Relevant bibliographies by topics / Navier-Stokes equations

Academic literature on the topic 'Navier-Stokes equations'

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Published: 4 June 2021
Last updated: 30 July 2024

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Journal articles on the topic "Navier-Stokes equations"

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Rannacher, Rolf. "Numerical analysis of the Navier-Stokes equations." Applications of Mathematics 38, no. 4 (1993): 361–80. http://dx.doi.org/10.21136/am.1993.104560.

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Acevedo Tapia, P., C. Amrouche, C. Conca, and A. Ghosh. "Stokes and Navier-Stokes equations with Navier boundary conditions." Journal of Differential Equations 285 (June 2021): 258–320. http://dx.doi.org/10.1016/j.jde.2021.02.045.

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Acevedo, Paul, Chérif Amrouche, Carlos Conca, and Amrita Ghosh. "Stokes and Navier–Stokes equations with Navier boundary condition." Comptes Rendus Mathematique 357, no. 2 (February 2019): 115–19. http://dx.doi.org/10.1016/j.crma.2018.12.002.

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Cholewa, Jan W., and Tomasz Dlotko. "Fractional Navier-Stokes equations." Discrete and Continuous Dynamical Systems - Series B 22, no. 5 (April 2017): 29. http://dx.doi.org/10.3934/dcdsb.2017149.

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Ramm, Alexander G. "Navier-Stokes equations paradox." Reports on Mathematical Physics 88, no. 1 (August 2021): 41–45. http://dx.doi.org/10.1016/s0034-4877(21)00054-9.

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Reddy, M. H. Lakshminarayana, S. Kokou Dadzie, Raffaella Ocone, Matthew K. Borg, and Jason M. Reese. "Recasting Navier–Stokes equations." Journal of Physics Communications 3, no. 10 (October 17, 2019): 105009. http://dx.doi.org/10.1088/2399-6528/ab4b86.

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Bensoussan, A. "Stochastic Navier-Stokes Equations." Acta Applicandae Mathematicae 38, no. 3 (March 1995): 267–304. http://dx.doi.org/10.1007/bf00996149.

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Capiński, Marek, and Nigel Cutland. "Stochastic Navier-Stokes equations." Acta Applicandae Mathematicae 25, no. 1 (October 1991): 59–85. http://dx.doi.org/10.1007/bf00047665.

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Yang, JianWei, and Shu Wang. "Convergence of compressible Navier-Stokes-Maxwell equations to incompressible Navier-Stokes equations." Science China Mathematics 57, no. 10 (February 28, 2014): 2153–62. http://dx.doi.org/10.1007/s11425-014-4792-4.

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Akysh, A. Sh. "The Cauchy problem for the Navier-Stokes equations." BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS 98, no. 2 (June 30, 2020): 15–23. http://dx.doi.org/10.31489/2020m2/15-23.

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Dissertations / Theses on the topic "Navier-Stokes equations"

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Shuttleworth, Robert. "Block preconditioning the Navier-Stokes equations." College Park, Md. : University of Maryland, 2007. http://hdl.handle.net/1903/7002.

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Thesis (Ph. D.) -- University of Maryland, College Park, 2007.
Thesis research directed by: Applied Mathematics and Scientific Computation Program. Title from t.p. of PDF. Includes bibliographical references. Published by UMI Dissertation Services, Ann Arbor, Mich. Also available in paper.
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Neklyudov, Mikhail. "Navier-Stokes equations and vector advection." Thesis, University of York, 2006. http://etheses.whiterose.ac.uk/11011/.

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Rejaiba, Ahmed. "Equations de Stokes et de Navier-Stokes avec des conditions aux limites de Navier." Thesis, Pau, 2014. http://www.theses.fr/2014PAUU3050/document.

