Space-time discontinuous Galerkin method for wet-chemical etching of microstructures

J.J. Sudirham, J.J.S. Janivita Joto Sudirham, Rudolf M.J. van Damme, Jacobus J.W. van der Vegt

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    Abstract

    In this paper we discuss the application of a space-time discontinuous Galerkin finite element method for convection-diffusion problems to the simulation of wet-chemical etching of microstructures. In the space-time DG method no distinction is made in the discretization between the space and time variables and discontinuous basis functions are used both in space and time. This approach results in an efficient numerical technique to deal with time-dependent flow domains as occur in wet-chemical etching, while maintaining a fully conservative discretization. The method offers great flexibility in mesh adaptation and special attention is given to the generation of an initial solution and mesh when there is no etching cavity yet. Numerical simulations of the etching of a two-dimensional slit are discussed for different regimes, namely diffusion-controlled and convection-dominated etching. These results show good agreement with analytical results in the diffusion-controlled regime. Using a simple model for the fluid velocity the typical asymmetric etching cavities are obtained in the convection dominated regime and the results agree qualitatively well with those obtained from full Navier-Stokes simulations.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Number of pages16
    ISBN (Print)0169-2690
    Publication statusPublished - 2004

    Publication series

    NameMemoranda
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1720
    ISSN (Print)0169-2690

    Keywords

    • EWI-3540
    • METIS-218342
    • MSC-76R50
    • IR-65905
    • MSC-76R10
    • MSC-65M60
    • MSC-35R35

    Cite this

    Sudirham, J. J., Janivita Joto Sudirham, J. J. S., van Damme, R. M. J., & van der Vegt, J. J. W. (2004). Space-time discontinuous Galerkin method for wet-chemical etching of microstructures. (Memoranda; No. 1720). Enschede: University of Twente, Department of Applied Mathematics.