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Volume 4, Issue 2
Semi-Implicit Interior Penalty Discontinuous Galerkin Methods for Viscous Compressible Flows

Vít Dolejsí

Commun. Comput. Phys., 4 (2008), pp. 231-274.

Published online: 2008-04

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  • Abstract

We deal with the numerical solution of the Navier-Stokes equations describing a motion of viscous compressible fluids. In order to obtain a sufficiently stable higher order scheme with respect to the time and space coordinates, we develop a combination of the discontinuous Galerkin finite element (DGFE) method for the space discretization and the backward difference formulae (BDF) for the time discretization. Since the resulting discrete problem leads to a system of nonlinear algebraic equations at each time step, we employ suitable linearizations of inviscid as well as viscous fluxes which give a linear algebraic problem at each time step. Finally, the resulting BDF-DGFE scheme is applied to steady as well as unsteady flows and achieved results are compared with reference data.

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@Article{CiCP-4-231, author = {Vít Dolejsí}, title = {Semi-Implicit Interior Penalty Discontinuous Galerkin Methods for Viscous Compressible Flows}, journal = {Communications in Computational Physics}, year = {2008}, volume = {4}, number = {2}, pages = {231--274}, abstract = {

We deal with the numerical solution of the Navier-Stokes equations describing a motion of viscous compressible fluids. In order to obtain a sufficiently stable higher order scheme with respect to the time and space coordinates, we develop a combination of the discontinuous Galerkin finite element (DGFE) method for the space discretization and the backward difference formulae (BDF) for the time discretization. Since the resulting discrete problem leads to a system of nonlinear algebraic equations at each time step, we employ suitable linearizations of inviscid as well as viscous fluxes which give a linear algebraic problem at each time step. Finally, the resulting BDF-DGFE scheme is applied to steady as well as unsteady flows and achieved results are compared with reference data.

}, issn = {1991-7120}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cicp/7789.html} }
TY - JOUR T1 - Semi-Implicit Interior Penalty Discontinuous Galerkin Methods for Viscous Compressible Flows AU - Vít Dolejsí JO - Communications in Computational Physics VL - 2 SP - 231 EP - 274 PY - 2008 DA - 2008/04 SN - 4 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cicp/7789.html KW - AB -

We deal with the numerical solution of the Navier-Stokes equations describing a motion of viscous compressible fluids. In order to obtain a sufficiently stable higher order scheme with respect to the time and space coordinates, we develop a combination of the discontinuous Galerkin finite element (DGFE) method for the space discretization and the backward difference formulae (BDF) for the time discretization. Since the resulting discrete problem leads to a system of nonlinear algebraic equations at each time step, we employ suitable linearizations of inviscid as well as viscous fluxes which give a linear algebraic problem at each time step. Finally, the resulting BDF-DGFE scheme is applied to steady as well as unsteady flows and achieved results are compared with reference data.

Vít Dolejsí. (2008). Semi-Implicit Interior Penalty Discontinuous Galerkin Methods for Viscous Compressible Flows. Communications in Computational Physics. 4 (2). 231-274. doi:
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