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Résumé : Cette thèse est consacrée à l'étude des équations de Stokes et de Navier-Stokes avec des conditions aux limites de Navier dans un ouvert borné de . Le manuscrit ici est composé de trois chapitres. Dans le premier, nous considérons les équations de Stokes stationnaires avec des conditions aux limites de Navier. Nous démontrons l'existence, l'unicité et la régularité de la solution d'abord dans un cadre hilbertien puis dans le cadre de la théorie . Nous traitons aussi le cas de solutions très faibles. Dans le deuxième chapitre, nous nous intéressons aux équations de Navier-Stokes avec la condition de Navier. Sous certaines hypothèses sur les données, nous démontrons l'existence de solution faible dans , avec en utilisant un théorème du point fixe appliqué à un problème d'Oseen. Nous démontrons examinons ensuite les questions de régularité des solutions en particulier dans . Dans le dernier chapitre, nous étudions le problème d'évolution de Stokes avec la condition de Navier. La résolution de ce problème se fait au moyen de la théorie des semi-groupes analytiques qui jouent un rôle important pour établir l'existence et l'unicité de la solution dans le cas homogène. Nous traitons le cas du problème non homogène par le biais des puissances imaginaires de l'opérateur de Stokes
This thesis is devoted to the study of the Stokes equations and Navier-Stokes equations with Navier boundary conditions in a bounded domain of . The work contains three chapters: In the first chapter, we consider the stationary Stokes equations with Navier boundary condition. We show the existence, uniqueness and regularity of the solution in the Hilbert case and in the -theory. We prove also the case of very weak solutions. In the second chapter, we focus on the Navier-Stokes equations with the Navier boundary condition. We show the existence of the weak solution in , with by a fixed point theorem over the Oseen equation. We show also the existence of the strong solution in . In chapter three, we study the evolution Stokes problem with Navier boundary condition. For this, we apply the analytic semi-groups theory, which plays a crucial role in the study of existence and uniqueness of solution in the case of the homogeneous evolution problem. We treat the case of non-homogeneous problem through imaginary powers of the Stokes operator
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Benson, D. J. A. "Finite volume solution of Stokes and Navier-Stokes equations." Thesis, University of Oxford, 1991. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.302883.

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Al-Jaboori, Mustafa Ali Hussain. "Navier-Stokes equations on the β-plane." Thesis, Durham University, 2012. http://etheses.dur.ac.uk/5582/.

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Mathematical analysis has been undertaken for the vorticity formulation of the two dimensional Navier–Stokes equation on the β-plane with periodic boundary conditions. This equation describes the flow of fluid near the equator of the Earth. The long time behaviour of the solution of this equation is investigated and we show that, given a sufficiently regular forcing, the solution of the equation is nearly zonal. We use this result to show that, for sufficiently large β, the global attractor of this system reduces to a point. Another result can be obtained if we assume that the forcing is time-independent and sufficiently smooth. If the forcing lies in some Gevrey space, the slow manifold of the Navier–Stokes equation on the β-plane can be approximated with O(εn/2) accuracy for arbitrary n = 0, 1, · · · , as well as with exponential accuracy.
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Haddon, E. W. "Numerical studies of the Navier-Stokes equations." Thesis, University of East Anglia, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.377745.

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Tang, Tao. "Numerical solutions of the Navier-Stokes equations." Thesis, University of Leeds, 1989. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.328961.

