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101.
Yousef Hashem Zahran 《国际流体数值方法杂志》2008,57(6):745-760
We describe a hybrid method for the solution of hyperbolic conservation laws. A third‐order total variation diminishing (TVD) finite difference scheme is conjugated with a random choice method (RCM) in a grid‐based adaptive way. An efficient multi‐resolution technique is used to detect the high gradient regions of the numerical solution in order to capture the shock with RCM while the smooth regions are computed with the more efficient TVD scheme. The hybrid scheme captures correctly the discontinuities of the solution and saves CPU time. Numerical experiments with one‐ and two‐dimensional problems are presented. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
102.
Daniel Castaño Díez Max Gunzburger Angela Kunoth 《Numerical Methods for Partial Differential Equations》2008,24(6):1388-1404
We extend the multiscale finite element viscosity method for hyperbolic conservation laws developed in terms of hierarchical finite element bases to a (pre‐orthogonal spline‐)wavelet basis. Depending on an appropriate error criterion, the multiscale framework allows for a controlled adaptive resolution of discontinuities of the solution. The nonlinearity in the weak form is treated by solving a least‐squares data fitting problem. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 相似文献
103.
XU Junquan BAO Hongchun WU Minxian 《Chinese Journal of Lasers》1999,8(1):55-60
1IntroductionWiththedevelopmentofmodernindustry,therearemanylargeandhugeelementsandequipments,suchaslargegeneratorsandwaterw... 相似文献
104.
In this paper, the locally conservative Galerkin (LCG) method (Numer. Heat Transfer B Fundam. 2004; 46 :357–370; Int. J. Numer. Methods Eng. 2007) has been extended to solve the incompressible Navier–Stokes equations. A new correction term is also incorporated to make the formulation to give identical results to that of the continuous Galerkin (CG) method. In addition to ensuring element‐by‐element conservation, the method also allows solution of the governing equations over individual elements, independent of the neighbouring elements. This is achieved within the CG framework by breaking the domain into elemental sub‐domains. Although this allows discontinuous trial function field, we have carried out the formulation using the continuous trial function space as the basis. Thus, the changes in the existing CFD codes are kept to a minimum. The edge fluxes, establishing the continuity between neighbouring elements, are calculated via a post‐processing step during the time‐stepping operation. Therefore, the employed formulation needs to be carried out using either a time‐stepping or an equivalent iterative scheme that allows post‐processing of fluxes. The time‐stepping algorithm employed in this paper is based on the characteristic‐based split (CBS) scheme. Both steady‐ and unsteady‐state examples presented show that the element‐by‐element formulation employed is accurate and robust. Copyright © 2007 John Wiley & Sons, Ltd. 相似文献
105.
106.
Zhiliang Xu Yingjie Liu Huijing Du Guang Lin Chi-Wang Shu 《Journal of computational physics》2011,230(17):6843-6865
We develop a new hierarchical reconstruction (HR) method and for limiting solutions of the discontinuous Galerkin and finite volume methods up to fourth order of accuracy without local characteristic decomposition for solving hyperbolic nonlinear conservation laws on triangular meshes. The new HR utilizes a set of point values when evaluating polynomials and remainders on neighboring cells, extending the technique introduced in Hu, Li and Tang [9]. The point-wise HR simplifies the implementation of the previous HR method which requires integration over neighboring cells and makes HR easier to extend to arbitrary meshes. We prove that the new point-wise HR method keeps the order of accuracy of the approximation polynomials. Numerical computations for scalar and system of nonlinear hyperbolic equations are performed on two-dimensional triangular meshes. We demonstrate that the new hierarchical reconstruction generates essentially non-oscillatory solutions for schemes up to fourth order on triangular meshes. 相似文献
107.
In the present paper the author investigates the global structure stability of Riemann solutions for general quasilinear hyperbolic systems of conservation laws under small BV perturbations of the initial data, where the Riemann solution contains rarefaction waves, while the perturbations are in BV but they are assumed to be C1-smooth, with bounded and possibly large C1-norms. Combining the techniques employed by Li–Kong with the modified Glimm’s functional, the author obtains a lower bound of the lifespan of the piecewise C1 solution to a class of generalized Riemann problems, which can be regarded as a small BV perturbation of the corresponding Riemann problem. This result is also applied to the system of traffic flow on a road network using the Aw–Rascle model. 相似文献
108.
《Communications in Nonlinear Science & Numerical Simulation》2014,19(10):3492-3512
In this paper we develop, study, and test a Lie group multisymplectic integrator for geometrically exact beams based on the covariant Lagrangian formulation. We exploit the multisymplectic character of the integrator to analyze the energy and momentum map conservations associated to the temporal and spatial discrete evolutions. 相似文献
109.
110.
In this article, a new methodology for developing discrete geometric conservation law (DGCL) compliant formulations is presented. It is carried out in the context of the finite element method for general advective–diffusive systems on moving domains using an ALE scheme. There is an extensive literature about the impact of DGCL compliance on the stability and precision of time integration methods. In those articles, it has been proved that satisfying the DGCL is a necessary and sufficient condition for any ALE scheme to maintain on moving grids the nonlinear stability properties of its fixed‐grid counterpart. However, only a few works proposed a methodology for obtaining a compliant scheme. In this work, a DGCL compliant scheme based on an averaged ALE Jacobians formulation is obtained. This new formulation is applied to the θ family of time integration methods. In addition, an extension to the three‐point backward difference formula is given. With the aim to validate the averaged ALE Jacobians formulation, a set of numerical tests are performed. These tests include 2D and 3D diffusion problems with different mesh movements and the 2D compressible Navier–Stokes equations. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献