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  • Open Access


    Variable Viscosity and Density Biofilm Simulations using an Immersed Boundary Method, Part I: Numerical Scheme and Convergence Results

    Jason F. Hammond1, Elizabeth J. Stewart2, John G. Younger3, Michael J.Solomon2, David M. Bortz4,5

    CMES-Computer Modeling in Engineering & Sciences, Vol.98, No.3, pp. 295-340, 2014, DOI:10.32604/cmes.2014.098.295

    Abstract The overall goal of this work is to develop a numerical simulation which correctly describes a bacterial biofilm fluid-structure interaction and separation process. In this, the first of a two-part effort, we fully develop a convergent scheme and provide numerical evidence for the method order as well as a full 3D separation simulation. We use an immersed boundary-based method (IBM) to model and simulate a biofilm with density and viscosity values different from than that of the surrounding fluid. The simulation also includes breakable springs connecting the bacteria in the biofilm which allows the inclusion of erosion and detachment into… More >

  • Open Access


    Algebraic Multigrid Methods Based on Generic Approximate Banded Inverse Matrix Techniques

    George A. Gravvanis1, Christos K. Filelis-Papadopoulos1, Paschalis I.Matskanidis1

    CMES-Computer Modeling in Engineering & Sciences, Vol.100, No.4, pp. 323-345, 2014, DOI:10.3970/cmes.2014.100.323

    Abstract Since the introduction of the Algebraic MultiGrid algorithm (AMG) over twenty years ago, significant progress has been made in improving the coarsening and the convergence behavior of the method. In this paper, an AMG method is introduced that utilizes a new generic approximate inverse algorithm as a smoother in conjunction with common coarsening techniques, such as classical Ruge-Stüben coarsening, CLJP and PMIS coarsening. The proposed approximate inverse scheme, namely Generic Approximate Banded Inverse (GenAbI), is a banded approximate inverse based on Incomplete LU factorization with zero fill–in (ILU(0)). The new class of Generic Approximate Banded Inverse can be computed for… More >

  • Open Access


    On the Multigrid Method Based on Finite Difference Approximate Inverses

    Christos K. Filelis-Papadopoulos1, George A. Gravvanis1

    CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.3, pp. 233-253, 2013, DOI:10.3970/cmes.2013.090.232

    Abstract During the last decades, multigrid methods have been extensively used in order to solve large scale linear systems derived from the discretization of partial differential equations using the finite difference method. Approximate Inverses in conjunction with Richardon’s iterative method could be used as smoothers in the multigrid method. Thus, a new class of smoothers based on approximate inverses could be derived. Effectiveness of explicit approximate inverses relies in the fact that they are close approximants to the inverse of the coefficient matrix and are fast to compute in parallel. Furthermore, the class of finite difference approximate inverses proposed in conjunction… More >

  • Open Access


    Thin Film Flow Over and Around Surface Topography: a General Solver for the Long-Wave Approximation and Related Equations

    P.H. Gaskell1, Y.C. Lee2, H.M. Thompson1

    CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.1, pp. 77-112, 2010, DOI:10.3970/cmes.2010.062.077

    Abstract The three-dimensional flow of a gravity-driven continuous thin liquid film on substrates containing micro-scale features is modelled using the long-wave lubrication approximation, encompassing cases when surface topography is either engulfed by the film or extends all the way though it. The discrete analogue of the time-dependent governing equations is solved accurately using a purpose designed multigrid strategy incorporating both automatic error-controlled adaptive time stepping and local mesh refinement/de-refinement. Central to the overall approach is a Newton globally convergent algorithm which greatly simplifies the inclusion of further physics via the solution of additional equations of the same form as the base… More >

  • Open Access


    Multigrid Implementation of Cellular Automata for Topology Optimization of Continuum Structures

    R. Zakhama1,2,3, M.M. Abdalla2, H. Smaoui1,3, Z. Gürdal2

    CMES-Computer Modeling in Engineering & Sciences, Vol.51, No.1, pp. 1-26, 2009, DOI:10.3970/cmes.2009.051.001

    Abstract A multigrid accelerated cellular automata algorithm for two and three dimensional continuum topology optimization problems is presented. The topology optimization problem is regularized using the traditional SIMP approach. The analysis rules are derived from the principle of minimum total potential energy, and the design rules are derived based on continuous optimality criteria interpreted as local Kuhn-Tucker conditions. Three versions of the algorithm are implemented; a cellular automata based design algorithm, a baseline multigrid algorithm for analysis acceleration and a full multigrid integrated analysis and design algorithm. It is shown that the multigrid accelerated cellular automata scheme is a powerful tool… More >

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