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Słomka, Jonasz. "Generalized Navier-Stokes equations for active turbulence." Thesis, Massachusetts Institute of Technology, 2018. http://hdl.handle.net/1721.1/117861.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 211-227).
Recent experiments show that active fluids stirred by swimming bacteria or ATPpowered microtubule networks can exhibit complex flow dynamics and emergent pattern scale selection. Here, I will investigate a simplified phenomenological approach to 'active turbulence', a chaotic non-equilibrium steady-state in which the solvent flow develops a dominant vortex size. This approach generalizes the incompressible Navier-Stokes equations by accounting for active stresses through a linear instability mechanism, in contrast to externally driven classical turbulence. This minimal model can reproduce experimentally observed velocity statistics and is analytically tractable in planar and curved geometry. Exact stationary bulk solutions include Abrikosovtype vortex lattices in 2D and chiral Beltrami fields in 3D. Numerical simulations for a plane Couette shear geometry predict a low viscosity phase mediated by stress defects, in qualitative agreement with recent experiments on bacterial suspensions. Considering the active analog of Stokes' second problem, our numerical analysis predicts that a periodically rotating ring will oscillate at a higher frequency in an active fluid than in a passive fluid, due to an activity-induced reduction of the fluid inertia. The model readily generalizes to curved geometries. On a two-sphere, we present exact stationary solutions and predict a new type of upward energy transfer mechanism realized through the formation of vortex chains, rather than the merging of vortices, as expected from classical 2D turbulence. In 3D simulations on periodic domains, we observe spontaneous mirror-symmetry breaking realized through Beltrami-like flows, which give rise to upward energy transfer, in contrast to the classical direct Richardson cascade. Our analysis of triadic interactions supports this numerical prediction by establishing an analogy with forced rigid body dynamics and reveals a previously unknown triad invariant for classical turbulence.
by Jonasz Słomka.
Ph. D.
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Ghosh, Amrita. "Naviers-Stokes equations with Navier boundary condition." Thesis, Pau, 2018. http://www.theses.fr/2018PAUU3021/document.

