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91.
In this paper, we propose a new lattice Boltzmann model for the compressible Navier–Stokes equations. The new model is based on a three‐energy‐level and three‐speed lattice Boltzmann equation by using a method of higher moments of the equilibrium distribution functions. As the 25‐bit model, we obtained the equilibrium distribution functions and the compressible Navier–Stokes equations with the second accuracy of the truncation errors. The numerical examples show that the model can be used to simulate the shock waves, contact discontinuities and supersonic flows around circular cylinder. The numerical results are compared with those obtained by traditional method. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
92.
A segregated method for compressible flow computation. Part II: general divariant compressible flows
Typically, segregated methods have been used for the computation of incompressible flows whereas coupled solvers, for compressible flows. Compared to coupled solvers, segregated methods present the advantage of computational savings in RAM memory and CPU time, although at the cost of an inferior robustness. However, previously published segregated algorithms for general compressible flows are known to present pitfalls, like convergence to wrong solutions, lack of robustness in the presence of strong discontinuities, such as normal and oblique shocks, and complicated boundary condition imposition. Therefore, in this paper a segregated method for non‐isothermal compressible flows is proposed that preserves the thermodynamic coupling and overcomes the criticisms of existing methods. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
93.
94.
95.
XIAO LING 《数学年刊B辑(英文版)》1995,(4)
LARGE-TIMEBEHMIOROFSOLUTIONSFORTHESYSTEMOFCOMPRESSIBLEADIABATICFLOWTHROUGHPOROUSMEDIA¥XIAOLING(L.HSIAO)D.SERRE(InstituteofMat... 相似文献
96.
We present an efficient mesh adaptation algorithm that can be successfully applied to numerical solutions of a wide range of 2D problems of physics and engineering described by partial differential equations. We are interested in the numerical solution of a general boundary value problem discretized on triangular grids. We formulate a necessary condition for properties of the triangulation on which the discretization error is below the prescribed tolerance and control this necessary condition by the interpolation error. For a sufficiently smooth function, we recall the strategy how to construct the mesh on which the interpolation error is below the prescribed tolerance. Solving the boundary value problem we apply this strategy to the smoothed approximate solution. The novelty of the method lies in the smoothing procedure that, followed by the anisotropic mesh adaptation (AMA) algorithm, leads to the significant improvement of numerical results. We apply AMA to the numerical solution of an elliptic equation where the exact solution is known and demonstrate practical aspects of the adaptation procedure: how to control the ratio between the longest and the shortest edge of the triangulation and how to control the transition of the coarsest part of the mesh to the finest one if the two length scales of all the triangles are clearly different. An example of the use of AMA for the physically relevant numerical simulation of a geometrically challenging industrial problem (inviscid transonic flow around NACA0012 profile) is presented. © 2004 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2004. 相似文献
97.
A. Mielke 《Journal of Nonlinear Science》1997,7(1):57-99
Summary We introduce a new method for the analysis of sideband instabilities which are important for periodic patterns appearing in
systems close to the instability threshold. The method relies on a two-fold application of the Liapunov-Schmidt reduction
procedure, a first application to the nonlinear bifurcation problem and a second application to the linear spectral problem.
We obtain rigorous results on the spectrum of the associated linearization in spaces allowing for general sideband perturbations
by treating the sideband vector and the spectral parameter as small bifurcation parameters.
We apply the theory to the small roll solutions in the Rayleigh-Bénard convection and derive domains in Rayleigh, Prandtl,
and wave number space where the rolls are unstable. We recover the Eckhaus, zigzag, and skew-varicose instabilities obtained
earlier by formal methods.
This paper is dedicated to the memory of Juan C. Simo
This paper was solicited by the editors to be part of a volume dedicated to the memory of Juan C. Simo. 相似文献
98.
We formulate a subgrid eddy viscosity method for solving the steady‐state incompressible flow problem. The eddy viscosity does not act on the large flow structures. Optimal error estimates are obtained for velocity and pressure. The numerical illustrations agree completely with the theoretical results. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2005 相似文献
99.
Jiajie Li Shengfeng Zhu Xiaoqin Shen 《Numerical Methods for Partial Differential Equations》2023,39(2):1604-1634
For shape optimization of fluid flows governed by the Navier–Stokes equation, we investigate effectiveness of shape gradient algorithms by analyzing convergence and accuracy of mixed finite element approximations to both the distributed and boundary types of shape gradients. We present convergence analysis with a priori error estimates for the two approximate shape gradients. The theoretical analysis shows that the distributed formulation has superconvergence property. Numerical results with comparisons are presented to verify theory and show that the shape gradient algorithm based on the distributed formulation is highly effective and robust for shape optimization. 相似文献
100.
In this work we consider a poroelastic, flexible material that may deform largely, which is situated in an incompressible fluid driven by the Navier–Stokes equations in two or three space dimensions. By a variational approach we show existence of weak solutions for a class of such coupled systems. We consider the unsteady case, this means that the PDE for the poroelastic solid involves the Fréchet-derivative of a non-convex functional as well as (second order in time) inertia terms. 相似文献