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

Research output: Book/ReportReportProfessional

20 Downloads (Pure)

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.
Sudirham, J.J. ; Janivita Joto Sudirham, J.J.S. ; van Damme, Rudolf M.J. ; van der Vegt, Jacobus J.W. / Space-time discontinuous Galerkin method for wet-chemical etching of microstructures. Enschede : University of Twente, Department of Applied Mathematics, 2004. 16 p. (Memoranda; 1720).
@book{da09b4c088884a769cd0aa2751dda0b7,
title = "Space-time discontinuous Galerkin method for wet-chemical etching of microstructures",
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.",
keywords = "EWI-3540, METIS-218342, MSC-76R50, IR-65905, MSC-76R10, MSC-65M60, MSC-35R35",
author = "J.J. Sudirham and {Janivita Joto Sudirham}, J.J.S. and {van Damme}, {Rudolf M.J.} and {van der Vegt}, {Jacobus J.W.}",
note = "Imported from MEMORANDA",
year = "2004",
language = "Undefined",
isbn = "0169-2690",
series = "Memoranda",
publisher = "University of Twente, Department of Applied Mathematics",
number = "1720",

}

Sudirham, JJ, Janivita Joto Sudirham, JJS, van Damme, RMJ & van der Vegt, JJW 2004, Space-time discontinuous Galerkin method for wet-chemical etching of microstructures. Memoranda, no. 1720, University of Twente, Department of Applied Mathematics, Enschede.

Space-time discontinuous Galerkin method for wet-chemical etching of microstructures. / Sudirham, J.J.; Janivita Joto Sudirham, J.J.S.; van Damme, Rudolf M.J.; van der Vegt, Jacobus J.W.

Enschede : University of Twente, Department of Applied Mathematics, 2004. 16 p. (Memoranda; No. 1720).

Research output: Book/ReportReportProfessional

TY - BOOK

T1 - Space-time discontinuous Galerkin method for wet-chemical etching of microstructures

AU - Sudirham, J.J.

AU - Janivita Joto Sudirham, J.J.S.

AU - van Damme, Rudolf M.J.

AU - van der Vegt, Jacobus J.W.

N1 - Imported from MEMORANDA

PY - 2004

Y1 - 2004

N2 - 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.

AB - 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.

KW - EWI-3540

KW - METIS-218342

KW - MSC-76R50

KW - IR-65905

KW - MSC-76R10

KW - MSC-65M60

KW - MSC-35R35

M3 - Report

SN - 0169-2690

T3 - Memoranda

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

PB - University of Twente, Department of Applied Mathematics

CY - Enschede

ER -

Sudirham JJ, Janivita Joto Sudirham JJS, van Damme RMJ, van der Vegt JJW. Space-time discontinuous Galerkin method for wet-chemical etching of microstructures. Enschede: University of Twente, Department of Applied Mathematics, 2004. 16 p. (Memoranda; 1720).