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Le titre de ma thèse de doctorat est "Equations de Stokes et de Navier-Stokes avec la con- dition de Navier", où j’ai considéré l’écoulement d’un fluide newtonien visqueux, incompressible dans un domaine borné de R3. L’écoulement du fluide est décrit par les équations bien connues de Navier-Stokes, données par le système suivant ∂t − ∆u + (u • ∇)u + ∇π = 0, div u = 0 dans Ω × (0, T )u • n = 0, 2[(Du)n]τ + αuτ = 0 sur Γ × (0, T )u(0) = u0 dans Ω (0.1) dans un domaine borné Ω ⊂ R3 de frontière Γ, éventuellement non simplement connexe, de classe C1,1. La vitesse initiale u0 et le coefficient de friction α, scalaire, sont des fonctions don- nées. Les vecteurs unitaires normal extérieur et tangents à Γ sont notés n et τ respectivement et Du = 1 (∇u + ∇uT ) est le tenseur des déformations. Les fonctions u et π décrivent respective- ment les champs de vitesses et de pression du fluide dans Ω satisfaisant la condition aux limites (0.1.2).Cette condition aux limites, proposée par H. Navier en 1823, a été abondamment étudiée ces dernières années, qui pour de nombreuses raisons convient parfois mieux que la condition aux limites de Dirichlet sans glissement : elle offre plus de liberté et est susceptible de fournir une solution physiquement acceptable au moins pour certains des phénomènes paradoxaux résultant de la condition de non-glissement, comme par exemple le paradoxe de D’Alembert ou le paradoxe de non-collision.Ma thèse comporte trois parties. Dans la première, je cherche à savoir si le problème (0.1) est bien posé en théorie Lp, en particulier l’existence, l’unicité de solutions faibles, fortes dans W 1,p(Ω) et W 2,p(Ω) pour tout p ∈ (1, ∞), en considérant la régularité minimale du coefficient de friction α. Ici α est une fonction, pas simplement une constante qui reflète les diverses propriétés du fluide et/ou de la frontière, ce qui nous permet d’analyser le comportement de la solution par rapport au coefficient de frottement.Utilisant le fait que les solutions sont bornées indépendamment de α, on montre que la solution des équations de Navier-Stokes avec la condition de Navier converge fortement vers une solution des équations de Navier-Stokes avec la condition de Dirichlet, correspondant à la même donnée initiale dans l’espace d’énergie lorsque α → ∞. Des résultats similaires ont été obtenus pour le cas stationnaire.Le dernier chapitre concerne les estimations pour le problème de Robin pour le laplacien : l’opérateur elliptique de second ordre suivant, sous forme divergentielle dans un domaine bornéΩ ⊂ Rn de classe C1, avec la condition aux limites de Robin a été considéré div(A∇)u = divf + F dans Ω, ∂u+ αu = f n + g sur Γ.∂n (0.2) Les coefficients de la matrice symétrique A sont supposés appartenir à l’espace V MO(R3). Aussi α est une fonction appartenant à un certain espace Lq . En plus de prouver l’existence, l’unicité de solutions faibles et fortes, nous obtenons une borne sur u, uniforme par rapport à α pour α suffisamment large, en norme Lp. Pour plus de clarté, nous avons étudié séparément les deux cas: l’estimation intérieure et l’estimation au bord
My PhD thesis title is "Navier-Stokes equations with Navier boundary condition" where I have considered the motion of an incompressible, viscous, Newtonian fluid in a bounded do- main in R3. The fluid flow is described by the well-known Navier-Stokes equations, given by thefollowing system 1 )t − L1u + (u ⋅ ∇)u + ∇n = 0, div u = 01u ⋅ n = 0, 2[(IDu)n]r + aur = 0 in Q × (0, T )on Γ × (0, T ) (0.1) 11lu(0) = u0 in Qin a bounded domain Q ⊂ R3 with boundary Γ, possibly not connected, of class C1,1. The initialvelocity u0 and the (scalar) friction coefficient a are given functions. The unit outward normal and tangent vectors on Γ are denoted by n and r respectively and IDu = 1 (∇u + ∇uT ) is the rate of strain tensor. The functions u and n describe respectively the velocity2 and the pressure of a fluid in Q satisfying the boundary condition (0.1.2).This boundary condition, first proposed by H. Navier in 1823, has been studied extensively in recent years, among many reasons due to its contrast with the no-slip Dirichlet boundary condition: it offers more freedom and are likely to provide a physically acceptable solution at least to some of the paradoxical phenomenons, resulting from the no-slip condition, for example, D’Alembert’s paradox or no-collision paradox.My PhD work consists of three parts. primarily I have discussed the Lp -theory of well-posedness of the problem (0.1), in particular existence, uniqueness of weak and strong solutions in W 1,p (Q) and W 2,p (Q) for all p ∈ (1, ∞) considering minimal regularity on the friction coefficienta. Here a is a function, not merely a constant which reflects various properties of the fluid and/or of the boundary. Moreover, I have deduced estimates showing explicitly the dependence of u on a which enables us to analyze the behavior of the solution with respect to the friction coefficient.Using this fact that the solutions are bounded with respect to a, we have shown the solution of the Navier-Stokes equations with Navier boundary condition converges strongly to a solution of the Navier-Stokes equations with Dirichlet boundary condition corresponding to the sameinitial data in the energy space as a → ∞. The similar results have also been deduced for thestationary case.The last chapter is concerned with estimates for a Laplace-Robin problem: the following second order elliptic operator in divergence form in a bounded domain Q ⊂ Rn of class C1, withthe Robin boundary condition has been considered1div(A∇)u = divf + F in Q, 11 )u + u = f ⋅ n + g on Γ. (0.2) 2The coefficient matrix A is symmetric and belongs to V MO(R3). Also a is a function belonging to some Lq -space. Apart from proving existence, uniqueness of weak and strong solutions, we obtain the bound on u, uniform in a for a sufficiently large, in the Lp -norm. We have separately studied the two cases: the interior estimate and the boundary estimate to make the main idea clear in the simple set up
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Landmann, Björn. "A parallel discontinuous Galerkin code for the Navier-Stokes and Reynolds-averaged Navier-Stokes equations." [S.l. : s.n.], 2008. http://nbn-resolving.de/urn:nbn:de:bsz:93-opus-35199.

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Books on the topic "Navier-Stokes equations"

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Łukaszewicz, Grzegorz, and Piotr Kalita. Navier–Stokes Equations. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-27760-8.

