By R. Glowinski, Jinchao Xu, Philippe G. Ciarlet
ISBN-10: 0444530479
ISBN-13: 9780444530479
Non-Newtonian flows and their numerical simulations have generated an plentiful literature, in addition to many courses and references to that are present in this volume's articles. This abundance of courses may be defined via the truth that non-Newtonian fluids happen in lots of actual existence events: the foodstuff undefined, oil & fuel undefined, chemical, civil and mechanical engineering, the bio-Sciences, to call quite a few. Mathematical and numerical research of non-Newtonian fluid stream types offer not easy difficulties to partial differential equations experts and utilized computational mathematicians alike. This quantity deals investigations. effects and conclusions that may without doubt be worthwhile to engineers and computational and utilized mathematicians who're eager about quite a few elements of non-Newtonian Fluid Mechanics. New evaluate of recognized computational tools for the simulation viscoelastic and viscoplastic types.; Discusses new numerical tools that experience confirmed to be extra effective and extra actual than conventional methods.; Articles that debate the numerical simulation of particulate stream for viscoelastic fluids.;
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Extra resources for Handbook of Numerical Analysis, Volume XVI, Special Volume: Numerical Methods for Non-Newtonian Fluids
Example text
9) is very difficult because these three equations are redundant and no fixed-point can use all three at the same time. The originality and power of construction by Cioranescu and Ouazar lie in that they did use all three equations. u 1 u/. 9). 11) in the discrete case. 0; T I H 3 . 0; T I H 1 . /3 /. 10), are justified because the basis functions are sufficiently smooth. 1). The above bounds allow us to pass to the limit in the discrete equations and prove local existence in time of a solution.
9, without additional assumption on and f . More precisely, we have the following results. 10. Let y D curl 1 v: be a convex polygon; let v 2 V and y 2 L2 . 4 29 Theoretical Results Then there exists r0 > 2 depending on the inner angles of @ , such that for all r 2 [2; r0 ], v 2 W 2;r . /2 , and there exists a constant C, depending only on r and , such that kvkW 2;r . C kykL2 . 11. 3) belongs to W 2;r . /2 , and there exists a constant Cr , depending only on r and , such that kukW 2;r . Cr / 1 kcurl ukL2 .
17) belongs to W 2;r . / with continuous dependence on f . 2. Let be a polyhedron in IR3 with a Lipschitz-continuous boundary. If f belongs to H s 1 . 17) belongs to H sC1 . / with continuous dependence on f . If f belongs to L3=2 . /, then u belongs to H 3=2 . / with continuous dependence on f . When f is smoother than in the above statements, the solution is also smoother provided the inner angles of @ are suitably restricted. For instance, it is well known that the next regularity holds in a convex domain (cf.
Handbook of Numerical Analysis, Volume XVI, Special Volume: Numerical Methods for Non-Newtonian Fluids by R. Glowinski, Jinchao Xu, Philippe G. Ciarlet
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