A46Z&amp;sp=r&amp;rscd=attachment%3B%20filename%2A%3DUTF-8%27%27fphy-08-500690.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4a/f1/4af11b27b0d61113a482d52fcd643088d7a2dbc3.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.3389/fphy.2020.500690"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="unlock alternate icon" style="background-color: #fb971f;"></i> frontiersin.org </button> </a>

A variational interface-preserving and conservative phase-field method for the surface tension effect in two-phase flows [article]

Xiaoyu Mao, Vaibhav Joshi, Rajeev Jaiman
<span title="2020-07-31">2020</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The mass conservation is achieved by enforcing a Lagrange multiplier with both temporal and spatial dependence on the phase-field function.  ...  The mobility coefficient is adjusted adaptively as a function of gradients of the velocity and the order parameter in the diffuse interface region in such a way that the free energy minimization properly  ...  The phase-field methods are generally based on the Cahn-Hilliard and the Allen-Cahn phase-field equations [19, 20] , which considers the gradient flow minimizing the free energy functional as the cause  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.15887v1">arXiv:2007.15887v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mcnobdbcm5ffvnmpyfz45yj6eq">fatcat:mcnobdbcm5ffvnmpyfz45yj6eq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20200825113257/https://arxiv.org/pdf/2007.15887v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/fb/ca/fbcae29f3b71955eae427e36ae564e369f5b4715.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2007.15887v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

A fourth-order phase-field fracture model: Formulation and numerical solution using a continuous/discontinuous Galerkin method

Lampros Svolos, Hashem M. Mourad, Gianmarco Manzini, Krishna Garikipati
<span title="">2022</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wlpckclmcbcnha5534mmr5yizi" style="color: black;">Journal of the mechanics and physics of solids</a> </i> &nbsp;
In addition, we propose a continuous/discontinuous Galerkin (C/DG) method for use in computing the approximate phase-field solution.  ...  The phase-field equation is coupled with the momentum balance equation to model dynamic fracture problems in hyper-elastic materials.  ...  Its use to treat higher-order PF problems (including those governed by the Cahn-Hilliard equation [44] ) results in discontinuities in the gradient of the phase field, and thus constitutes a variational  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jmps.2022.104910">doi:10.1016/j.jmps.2022.104910</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/aixqwu7s6be6xbhs7yqhdsbesq">fatcat:aixqwu7s6be6xbhs7yqhdsbesq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220518125152/https://arxiv.org/pdf/2205.06815v1.pdf" title="fulltext PDF download [not primary version]" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <span style="color: #f43e3e;">&#10033;</span> <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/ca/28/ca280e8317315044e6ace4fe29c394b3148edad1.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jmps.2022.104910"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Numerical Stabilization of the Melt Front for Laser Beam Cutting [chapter]

Torsten Adolph, Willi Schönauer, Markus Niessen, Wolfgang Schulz
<span title="">2010</span> <i title="Springer Berlin Heidelberg"> Numerical Mathematics and Advanced Applications 2009 </i> &nbsp;
This can be reasonably included by assuming an additively decoupled energy function into an undamaged isotropic part, for the ground substance, and superimposed transversely isotropic parts, for the embedded  ...  Numerical experiments will be done for simple linear problems, the Burger's equation, and for the Euler equations with high Mach numbers. 24 This contribution deals with the modeling of soft biological  ...  interface with a discontinuous Galerkin method to solve the associated transport equation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-11795-4_6">doi:10.1007/978-3-642-11795-4_6</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nx4nvuxaxfbcdjknopny53ck5e">fatcat:nx4nvuxaxfbcdjknopny53ck5e</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180721182541/http://www.it.uu.se/research/tdb/enumath2009/final/enumath_abstracts.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/4c/34/4c343b1ce275f64d03689c4505c2c1011604403d.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-3-642-11795-4_6"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

CD-MPM

Joshuah Wolper, Yu Fang, Minchen Li, Jiecong Lu, Ming Gao, Chenfanfu Jiang
<span title="2019-07-12">2019</span> <i title="Association for Computing Machinery (ACM)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/cqrugwalkvcezgalqorn4fwnuu" style="color: black;">ACM Transactions on Graphics</a> </i> &nbsp;
We tear a slice of bread with more than 11 million PFF-MPM particles, revealing intricate fracture patterns and natural dynamics.  ...  In contrast to traditional mesh-based techniques, where sharp discontinuity is introduced to split the continuum at material fracture effects on its own.  ...  This work was supported in part by NSF Grants IIS-1755544 and CCF-1813624, a gift from Harlan Stone, a gift from Adobe Inc., NVIDIA GPU grants, and Houdini licenses from SideFX.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/3306346.3322949">doi:10.1145/3306346.3322949</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mweli7pdhzbu3cvnycnmaqsyx4">fatcat:mweli7pdhzbu3cvnycnmaqsyx4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191001092209/https://www.seas.upenn.edu/%7Ecffjiang/research/wolper2019fracture/wolper2019fracture.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/e9/f2/e9f287f041f062de3a5a5df55ee4bdc245beb440.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1145/3306346.3322949"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> acm.org </button> </a>