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Constantin, P. Navier-Stokes equations. Chicago: University of Chicago Press, 1988.

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Plotnikov, Pavel, and Jan Sokołowski. Compressible Navier-Stokes Equations. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0367-0.

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Sohr, Hermann. The Navier-Stokes Equations. Basel: Springer Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-0551-3.

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Sohr, Hermann. The Navier-Stokes Equations. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8255-2.

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Zeytounian, Radyadour Kh. Navier-Stokes-Fourier Equations. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-20746-4.

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Hărăguș, D. Equations du type Navier-Stokes. Timișoara: Tipografia Universitătii din Timișoara, 1994.

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Joanna, Rencławowicz, Zajączkowski Wojciech M, and Instytut Matematyczny (Polska Akademia Nauk), eds. Parabolic and Navier-Stokes equations. Warszawa: Institute of Mathematics, Polish Academy of Sciences, 2008.

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Joanna, Rencławowicz, Zajączkowski Wojciech M, and Instytut Matematyczny (Polska Akademia Nauk), eds. Parabolic and Navier-Stokes equations. Warszawa: Institute of Mathematics, Polish Academy of Sciences, 2008.

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Ciprian, Foiaş, ed. Navier-Stokes equations and turbulence. Cambridge, UK: Cambridge University Press, 2001.

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Book chapters on the topic "Navier-Stokes equations"

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Kollmann, Wolfgang. "Navier–Stokes Equations." In Navier-Stokes Turbulence, 17–53. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31869-7_2.

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Kollmann, Wolfgang. "Navier-Stokes Equations." In Navier-Stokes Turbulence, 19–57. Cham: Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-59578-3_2.

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Kollmann, Wolfgang. "Functional Differential Equations." In Navier-Stokes Turbulence, 115–17. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-31869-7_7.

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Kollmann, Wolfgang. "Functional Differential Equations." In Navier-Stokes Turbulence, 121–23. Cham: Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-59578-3_7.

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Debussche, Arnaud, Berenger Hug, and Etienne Mémin. "Modeling Under Location Uncertainty: A Convergent Large-Scale Representation of the Navier-Stokes Equations." In Mathematics of Planet Earth, 15–26. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-18988-3_2.

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AbstractWe construct martingale solutions for the stochastic Navier-Stokes equations in the framework of the modelling under location uncertainty (LU). These solutions are pathwise and unique when the spatial dimension is 2D. We then prove that if the noise intensity goes to zero, these solutions converge, up to a subsequence in dimension 3, to a solution of the deterministic Navier-Stokes equation. This warrants that the LU Navier-Stokes equations can be interpreted as a large-scale model of the deterministic Navier-Stokes equation.
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Thomasset, F. "Implementation of non-conforming linear finite elements (Approximation APX5—Two-dimensional case)." In Navier–Stokes Equations, 321–35. Providence, Rhode Island: American Mathematical Society, 2001. http://dx.doi.org/10.1090/chel/343/05.

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Quarteroni, Alfio. "Navier-Stokes equations." In Numerical Models for Differential Problems, 457–510. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-49316-9_17.

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Xu, Xiaoping. "Navier–Stokes Equations." In Algebraic Approaches to Partial Differential Equations, 269–316. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-36874-5_9.

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Capiński, M., and N. J. Cutland. "Navier-Stokes Equations." In Advances in Analysis, Probability and Mathematical Physics, 20–36. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8451-7_2.

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Quarteroni, Alfio. "Navier-Stokes equations." In Numerical Models for Differential Problems, 429–82. Milano: Springer Milan, 2014. http://dx.doi.org/10.1007/978-88-470-5522-3_16.

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Conference papers on the topic "Navier-Stokes equations"

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Wolf, Jörg. "A direct proof of the Caffarelli-Kohn-Nirenberg theorem." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-34.

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Wrzosek, Dariusz. "Chemotaxis models with a threshold cell density." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-35.

