article · International Journal of Numerical Methods for Heat &amp Fluid Flow · 1997

Parallel adaptive finite element analysis of viscous flows based on a combined compressible‐incompressible formulation

Dan Givoli, Joseph E. Flaherty, Mark S. Shephard

Cited by 5Abstract and details only

Abstract

Describes a new finite element scheme for the large‐scale analysis of compressible and incompressible viscous flows. The scheme is based on a combined compressible‐ incompressible Galerkin least‐squares (GLS) space‐time variational formulation. Three‐ dimensional unstructured meshes are employed, with piecewise‐constant temporal interpolation, local time‐stepping for steady flows, and linear continuous spatial interpolation in all the variables. The scheme incorporates automatic adaptive mesh refinement, with a choice of various error indicators. It is implemented on a distributed‐memory parallel computer, and includes an automatic load‐balancing procedure. Demonstrates the ability to solve both compressible and incompressible viscous flow problems using the parallel adaptive framework via numerical examples. These include Mach 3 flow over a flat plate, and a divergence‐free buoyancy‐driven flow in a cavity. The latter is a model for the steady melt flow in a Czochralski crystal growth process.

Cite this paper

APA 7

Givoli, D., Flaherty, J. E., & Shephard, M. S. (1997). Parallel adaptive finite element analysis of viscous flows based on a combined compressible‐incompressible formulation. International Journal of Numerical Methods for Heat &amp Fluid Flow, 7(8), 880–906. https://doi.org/10.1108/09615539710193056

MLA 9

Givoli, Dan, et al. “Parallel adaptive finite element analysis of viscous flows based on a combined compressible‐incompressible formulation.” International Journal of Numerical Methods for Heat &amp Fluid Flow, vol. 7, no. 8, 1997, pp. 880–906, https://doi.org/10.1108/09615539710193056.

Chicago

Givoli, Dan, Joseph E. Flaherty, and Mark S. Shephard. 1997. “Parallel adaptive finite element analysis of viscous flows based on a combined compressible‐incompressible formulation.” International Journal of Numerical Methods for Heat &amp Fluid Flow 7 (8): 880–906. https://doi.org/10.1108/09615539710193056.

Harvard

Givoli, D., Flaherty, J.E. and Shephard, M.S. (1997) ‘Parallel adaptive finite element analysis of viscous flows based on a combined compressible‐incompressible formulation’, International Journal of Numerical Methods for Heat &amp Fluid Flow, 7(8), pp. 880–906. Available at: https://doi.org/10.1108/09615539710193056.

BibTeX

@article{givoli1997parallel,
  title = {{Parallel adaptive finite element analysis of viscous flows based on a combined compressible‐incompressible formulation}},
  author = {Givoli, Dan and Flaherty, Joseph E. and Shephard, Mark S.},
  journal = {International Journal of Numerical Methods for Heat &amp Fluid Flow},
  volume = {7},
  number = {8},
  pages = {880--906},
  year = {1997},
  doi = {10.1108/09615539710193056}
}

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