dorsal/arxiv
View SchemaDynamic Model for LES Without Test Filtering: Quantifying the Accuracy of Taylor Series Approximations
| Authors | Stuart Chester, Fabrice Charlette, Charles Meneveau |
|---|---|
| Categories | |
| ArXiv ID | physics/0105100 |
| URL | https://arxiv.org/abs/physics/0105100 |
| DOI | 10.1007/PL00013289 |
Abstract
The dynamic model for large-eddy simulation (LES) of turbulent flows requires test filtering the resolved velocity fields in order to determine model coefficients. However, test filtering is costly to perform in large-eddy simulation of complex geometry flows, especially on unstructured grids. The objective of this work is to develop and test an approximate but less costly dynamic procedure which does not require test filtering. The proposed method is based on Taylor series expansions of the resolved velocity fields. Accuracy is governed by the derivative schemes used in the calculation and the number of terms considered in the approximation to the test filtering operator. The expansion is developed up to fourth order, and results are tested a priori based on direct numerical simulation data of forced isotropic turbulence in the context of the dynamic Smagorinsky model. The tests compare the dynamic Smagorinsky coefficient obtained from filtering with those obtained from application of the Taylor series expansion. They show that the expansion up to second order provides a reasonable approximation to the true dynamic coefficient (with errors on the order of about 5 % for c_s^2), but that including higher-order terms does not necessarily lead to improvements in the results due to inherent limitations in accurately evaluating high-order derivatives. A posteriori tests using the Taylor series approximation in LES of forced isotropic turbulence and channel flow confirm that the Taylor series approximation yields accurate results for the dynamic coefficient. Moreover, the simulations are stable and yield accurate resolved velocity statistics.
{
"annotation_id": "6ee1a346-7f99-4a5d-9b7a-af19fcb41581",
"date_created": "2026-03-02T18:00:36.156000Z",
"date_modified": "2026-03-02T18:00:36.156000Z",
"file_hash": "e374343eb31cea37e025a9e105ddcf514d2c48f19fe7a3bbcbf3b13b968da725",
"private": false,
"record": {
"abstract": "The dynamic model for large-eddy simulation (LES) of turbulent flows requires\ntest filtering the resolved velocity fields in order to determine model\ncoefficients. However, test filtering is costly to perform in large-eddy\nsimulation of complex geometry flows, especially on unstructured grids. The\nobjective of this work is to develop and test an approximate but less costly\ndynamic procedure which does not require test filtering. The proposed method is\nbased on Taylor series expansions of the resolved velocity fields. Accuracy is\ngoverned by the derivative schemes used in the calculation and the number of\nterms considered in the approximation to the test filtering operator. The\nexpansion is developed up to fourth order, and results are tested a priori\nbased on direct numerical simulation data of forced isotropic turbulence in the\ncontext of the dynamic Smagorinsky model. The tests compare the dynamic\nSmagorinsky coefficient obtained from filtering with those obtained from\napplication of the Taylor series expansion. They show that the expansion up to\nsecond order provides a reasonable approximation to the true dynamic\ncoefficient (with errors on the order of about 5 % for c_s^2), but that\nincluding higher-order terms does not necessarily lead to improvements in the\nresults due to inherent limitations in accurately evaluating high-order\nderivatives. A posteriori tests using the Taylor series approximation in LES of\nforced isotropic turbulence and channel flow confirm that the Taylor series\napproximation yields accurate results for the dynamic coefficient. Moreover,\nthe simulations are stable and yield accurate resolved velocity statistics.",
"arxiv_id": "physics/0105100",
"authors": [
"Stuart Chester",
"Fabrice Charlette",
"Charles Meneveau"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1007/PL00013289",
"title": "Dynamic Model for LES Without Test Filtering: Quantifying the Accuracy of Taylor Series Approximations",
"url": "https://arxiv.org/abs/physics/0105100"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "6eaa7b73-05ae-4fdc-835d-2ce6c90179d2",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}