Comparison of numerical schemes in large-eddy simulation of the temporal mixing layer

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Abstract

A posteriori tests of large-eddy simulations for the temporal mixing layer are performed using a variety of numerical methods in conjunction with the dynamic mixed subgrid model for the turbulent stress tensor. The results of the large-eddy simulations are compared with filtered direct numerical simulation (DNS) results. Five numerical methods are considered. The cell vertex scheme (A) is a weighted second-order central difference. The transverse weighting is shown to be necessary, since the standard second-order central difference (A) gives rise to instabilities. By analogy, a new weighted fourth-order central difference (B) is constructed in order to overcome the instability in simulations with the standard fourth-order central method (B). Furthermore, a spectral scheme (C) is tested. Simulations using these schemes have been performed for the case where the filter width equals the grid size (I) and the case where the filter width equals twice the grid size (II). The filtered DNS results are best approximated in case II for each of the numerical methods A, B and C. The deviations from the filtered DNS data are decomposed into modelling error effects and discretization error effects. In case I the absolute modelling error effects are smaller than in case II owing to the smaller filter width, whereas the discretization error effects are larger, since the flow field contains more small-scale contributions. In case I scheme A is preferred over scheme B, whereas in case II the situation is the reverse. In both cases the spectral scheme C provides the most accurate results but at the expense of a considerably increased computational cost. For the prediction of some quantities the discretization errors are observed to eliminate the modelling errors to some extent and give rise to reduced total errors.
LanguageUndefined
Pages297-312
Number of pages16
JournalInternational journal for numerical methods in fluids
Volume22
Issue number4
DOIs
StatePublished - 1996

Keywords

  • METIS-140923
  • numerical schemes
  • Large eddy simulation
  • IR-71292
  • mixing laye

Cite this

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title = "Comparison of numerical schemes in large-eddy simulation of the temporal mixing layer",
abstract = "A posteriori tests of large-eddy simulations for the temporal mixing layer are performed using a variety of numerical methods in conjunction with the dynamic mixed subgrid model for the turbulent stress tensor. The results of the large-eddy simulations are compared with filtered direct numerical simulation (DNS) results. Five numerical methods are considered. The cell vertex scheme (A) is a weighted second-order central difference. The transverse weighting is shown to be necessary, since the standard second-order central difference (A) gives rise to instabilities. By analogy, a new weighted fourth-order central difference (B) is constructed in order to overcome the instability in simulations with the standard fourth-order central method (B). Furthermore, a spectral scheme (C) is tested. Simulations using these schemes have been performed for the case where the filter width equals the grid size (I) and the case where the filter width equals twice the grid size (II). The filtered DNS results are best approximated in case II for each of the numerical methods A, B and C. The deviations from the filtered DNS data are decomposed into modelling error effects and discretization error effects. In case I the absolute modelling error effects are smaller than in case II owing to the smaller filter width, whereas the discretization error effects are larger, since the flow field contains more small-scale contributions. In case I scheme A is preferred over scheme B, whereas in case II the situation is the reverse. In both cases the spectral scheme C provides the most accurate results but at the expense of a considerably increased computational cost. For the prediction of some quantities the discretization errors are observed to eliminate the modelling errors to some extent and give rise to reduced total errors.",
keywords = "METIS-140923, numerical schemes, Large eddy simulation, IR-71292, mixing laye",
author = "A.W. Vreman and Geurts, {Bernardus J.} and Kuerten, {Johannes G.M.}",
year = "1996",
doi = "10.1002/(SICI)1097-0363(19960229)22:4<297::AID-FLD361>3.0.CO;2-X",
language = "Undefined",
volume = "22",
pages = "297--312",
journal = "International journal for numerical methods in fluids",
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TY - JOUR

T1 - Comparison of numerical schemes in large-eddy simulation of the temporal mixing layer

AU - Vreman,A.W.

AU - Geurts,Bernardus J.

AU - Kuerten,Johannes G.M.

PY - 1996

Y1 - 1996

N2 - A posteriori tests of large-eddy simulations for the temporal mixing layer are performed using a variety of numerical methods in conjunction with the dynamic mixed subgrid model for the turbulent stress tensor. The results of the large-eddy simulations are compared with filtered direct numerical simulation (DNS) results. Five numerical methods are considered. The cell vertex scheme (A) is a weighted second-order central difference. The transverse weighting is shown to be necessary, since the standard second-order central difference (A) gives rise to instabilities. By analogy, a new weighted fourth-order central difference (B) is constructed in order to overcome the instability in simulations with the standard fourth-order central method (B). Furthermore, a spectral scheme (C) is tested. Simulations using these schemes have been performed for the case where the filter width equals the grid size (I) and the case where the filter width equals twice the grid size (II). The filtered DNS results are best approximated in case II for each of the numerical methods A, B and C. The deviations from the filtered DNS data are decomposed into modelling error effects and discretization error effects. In case I the absolute modelling error effects are smaller than in case II owing to the smaller filter width, whereas the discretization error effects are larger, since the flow field contains more small-scale contributions. In case I scheme A is preferred over scheme B, whereas in case II the situation is the reverse. In both cases the spectral scheme C provides the most accurate results but at the expense of a considerably increased computational cost. For the prediction of some quantities the discretization errors are observed to eliminate the modelling errors to some extent and give rise to reduced total errors.

AB - A posteriori tests of large-eddy simulations for the temporal mixing layer are performed using a variety of numerical methods in conjunction with the dynamic mixed subgrid model for the turbulent stress tensor. The results of the large-eddy simulations are compared with filtered direct numerical simulation (DNS) results. Five numerical methods are considered. The cell vertex scheme (A) is a weighted second-order central difference. The transverse weighting is shown to be necessary, since the standard second-order central difference (A) gives rise to instabilities. By analogy, a new weighted fourth-order central difference (B) is constructed in order to overcome the instability in simulations with the standard fourth-order central method (B). Furthermore, a spectral scheme (C) is tested. Simulations using these schemes have been performed for the case where the filter width equals the grid size (I) and the case where the filter width equals twice the grid size (II). The filtered DNS results are best approximated in case II for each of the numerical methods A, B and C. The deviations from the filtered DNS data are decomposed into modelling error effects and discretization error effects. In case I the absolute modelling error effects are smaller than in case II owing to the smaller filter width, whereas the discretization error effects are larger, since the flow field contains more small-scale contributions. In case I scheme A is preferred over scheme B, whereas in case II the situation is the reverse. In both cases the spectral scheme C provides the most accurate results but at the expense of a considerably increased computational cost. For the prediction of some quantities the discretization errors are observed to eliminate the modelling errors to some extent and give rise to reduced total errors.

KW - METIS-140923

KW - numerical schemes

KW - Large eddy simulation

KW - IR-71292

KW - mixing laye

U2 - 10.1002/(SICI)1097-0363(19960229)22:4<297::AID-FLD361>3.0.CO;2-X

DO - 10.1002/(SICI)1097-0363(19960229)22:4<297::AID-FLD361>3.0.CO;2-X

M3 - Article

VL - 22

SP - 297

EP - 312

JO - International journal for numerical methods in fluids

T2 - International journal for numerical methods in fluids

JF - International journal for numerical methods in fluids

SN - 0271-2091

IS - 4

ER -