Zichun Yang^1,2,3, Lei Zhang^1,4, Yueyun Cao¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 101-130, 2014, DOI:10.3970/cmes.2014.097.101

Abstract Discretization of inverse problems often leads to systems of linear equations with a highly ill-conditioned coefficient matrix. To find meaningful solutions of such systems, one kind of prevailing and representative approaches is the so-called regularized total least squares (TLS) method when both the system matrix and the observation term are contaminated by some noises. We will survey two such regularization methods in the TLS setting. One is the iterative truncated TLS (TTLS) method which can solve a convergent sequence of projected linear systems generated by Lanczos bidiagonalization. The other one is to convert the Tikhonov regularization TLS problem to an… More >

Zhendong Luo¹, Fei Teng²

CMES-Computer Modeling in Engineering & Sciences, Vol.101, No.1, pp. 33-58, 2014, DOI:10.3970/cmes.2014.101.033

Abstract A semi-discrete Crank-Nicolson (CN) formulation about time and a fully discrete stabilized CN finite volume element (SCNFVE) formulation based on two local Gauss integrals and parameter-free with the second-order time accuracy are established for the non-stationary Navier-Stokes equations. The error estimates of the semi-discrete and fully discrete SCNFVE solutions are derived. Some numerical experiments are presented to illustrate that the fully discrete SCNFVE formulation possesses more advantages than its stabilized finite volume element formulation with the first-order time accuracy, thus validating that the fully discrete SCNFVE formulation is feasible and efficient for finding the numerical solutions of the non-stationary Navier-Stokes… More >

Mikael A. Langthjem¹, Masami Nakano²

CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.4, pp. 227-241, 2013, DOI:10.3970/cmes.2013.096.227

Abstract This paper is concerned with a mathematical model of a simple axisymmetric silencer-like model, consisting of a hole-tone feedback system equipped with a tailpipe. The unstable shear layer is modeled via a discrete vortex method, based on axisymmetric vortex rings. The aeroacoustic model is based on the Powell- Howe theory of vortex sound. Boundary integrals are discretized via the boundary element method; but the tailpipe is represented by the exact (one-dimensional) solution. It is demonstrated though numerical examples that this numerical model can display lock-in of the self-sustained flow oscillations to the resonant acoustic oscillations. More >

Martino Pani¹, Fulvia Taddei¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.4, pp. 279-300, 2013, DOI:10.3970/cmes.2013.094.279

Abstract The Cell Method (CM) is a numerical method to solve field equations starting from its direct algebraic formulation. For two-dimensional problems it has been demonstrated that using simplicial elements with an affine interpolation, the CM obtains the same fundamental equation of the Finite Element Method (FEM); using the quadratic interpolation functions, the fundamental equation differs depending on how the dual cell is defined. In spite of that, the CM can still provide the same convergence rate obtainable with the FEM. Particularly, adopting a uniform triangulation and basing the dual cells on the Gauss points of the primal edges, the CM… More >

A.P.S.Selvadurai¹

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.3, pp. 259-278, 2009, DOI:10.3970/cmes.2009.052.259

Abstract The paper deals with a computational approach for modelling the fragmentation of ice sheets during their impact with stationary structures. The modelling takes into consideration the intact continuum behaviour of the ice as a rate-sensitive elastoplastic material. During impact, the ice sheet can undergo fragmentation, which is controlled by a brittle strength criterion based on the current stress state. The fragmentation allows the generation of discrete elements of the ice sheet, the movements of which are governed by the equations of motion. The contact between individual fragments is governed by a Coulomb criterion. The individual fragments can themselves undergo further… More >

F. Fleissner¹, T. Haag², M. Hanss², P. Eberhard¹

CMES-Computer Modeling in Engineering & Sciences, Vol.52, No.2, pp. 181-196, 2009, DOI:10.3970/cmes.2009.052.181

Abstract In alpine regions human settlements and infrastructure are at risk to be hit by landslides or other types of geological flows. This paper presents a new approach that can aid the design of protective constructions. An uncertainty analysis of the flow around a debris barrier is carried out using a chute flow laboratory model of the actual debris flow. A series of discrete element simulations thereby serves to compare and assess two different barrier designs. In this study, the transformation method of fuzzy arithmetic is used to investigate the influence of epistemically uncertain model parameters. It turns out that parameter… More >

Jin Ma, Yang Liu, Hongbing Lu, Ranga Komanduri¹

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.1, pp. 41-56, 2006, DOI:10.3970/cmes.2006.016.041

Abstract A multiscale simulation technique coupling three scales, namely, the molecular dynamics (MD) at the atomistic scale, the discrete dislocations at the meso scale and the generalized interpolation material point (GIMP) method at the continuum scale is presented. Discrete dislocations are first coupled with GIMP using the principle of superposition (van der Giessen and Needleman (1995)). A detection band seeded in the MD region is used to pass the dislocations to and from the MD simulations (Shilkrot, Miller and Curtin (2004)). A common domain decomposition scheme for each of the three scales was implemented for parallel processing. Simulations of indentation were… More >

P. Castillo², J. Koning³, R. Rieben⁴, D. White⁵

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.4, pp. 331-346, 2004, DOI:10.3970/cmes.2004.005.331

Abstract In this article, we present a computational framework for solving problems arising in electromagnetism. The framework is derived from a modern geometrical approach and is based on differential forms (or p-forms). These geometrical entities provide a natural framework for modeling of physical quantities such as electric potentials, electric and magnetic fields, electric and magnetic fluxes, etc. We have implemented an object oriented class library, called FEMSTER. The library is designed for high order finite element approximations. In addition, it can be expanded by including user-defined data types or by deriving new classes. Finally, the versatility of the software is shown… More >

Roman Chapko¹, B. Tomas Johansson²

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.2, pp. 105-128, 2012, DOI:10.3970/cmes.2012.085.105

Abstract We consider a Cauchy problem for the Laplace equation in a 3-dimen -sional semi-infinite domain that contains a bounded inclusion. The canonical situation is the upper half-space in I\tmspace -.1667em R3 containing a bounded smooth domain. The function value of the solution is specified throughout the plane bounding the upper half-space, and the normal derivative is given only on a finite portion of this plane. The aim is to reconstruct the solution on the surface of the bounded inclusion. This is a generalisation of the situation in Chapko and Johansson (2008) to three-dimensions and with Cauchy data only partially given.… More >

Li Shan, Ning Cui, Ming Cheng, Kaixin Liu

CMES-Computer Modeling in Engineering & Sciences, Vol.83, No.4, pp. 353-384, 2012, DOI:10.3970/cmes.2012.083.353

Abstract In the present paper, a combined scheme of discrete element method (DEM) and meshless method for numerical simulation of impact problems is proposed. Based on the basic principle of continuum mechanics, an axisymmetric DEM framework is established for modeling the elastoplastic behavior of solid materials. Failure criteria are introduced to model the transformation from a continuum to a discontinuum. The friction force between contact elements is also considered after the failure appears. So our scheme can calculate not only the behavior of continuum and discontinuum, but also the transformation process from a continuum to a discontinuum. In addition, a meshless… More >