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Arkhipova, Arina. "New a priori estimates for nondiagonal strongly nonlinear parabolic systems." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-1.

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Escher, Joachim, and Zhaoyang Yin. "Initial boundary value problems of the Degasperis-Procesi equation." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-10.

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Farwig, Reinhard, Hideo Kozono, and Hermann Sohr. "Criteria of local in time regularity of the Navier-Stokes equations beyond Serrin's condition." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-11.

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Feireisl, Eduard, and Hana Petzeltová. "Non-standard applications of the Łojasiewicz-Simon theory: Stabilization to equilibria of solutions to phase-field models." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-12.

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Goncerzewicz, Jan. "On the initial-boundary value problems for a degenerate parabolic equation." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-13.

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Gramchev, Todor, and Grzegorz Łysik. "Uniform analytic-Gevrey regularity of solutions to a semilinear heat equation." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-14.

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Janela, João, and Adélia Sequeira. "On a constrained minimization problem arising in hemodynamics." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-15.

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Konieczny, Paweł. "Linear flow problems in 2D exterior domains for 2D incompressible fluid flows." In Parabolic and Navier–Stokes equations. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2008. http://dx.doi.org/10.4064/bc81-0-16.

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Reports on the topic "Navier-Stokes equations"

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Newman, Christopher K. Exponential integrators for the incompressible Navier-Stokes equations. Office of Scientific and Technical Information (OSTI), July 2004. http://dx.doi.org/10.2172/975250.

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Kilic, M. S., G. B. Jacobs, J. S> Hesthaven, and G. Haller. Reduced Navier-Stokes Equations Near a Flow Boundary. Fort Belvoir, VA: Defense Technical Information Center, August 2005. http://dx.doi.org/10.21236/ada458888.

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Elman, Howard, and David Silvester. Fast Nonsymmetric Iterations and Preconditioning for Navier-Stokes Equations. Fort Belvoir, VA: Defense Technical Information Center, June 1994. http://dx.doi.org/10.21236/ada599710.

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Mikulevicius, R., and B. Rozovskii. Stochastic Navier-Stokes Equations. Propagation of Chaos and Statistical Moments. Fort Belvoir, VA: Defense Technical Information Center, January 2001. http://dx.doi.org/10.21236/ada413558.

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Luskin, Mitchell, and George R. Sell. Inertial Manifolds for Navier-Stokes Equations and Related Dynamical Systems. Fort Belvoir, VA: Defense Technical Information Center, May 1991. http://dx.doi.org/10.21236/ada241805.

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6

Szymczak, William G. Viscous Split Algorithms for the Time Dependent Incompressible Navier Stokes Equations. Fort Belvoir, VA: Defense Technical Information Center, June 1989. http://dx.doi.org/10.21236/ada211592.

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7

McDonough, J. M., Y. Yang, and X. Zhong. Additive Turbulent Decomposition of the Incompressible and Compressible Navier-Stokes Equations. Fort Belvoir, VA: Defense Technical Information Center, January 1993. http://dx.doi.org/10.21236/ada277321.

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8

Evans, John A., and Thomas J. Hughes. Isogeometric Divergence-conforming B-splines for the Steady Navier-Stokes Equations. Fort Belvoir, VA: Defense Technical Information Center, April 2012. http://dx.doi.org/10.21236/ada560496.

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9

Evans, John A., and Thomas J. Hughes. Isogeometric Divergence-conforming B-splines for the Unsteady Navier-Stokes Equations. Fort Belvoir, VA: Defense Technical Information Center, April 2012. http://dx.doi.org/10.21236/ada560939.

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10

Gaitonde, Datta V., and Miguel R. Visbal. High-Order Schemes for Navier-Stokes Equations: Algorithm and Implementation Into FDL3DI. Fort Belvoir, VA: Defense Technical Information Center, August 1998. http://dx.doi.org/10.21236/ada364301.

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