A High-Order Unifying Discontinuous Formulation for the Navier-Stokes Equations on 3D Mixed Grids

T. Haga; H. Gao; Z. J. Wang

Mathematical Modelling of Natural Phenomena (2011)

  • Volume: 6, Issue: 3, page 28-56
  • ISSN: 0973-5348

Abstract

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The newly developed unifying discontinuous formulation named the correction procedure via reconstruction (CPR) for conservation laws is extended to solve the Navier-Stokes equations for 3D mixed grids. In the current development, tetrahedrons and triangular prisms are considered. The CPR method can unify several popular high order methods including the discontinuous Galerkin and the spectral volume methods into a more efficient differential form. By selecting the solution points to coincide with the flux points, solution reconstruction can be completely avoided. Accuracy studies confirmed that the optimal order of accuracy can be achieved with the method. Several benchmark test cases are computed by solving the Euler and compressible Navier-Stokes equations to demonstrate its performance.

How to cite

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Haga, T., Gao, H., and Wang, Z. J.. "A High-Order Unifying Discontinuous Formulation for the Navier-Stokes Equations on 3D Mixed Grids." Mathematical Modelling of Natural Phenomena 6.3 (2011): 28-56. <http://eudml.org/doc/222205>.

@article{Haga2011,
abstract = {The newly developed unifying discontinuous formulation named the correction procedure via reconstruction (CPR) for conservation laws is extended to solve the Navier-Stokes equations for 3D mixed grids. In the current development, tetrahedrons and triangular prisms are considered. The CPR method can unify several popular high order methods including the discontinuous Galerkin and the spectral volume methods into a more efficient differential form. By selecting the solution points to coincide with the flux points, solution reconstruction can be completely avoided. Accuracy studies confirmed that the optimal order of accuracy can be achieved with the method. Several benchmark test cases are computed by solving the Euler and compressible Navier-Stokes equations to demonstrate its performance. },
author = {Haga, T., Gao, H., Wang, Z. J.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {high-order; mixed unstructured grids; Navier-Stokes equations; discontinuous Galerkin; spectral collocation; finite difference; finite difference method; tetrahedrons; triangular prisms},
language = {eng},
month = {5},
number = {3},
pages = {28-56},
publisher = {EDP Sciences},
title = {A High-Order Unifying Discontinuous Formulation for the Navier-Stokes Equations on 3D Mixed Grids},
url = {http://eudml.org/doc/222205},
volume = {6},
year = {2011},
}

TY - JOUR
AU - Haga, T.
AU - Gao, H.
AU - Wang, Z. J.
TI - A High-Order Unifying Discontinuous Formulation for the Navier-Stokes Equations on 3D Mixed Grids
JO - Mathematical Modelling of Natural Phenomena
DA - 2011/5//
PB - EDP Sciences
VL - 6
IS - 3
SP - 28
EP - 56
AB - The newly developed unifying discontinuous formulation named the correction procedure via reconstruction (CPR) for conservation laws is extended to solve the Navier-Stokes equations for 3D mixed grids. In the current development, tetrahedrons and triangular prisms are considered. The CPR method can unify several popular high order methods including the discontinuous Galerkin and the spectral volume methods into a more efficient differential form. By selecting the solution points to coincide with the flux points, solution reconstruction can be completely avoided. Accuracy studies confirmed that the optimal order of accuracy can be achieved with the method. Several benchmark test cases are computed by solving the Euler and compressible Navier-Stokes equations to demonstrate its performance.
LA - eng
KW - high-order; mixed unstructured grids; Navier-Stokes equations; discontinuous Galerkin; spectral collocation; finite difference; finite difference method; tetrahedrons; triangular prisms
UR - http://eudml.org/doc/222205
ER -

References

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