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941.
Jérôme Droniou Robert Eymard 《Numerical Methods for Partial Differential Equations》2009,25(1):137-171
We present finite volume schemes for Stokes and Navier‐Stokes equations. These schemes are based on the mixed finite volume introduced in (Droniou and Eymard, Numer Math 105 (2006), 35‐71), and can be applied to any type of grid (without “orthogonality” assumptions as for classical finite volume methods) and in any space dimension. We present numerical results on some irregular grids, and we prove, for both Stokes and Navier‐Stokes equations, the convergence of the scheme toward a solution of the continuous problem. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
942.
A kind of the proper orthogonal decomposition (POD) is used for data compression of rugged surface and reduction of the Navier–Stokes equations. An error estimate of the POD in model reduction and data compression is discussed. The numerical examples show that the error between the POD approximate solution and reference solution is consistent with theoretical results, and also show that the proposed algorithm is feasible and efficient. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
943.
A method for solving the time dependent Navier‐Stokes equations, aiming at higher Reynolds' number, is presented. The direct numerical simulation of flows with high Reynolds' number is computationally expensive. The method presented is unconditionally stable, computationally cheap, and gives an accurate approximation to the quantities sought. In the defect step, the artificial viscosity parameter is added to the inverse Reynolds number as a stability factor, and the system is antidiffused in the correction step. Stability of the method is proven, and the error estimations for velocity and pressure are derived for the one‐ and two‐step defect‐correction methods. The spacial error is O(h) for the one‐step defect‐correction method, and O(h2) for the two‐step method, where h is the diameter of the mesh. The method is compared to an alternative approach, and both methods are applied to a singularly perturbed convection–diffusion problem. The numerical results are given, which demonstrate the advantage (stability, no oscillations) of the method presented. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 相似文献
944.
In this paper, we study a Green’s functions G
E
, G
S
for an elasto-static equations and Stokes equations in a three-dimensional bounded Lipschitz domain Ω. We prove that there
is a positive constant c > 0 depending on the Lipschitz constant such that for all . Furthermore, we show that there is a positive constant η ∈ (0,1) depending on the Lipschitz constant such that for all .
The second author is partially supported by Korea Research Foundation Grant KRF C-00005. 相似文献
945.
1 引言 Stokes问题是标准的混合问题,速度与压力同时计算,关于该问题有限元求解的文章很多(见文献[1-5])但大多都是基于对区域的正则剖分或拟一致剖分,即要求网格剖分满足hk/pK≤C,(A)K∈Jh,其中C>0为一常数,hk,pK分别为单元K的直径及内切园直径,在实际应用问题中,由于边界层或区域的拐角处需考虑物质的各向异性特征,此时对空间区域Q的剖分不再满足正则性或拟一致条件,而需要用各向异性网格剖分,才能更贴切地描述其真实情形. 相似文献
946.
就流体力学中的Helmholtz最小耗散原理的几种变分推导方法进行综述,利用Hodge分解定理给出一个新的推导方法. 相似文献
947.
Yasushi Taniuchi 《Mathematische Zeitschrift》2009,261(3):597-615
We present a uniqueness theorem for time-periodic solutions to the Navier–Stokes equations in unbounded domains. Thus far,
results on the uniqueness of time-periodic solutions to the Navier–Stokes equations in unbounded domain, roughly speaking,
have only found that a small time-periodic L
n
-solution is unique within the class of solutions which have sufficiently small L
∞(L
n
)-norm. In this paper, we show that a small time-periodic L
n
-solution is unique within the class of all time-periodic L
n
-solutions, which contains large solutions. We also consider the uniqueness of solutions in weak-L
n
space. The proof of the present uniqueness theorem is based on the method of dual equations.
相似文献
948.
Yong Zhou 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(2):191-204
Considering the Navier–Stokes equations in , we prove the asymptotic stability for weak solutions in the marginal class u ∈ C
B
(0, ∞; L
n
) with arbitrary initial and external perturbations.
相似文献
949.
Corina Fetecau Muhammad Jamil Constantin Fetecau Dumitru Vieru 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2009,60(5):921-933
The velocity field corresponding to the Rayleigh–Stokes problem for an edge, in an incompressible generalized Oldroyd-B fluid
has been established by means of the double Fourier sine and Laplace transforms. The fractional calculus approach is used
in the constitutive relationship of the fluid model. The obtained solution, written in terms of the generalized G-functions, is presented as a sum of the Newtonian solution and the corresponding non-Newtonian contribution. The solution
for generalized Maxwell fluids, as well as those for ordinary Maxwell and Oldroyd-B fluids, performing the same motion, is
obtained as a limiting case of the present solution. This solution can be also specialized to give the similar solution for
generalized second grade fluids. However, for simplicity, a new and simpler exact solution is established for these fluids.
For β → 1, this last solution reduces to a previous solution obtained by a different technique.
相似文献
950.
Stokes型积分-微分方程的Crouzeix-Raviart型非协调三角形各向异性有限元方法 总被引:1,自引:0,他引:1
在半离散格式下.研究了Stokes型积分一微分方程的Crouzeix-Raviart型非协调三角形各向异性有限元方法,在不需要传统Ritz-Volterra投影下,通过辅助空间等新的技巧得到了与传统有限元方法相同的误差估计. 相似文献