Andrew Lundberg¹, Pengtao Sun^1,∗, Cheng Wang², Chen-song Zhang³

CMES-Computer Modeling in Engineering & Sciences, Vol.119, No.1, pp. 35-62, 2019, DOI:10.32604/cmes.2019.04804

Abstract The distributed Lagrange multiplier/fictitious domain (DLM/FD)-mixed finite element method is developed and analyzed in this paper for a transient Stokes interface problem with jump coefficients. The semi- and fully discrete DLM/FD-mixed finite element scheme are developed for the first time for this problem with a moving interface, where the arbitrary Lagrangian-Eulerian (ALE) technique is employed to deal with the moving and immersed subdomain. Stability and optimal convergence properties are obtained for both schemes. Numerical experiments are carried out for different scenarios of jump coefficients, and all theoretical results are validated. More >

N. Simões^1,2, A. Tadeu²

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.3, pp. 221-234, 2005, DOI:10.3970/cmes.2005.009.221

Abstract The use of the Boundary Element Method (BEM) to formulate the 3D transient heat transfer through cylindrical structures with irregular cross-sections, bounded by a homogeneous elastic medium, is described in this paper. In this formulation, both the conduction and the convection phenomena are modeled. This system can be subjected to heat emitted by either point or line sources located somewhere in the media. The solution is first obtained in the frequency domain for a wide range of frequencies and axial wavenumbers. Time domain responses are later calculated by means of (fast) inverse Fourier transforms into space-time. The appropriate fundamental solution… More >

Jin Yeon Cho¹, Jae Mo An², You Me Song¹, Seungsoo Lee¹, Dong Whan Choi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.1, pp. 1-18, 2005, DOI:10.3970/cmes.2005.009.001

Abstract A displacement welding technique is proposed to carry out coupled analysis of the integrated whole model which consists of independently modeled finite element substructures. In the proposed method, the incompatible displacement fields in the interfaces of independently modeled substructures are directly welded together through a blended function that is newly defined in the transient region of mismatching interface. To construct the blended function, the moving least squares function, which does not require well-defined nodal connectivity, is utilized along with the original finite element shape function. The meshless character of the moving least squares function makes it possible to efficiently handle… More >

J. Sladek¹, V. Sladek¹, J. Krivacek¹, Ch. Zhang²

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.3, pp. 259-270, 2005, DOI:10.3970/cmes.2005.008.259

Abstract A meshless method based on the local Petrov-Galerkin approach is presented for stress analysis in three-dimensional (3-d) axisymmetric linear elastic solids with continuously varying material properties. The inertial effects are considered in dynamic problems. A unit step function is used as the test functions in the local weak-form. It is leading to local boundary integral equations (LBIEs). For transient elastodynamic problems the Laplace-transform technique is applied and the LBIEs are given in the Laplace-transformed domain. Axial symmetry of the geometry and the boundary conditions for a 3-d linear elastic solid reduces the original 3-d boundary value problem into a 2-d… More >

F. Cosmi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.3, pp. 191-200, 2005, DOI:10.3970/cmes.2005.008.191

Abstract The Cell Method is a recently developed numerical method that is giving interesting results in several fields of physics and engineering. In this paper, first a brief description of the method for elasticity problems is given and successively the elastodynamics formulation is derived. The method leads to an explicit solution system, combining the advantages of a diagonal mass matrix and the possibility of using unstructured meshes. The convergence rate has been tested in reference to the problem of free harmonic vibrations in a system with one degree of freedom, showing that the Cell Method has the same convergence rate of… More >

L. Mai-Cao¹, T. Tran-Cong²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 149-172, 2005, DOI:10.3970/cmes.2005.007.149

Abstract The Indirect Radial Basis Function Network (IRBFN) method has been reported to be a highly accurate tool for approximating multivariate functions and solving elliptic partial differential equations (PDEs). The present method is a truly meshless method as defined in [\citet *{Atluri_Shen_02a}]. A recent development of the method for solving transient problems is presented in this paper. Two numerical schemes combining the IRBFN method with different time integration techniques based on either fully or semi-discrete framework are proposed. The two schemes are implemented making use of Hardy's multiquadrics (MQ) and Duchon's thin plate splines (TPS). Some example problems are solved by… More >

António Tadeu¹, Julieta António and Nuno Simões

CMES-Computer Modeling in Engineering & Sciences, Vol.6, No.1, pp. 43-58, 2004, DOI:10.3970/cmes.2004.006.043

Abstract This Analytical Green's functions for the steady-state response of homogeneous three-dimensional unbounded, half-space, slab and layered solid media subjected to a spatially sinusoidal harmonic heat line source are presented. In the literature, this problem is frequently referred to as the two-and-a-half dimensional fundamental solution or 2.5D Green's functions.
The proposed equations are theoretically interesting in themselves and they are also useful as benchmark results for validating numerical applications. They are also of great practical use in the formulation of three dimensional heat transfer problems in layered solid formations using integral transform methods and/or boundary elements.
The final expressions… More >

S. Kucukcoban¹, L.F. Kallivokas²

CMES-Computer Modeling in Engineering & Sciences, Vol.64, No.2, pp. 109-146, 2010, DOI:10.3970/cmes.2010.064.109

Abstract We are concerned with elastic wave simulations arising in elastic, semi-infinite, heterogeneous, three-dimensional media with a vertical axis of symmetry through the coordinate origin. Specifically, we discuss the development of a new mixed displacement-stress formulation in PML-truncated axisymmetric media for forward elastic wave simulations. Typically, a perfectly-matched-layer (PML) is used to surround a truncated finite computational domain in order to attenuate outwardly propagating waves without reflections for all non-zero angles-of-incidence and frequencies. To date, standard formulations use split fields, where the displacement components are split into normal and parallel to the PML interface components. In this work, we favor unsplit… More >

PoojaJhunjhunwala¹, P.M. Padole², S.B. Thombre³

Molecular & Cellular Biomechanics, Vol.13, No.1, pp. 1-21, 2016, DOI:10.3970/mcb.2016.013.001

Abstract This paper presents Computational fluid dynamic (CFD) analysis of blood flow in three different 3-D models of left coronary artery (LCA). A comparative study of flow parameters (pressure distribution, velocity distribution and wall shear stress) in each of the models is done for a non-Newtonian (Carreau) as well as the Newtonian nature of blood viscosity over a complete cardiac cycle. The difference between these two types of behavior of blood is studied for both transient and steady states of flow. Additionally, flow parameters are compared for steady and transient boundary conditions considering blood as non-Newtonian fluid. The study shows that… More >

Ze-Wei Zhang^*, Hui Wang^†, Qing-Hua Qin^∗,‡

Molecular & Cellular Biomechanics, Vol.9, No.1, pp. 31-54, 2012, DOI:10.3970/mcb.2012.009.031

Abstract This paper presents a hybrid finite element model for describing quantitatively the thermal responses of skin tissue under laser irradiation. The model is based on the boundary integral-based finite element method and the Pennes bioheat transfer equation. In this study, temporal discretization of the bioheat system is first performed and leads to the well-known modified Helmholtz equation. A radial basis function approach and the boundary integral based finite element method are employed to obtain particular and homogeneous solutions of the laser-tissue interaction problem. In the boundary integral based finite element formulation, two independent fields are assumed: intra-element field and frame… More >