期刊
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
卷 100, 期 6, 页码 399-418出版社
WILEY
DOI: 10.1002/nme.4734
关键词
finite volume methods; geomechanics; elasticity; differential equations
The development of cell-centered finite volume discretizations for deformation is motivated by the desire for a compatible approach with the discretization of fluid flow in deformable porous media. We express the conservation of momentum in the finite volume sense, and introduce three approximations methods for the cell-face stresses. The discretization method is developed for general grids in one to three spatial dimensions, and leads to a global discrete system of equations for the displacement vector in each cell, after which the stresses are calculated based on a local expression. The method allows for anisotropic, heterogeneous and discontinuous coefficients. The novel finite volume discretization is justified through numerical validation tests, designed to investigate classical challenges in discretization of mechanical equations. In particular our examples explore the stability with respect to the Poisson ratio and spatial discontinuities in the material parameters. For applications, logically Cartesian grids are prevailing, and we also explore the performance on perturbations on such grids, as well as on unstructured grids. For reference, comparison is made in all cases with the lowest-order Lagrangian finite elements, and the finite volume methods proposed herein is comparable for approximating displacement, and is superior for approximating stresses. (C) 2014 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据