Meshless techniques for anisotropic diffusion

Annamaria Mazzia, Giorgio Pini, Flavio Sartoretto
<span title="">2014</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/xkk23xlywfez5l246cnmlit4qq" style="color: black;">Applied Mathematics and Computation</a> </i> &nbsp;
Our approach is to develop locally conservative Eulerian-Lagrangian (or semi-Lagrangian) methods combined with ideas from Eulerian WENO schemes, since they have the potential to attain the desired properties  ...  The latter would allow better use of parallel computers, since time-stepping is essentially a serial process. Moreover, it would be good for the methods to be of high order accuracy.  ...  We show how to solve the equations using a global implicit approach in an efficient way, and we present the derived computational results.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.amc.2014.03.032">doi:10.1016/j.amc.2014.03.032</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/c527226gyfgbffnq4p67qxd7wi">fatcat:c527226gyfgbffnq4p67qxd7wi</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20180721235820/https://archive.siam.org/meetings/gs13/gs13_abstracts.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/73/5a/735a36ebd6e2272a87325f3146a078c430812c4c.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.amc.2014.03.032"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

Overview of the Incompressible Navier-Stokes simulation capabilities in the MOOSE Framework [article]

John W. Peterson, Alexander D. Lindsay, Fande Kong
<span title="2018-02-21">2018</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
While the core MOOSE framework itself does not contain code for simulating any particular physical application, it is distributed with a number of physics "modules" which are tailored to solving e.g. heat  ...  the Incompressible Navier-Stokes (INS) equations.  ...  This manuscript has been authored by a contractor of the U.S. Government under Contract DE-AC07-05ID14517. Accordingly, the U.S.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1710.08898v2">arXiv:1710.08898v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lirpd6eofre5znuzdmkslqfx3i">fatcat:lirpd6eofre5znuzdmkslqfx3i</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20191025151449/https://arxiv.org/pdf/1710.08898v2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/b5/53/b553da7c0095a2eac772f711da0c0a7b52883fc2.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1710.08898v2" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

A computational study of turbulent flow separation for a circular cylinder using skin friction boundary conditions [chapter]

Johan Hoffman, Niclas Jansson
<span title="">2011</span> <i title="Springer Netherlands"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/g3csodoczva5nkbpaz5wdq6o7e" style="color: black;">ERCOFTAC Series</a> </i> &nbsp;
The approximate stress fields are split into two parts: a divergence-free (static) part, taken as the solution of the homogeneous momentum equations, and a dynamic part, taken as the particular solution  ...  This procedure can in fact be conceived of as a Galerkin approximation. The closure is chosen such that the structural properties of the BE are retained.  ...  ACKNOWLEDGEMENTS The editors and conference organizers acknowledge the support by the following organizations, which made possible the publication of this book of Abstracts, the (online or CD) publication  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-94-007-0231-8_5">doi:10.1007/978-94-007-0231-8_5</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/f6ll6iawcbeo7pbj4rb7t4o2tq">fatcat:f6ll6iawcbeo7pbj4rb7t4o2tq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170818082812/http://upcommons.upc.edu/bitstream/handle/2117/22099/ADMOS_2013_EBOOK_ABSTRACTS_PROCEEDINGS.pdf?sequence=1" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/0c/af/0cafaa9ec09264c72a7b7678fcc950343a9b1983.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1007/978-94-007-0231-8_5"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> springer.com </button> </a>

Stress-Driven Phase Transformation and the Roughening of Solid-Solid Interfaces

L. Angheluta, E. Jettestuen, J. Mathiesen, F. Renard, B. Jamtveit
<span title="2008-03-07">2008</span> <i title="American Physical Society (APS)"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/pkmpevvs3bgkhal5dvrmsu5mvq" style="color: black;">Physical Review Letters</a> </i> &nbsp;
This instability is triggered by a finite jump in the free energy density across the interface, and it leads to the formation of finger-like structures aligned with the principal direction of compaction  ...  The model is proposed as an explanation for the roughening of stylolites - irregular interfaces associated with the compaction of sedimentary rocks that fluctuate about a plane perpendicular to the principal  ...  For this purpose we utilize the Cahn-Hilliard formalism ͓14͔ of a diffuse interface.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physrevlett.100.096105">doi:10.1103/physrevlett.100.096105</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/18352730">pmid:18352730</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ml3u33lxfvallnjgdf4zyjtdqe">fatcat:ml3u33lxfvallnjgdf4zyjtdqe</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20171120171110/https://core.ac.uk/download/pdf/30832240.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d5/91/d59158a8d6cf919150b160f524f47e560ae27ebe.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1103/physrevlett.100.096105"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> aps.org </button> </a>

Thermodynamically-consistent derivation and computation of twinning and fracture in brittle materials by means of phase-field approaches in the finite element method [article]

Benhour Amirian, Hossein Jafarzadeh, Bilen Emek Abali, Alessandro Reali, James David Hogan
<span title="2022-02-24">2022</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
Constitutive equations are derived by using thermodynamics in order to establish a fully coupled and transient fracture mechanics model.  ...  The results are verified by steady-state phase-field approach and validated by available experimental data in the literature.  ...  The authors acknowledge support from Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant 2016-04685 and NSERC DNDPJ 531130-18, and partial support of the MIUR-PRIN project  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2202.13781v1">arXiv:2202.13781v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ea2fene2rbcp7nv35ypilmwuhq">fatcat:ea2fene2rbcp7nv35ypilmwuhq</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20220516094949/https://arxiv.org/pdf/2202.13781v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/99/ca/99ca15db65850cc14a375cc7a885b243259f5434.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2202.13781v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>
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