Jacek Narski^1,2, Marco Picasso¹

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 49-64, 2007, DOI:10.3970/fdmp.2007.003.049

Abstract An adaptive phase field model for the solidification of binary alloys in three space dimensions is presented. The fluid flow in the liquid due to different liquid/solid densities is taken into account. The unknowns are the phase field, the alloy concentration and the velocity/pressure in the liquid. Continuous, piecewise linear finite elements are used for the space discretization, a semi-implicit scheme is used for time discretization. An adaptive method allows the number of degrees of freedom to be reduced, the mesh tetrahedrons having high aspect ratio whenever needed. Numerical results show that our method is More >

Frédéric Gibou¹, Chohong Min², Hector D. Ceniceros³

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 37-48, 2007, DOI:10.3970/fdmp.2007.003.037

Abstract We describe two finite difference schemes for simulating incompressible flows on nonuniform meshes using quadtree/octree data structures. The first one uses a cell-centered Poisson solver that yields first-order accurate solutions, while producing symmetric linear systems. The second uses a node-based Poisson solver that produces second-order accurate solutions and second-order accurate gradients, while producing nonsymmetric linear systems as the basis for a second-order accurate Navier-Stokes solver. The grids considered can be non-graded, i.e. the difference of level between two adjacent cells can be arbitrary. In both cases semi-Lagrangian methods are used to update the intermediate fluid More >

Mark Sussman¹, Mitsuhiro Ohta²

FDMP-Fluid Dynamics & Materials Processing, Vol.3, No.1, pp. 21-36, 2007, DOI:10.3970/fdmp.2007.003.021

Abstract In this paper, we describe new techniques for numerically approximating two-phase flows. Specifically, we present new techniques for treating the viscosity and surface tension terms that appear in the Navier-Stokes equations for incompressible two-phase flow. Our resulting numerical method has the property that results computed using our two-phase algorithm approach the corresponding "one-phase'' algorithm in the limit of zero gas density/viscosity; i.e. the two-phase results approach the one-phase free-boundary results in the limit that the gas is assumed to become a uniform pressure void. By grid convergence checks and comparison with previous experimental data, we More >

V. Kozulić¹, H. Gotovac¹, B. Gotovac¹

CMC-Computers, Materials & Continua, Vol.6, No.2, pp. 51-70, 2007, DOI:10.3970/cmc.2007.006.051

Abstract In this paper, we present a multi-resolution adaptive algorithm for solving problems described by partial differential equations. The technique is based on the collocation method using Fup basis functions, which belong to a class of Rvachev's infinitely differentiable finite functions. As it is possible to calculate derivation values of Fup basis functions of high degree in a precise yet simple way, so it is possible to efficiently apply strong formulation procedures. The mesh free method developed in this work is named Adaptive Fup Collocation Method (AFCM). The distribution of collocation points within the observed area… More >

A. P. S. Selvadurai¹, Wenjun Dong

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 41-54, 2006, DOI:10.3970/cmes.2006.012.041

Abstract A Fourier analysis conducted on both the spatial and the temporal discretizations of the governing partial differential equation shows that the Courant number as well as the time marching scheme have significant influences on the numerical behaviour of a Modified Least Squares (MLS) method for the solution of the advection equation. The variations of the amplification factor and the relative phase velocity with the Courant number and the dimensionless wave number indicate that when Courant number is equal to unity, the MLS method with the specified time-weighting and upwind function gives accurate results. This conclusion… More >

G.S. Palani¹, Nagesh R. Iyer¹, B. Dattaguru²

Structural Durability & Health Monitoring, Vol.1, No.2, pp. 107-120, 2005, DOI:10.3970/sdhm.2005.001.107

Abstract A posteriori error estimation and adaptive refinement technique for 2-D/3-D crack problems is the state-of-the-art. In this paper a new a posteriori error estimator based on strain energy release rate (SERR) or stress intensity factor (SIF) at the crack tip region has been proposed and used along with the stress based error estimator for reliable fracture analysis of 2-D crack problems. The proposed a posteriori error estimator is called the K-S error estimator. Further, h-adaptive mesh refinement strategy which can be used with K-S error estimator has been proposed for fracture analysis of 2-D crack problems. The performance More >

Armin Iske¹, Martin Käser²

CMES-Computer Modeling in Engineering & Sciences, Vol.7, No.2, pp. 133-148, 2005, DOI:10.3970/cmes.2005.007.133

Abstract Petroleum reservoir modelling requires effective multiscale methods for the numerical simulation of two-phase flow in porous media. This paper proposes the application of a novel meshfree particle method to the Buckley-Leverett model. The utilized meshfree advection scheme, called AMMoC, is essentially a method of characteristics, which combines an adaptive semi-Lagrangian method with local meshfree interpolation by polyharmonic splines. The method AMMoC is applied to the five-spot problem, a well-established model problem in petroleum reservoir simulation. The numerical results and subsequent numerical comparisons with two leading commercial reservoir simulators, ECLIPSE and FrontSim, show the good performance of More >

Edwin Jim ´enez¹, Mark Sussman², Mitsuhiro Ohta³

FDMP-Fluid Dynamics & Materials Processing, Vol.1, No.2, pp. 97-108, 2005, DOI:10.3970/fdmp.2005.001.097

Abstract The aim of this paper is to utilize a numerical model to compute bubble motion in quiescent Newtonian and viscoelastic liquids. For our numerical method, we use a coupled level set and volume-of-fluid method with a second order treatment for the jump conditions related to surface tension. We investigate axisymmetric gas-liquid systems with large density and viscosity ratios as well as buoyancy-driven flows with complex changes in topology. We present comparisons to previous computational results as well as experimental results. More >

P. Raghavan¹, S. Ghosh²

CMES-Computer Modeling in Engineering & Sciences, Vol.5, No.2, pp. 151-170, 2004, DOI:10.3970/cmes.2004.005.151

Abstract This paper presents an adaptive multi-level computational model that combines a conventional displacement based finite element model with a microstructural Voronoi cell finite element model for multi-scale analysis of composite structures with non-uniform microstructural heterogeneities as obtained from optical or scanning electron micrographs. Three levels of hierarchy, with different resolutions, are introduced in this model to overcome shortcomings posed by modeling and discretization errors. Among the three levels are: (a) level-0 of pure macroscopic analysis; (b) level-1 of macro-micro coupled modeling, used for signaling the switch over from macroscopic analyses to pure microscopic analyses; and More >

R. Gangadharan¹, A. Rajagopal¹, S.M. Sivakumar^{1, 2}

CMC-Computers, Materials & Continua, Vol.1, No.3, pp. 229-244, 2004, DOI:10.3970/cmc.2004.001.229

Abstract A new r-h adaptive scheme is proposed and formulated. It involves a combination of the configurational force based r-adaption with weighted Laplacian smoothing and mesh enrichment by h-refinement. A Zienkiewicz-Zhu best guess stress error estimator is used in the h-refinement strategy. The best sequence for combining the effectiveness of r- and h- adaption has been evolved at in this study. A further reduction in the potential energy and the relative error norm of the system is found to be achieved with combined r-adaption and mesh enrichment (in the form h-refinement). Numerical study confirms that the More >