Pengfei Zhu¹, Qinghui Zhang^2,*

CMES-Computer Modeling in Engineering & Sciences, Vol.124, No.1, pp. 107-127, 2020, DOI:10.32604/cmes.2020.09831

Abstract There are several difficulties in generalized/extended finite element methods (GFEM/XFEM) for moving interface problems. First, the GFEM/XFEM may be unstable in a sense that condition numbers of system matrices could be much bigger than those of standard FEM. Second, they may not be robust in that the condition numbers increase rapidly as interface curves approach edges of meshes. Furthermore, time stepping schemes need carrying out carefully since both enrichment functions and enriched nodes in the GFEM/XFEM vary in time. This paper is devoted to proposing the stable and robust GFEM/XFEM with effi- cient time stepping schemes for the parabolic interface… More >

Louis C. Foucard¹, John Pellegrino¹, Franck J. Vernerey^1,2

CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.1, pp. 101-127, 2014, DOI:10.3970/cmes.2014.098.101

Abstract Many colloidal-sized particles encountered in biological and membranebased separation applications can be characterized as soft vesicles such as cells, yeast, viruses and surfactant micelles. The deformation of these vesicles is expected to critically affect permeation by accommodating pore shapes and sizes or enhancing the adhesion with a pore surface. Numerical and theoretical modelings will be critical to fully understand these processes and thus design novel filtration membranes that target, not only size, but deformability as a selection criterion. The present paper therefore introduces a multiscale strategy that enables the determination of the permeability of a fibrous network with respect to… More >

L. Mai-Cao¹, T. Tran-Cong²

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.3, pp. 157-188, 2008, DOI:10.3970/cmes.2008.031.157

Abstract This paper presents a new meshless numerical approach to solving a special class of moving interface problems known as the passive transport where an ambient flow characterized by its velocity field causes the interfaces to move and deform without any influences back on the flow. In the present approach, the moving interface is captured by the level set method at all time as the zero contour of a smooth function known as the level set function whereas one of the two new meshless schemes, namely the SL-IRBFN based on the semi-Lagrangian method and the Taylor-IRBFN scheme based on Taylor series… More >