检索结果-南通市图书馆

Communications on Applied Mathematics and Computation 2020年第4期2卷 581-611页

作者： Hendrik Ranocha Katharina Ostaszewski Philip Heinisch Institute Computational Mathematics TU BraunschweigUniversitatsplatz 238106 BrunswickGermany Extreme Computing Research Center(ECRC) Computer Electrical and Mathematical Science and Engineering Division(CEMSE)King Abdullah University of Science and Technology(KAUST)Thuwal 23955-6900Saudi Arabia Institut für Angewandte Numerische Wissenschaft e.V.(IANW) Bienroder Straae 338110 BrunswickGermany Institut für Geophysik und Extraterrestrische Physik TU BraunschweigMendelssohnstraBe 338106 BrunswickGermany

In this article,discrete variants of several results from vector calculus are studied for clas-sical finite difference summation by parts operators in two and three space *** is shown that existence theorems for scalar/vector potentials of irrotational/solenoidal vector fields cannot hold discretely because of grid oscillations,which are characterised *** results in a non-vanishing remainder associated with grid oscillations in the discrete Helmholtz Hodge ***,iterative numerical methods based on an interpretation of the Helmholtz Hodge decomposition via orthogonal projections are pro-posed and applied *** numerical experiments,the discrete remainder vanishes and the potentials converge with the same order of accuracy as usual in other first-order partial differential *** by the successful application of the Helmholtz Hodge decomposition in theoretical plasma physics,applications to the discrete analysis of magnetohydrodynamic(MHD) wave modes are presented and discussed.

关键词： summation by parts Vector calculus Helmholtz Hodge decomposition Mimetic properties Wave mode analysis

Stability of Finite Difference Discretizations of Multi-Physics Interface Conditions

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Computational Physics 2013年第2期13卷 386-410页

作者： Björn Sjögreen Jeffrey W.Banks Center for Applied Scientific Computing Lawrence Livermore National LaboratoryLivermoreCA 94551USA

We considermulti-physics computationswhere theNavier-Stokes equations of compressible fluid flow on some parts of the computational domain are coupled to the equations of elasticity on other parts of the computational *** different subdomains are separated by well-defined *** consider time accurate computations resolving all time *** such computations,explicit time stepping is very *** address the issue of discrete interface conditions between the two domains of different physics that do not lead to instability,or to a significant reduction of the stable time step *** such interface conditions is *** discretize the problem with high order centered difference approximations with summation by parts boundary *** derive L2 stable interface conditions for the linearized one dimensional discretized ***,we generalize the interface conditions to the full non-linear equations and numerically demonstrate their stable and accurate performance on a simple model *** energy stable interface conditions derived here through symmetrization of the equations contain the interface conditions derived through normal mode analysis by Banks and Sj¨ogreen in[8]as a special case.

关键词： Fluid-structure interaction finite difference method summation by parts multiphysics interface condition

Stable and Efficient Modeling of Anelastic Attenuation in Seismic Wave Propagation

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Computational Physics 2012年第6期12卷 193-225页

作者： N.Anders Petersson Bjorn Sjogreen Center for Applied Scientific Computing L-422Lawrence Livermore National LaboratoryP.O.Box 808LivermoreCA 94551USA

We develop a stable finite difference approximation of the three-dimensional viscoelastic wave *** material model is a super-imposition of N standard linear solid mechanisms,which commonly is used in seismology to model a material with constant quality factor *** proposed scheme discretizes the governing equations in second order displacement formulation using 3N memory variables,making it significantly more memory efficient than the commonly used first order velocitystress *** new scheme is a generalization of our energy conserving finite difference scheme for the elastic wave equation in second order formulation[SIAM ***.,45(2007),pp.1902–1936].Our main result is a proof that the proposed discretization is energy stable,even in the case of variable material *** proof relies on the summation-by-parts property of the *** newscheme is implemented with grid refinement with hanging nodes on the *** experiments verify the accuracy and stability of the new ***-analytical solutions for a half-space problem and the LOH.3 layer over half-space problem are used to demonstrate how the number of viscoelastic mechanisms and the grid resolution influence the *** find that three standard linear solid mechanisms usually are sufficient to make the modeling error smaller than the discretization error.

关键词： Viscoelastic standard linear solid finite difference summation by parts

Stable Grid Refinement and Singular Source Discretization for Seismic Wave Simulations

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Computational Physics 2010年第10期8卷 1074-1110页

作者： N.Anders Petersson Bjorn Sjogreen Center for Applied Scientific Computing L-422Lawrence Livermore National LaboratoryPO Box 808LivermoreCA 94551.

An energy conserving discretization of the elastic wave equation in second order formulation is developed for a composite grid,consisting of a set of structured rectangular component grids with hanging nodes on the grid refinement *** developed summation-by-parts properties are generalized to devise a stable second order accurate coupling of the solution across mesh refinement *** discretization of singular source terms of point force and point moment tensor type are also *** on enforcing discrete moment conditions that mimic properties of the Dirac distribution and its gradient,previous single grid formulas are generalized to work in the vicinity of grid refinement *** source discretization formulas are shown to give second order accuracy in the solution,with the error being essentially independent of the distance between the source and the grid refinement *** numerical examples are given to illustrate the properties of the proposed method.

关键词： Elastic wave equation mesh refinement stability summation by parts singular source term