A Novel Explicit Filter for the Approximate Deconvolution in Large-Eddy Simulation on General Unstructured Grids: A posteriori tests on highly stretched grids

TL;DR

This paper introduces a new explicit filter for large-eddy simulation on unstructured grids, improving turbulence predictions especially on highly stretched grids by optimizing spectral properties and reducing errors.

Contribution

A novel explicit filter combining face-averaging and recursive filtering, optimized via multi-objective methods, enhances LES accuracy on unstructured, stretched grids.

Findings

Improved turbulent flow predictions on highly stretched grids.

Enhanced spectral attenuation near Nyquist wavenumber.

Successful application to 3D Taylor-Green vortex benchmark.

Abstract

Explicit filters play a pivotal role in the scale separation and numerical stability of advanced Large Eddy Simulation (LES) closures, such as dynamic eddy-viscosity or Approximate Deconvolution (AD) methods. In the present study, it is demonstrated that the performance of commonly used explicit filters applicable to general unstructured grids highly depends on the grid configuration, specifically the cell aspect ratio, which can result in poor filter spectral properties, ultimately leading to large errors and even solution divergence. This study introduces a novel, efficient explicit filter for general unstructured grids, addressing this shortcoming through a combination of a face-averaging technique and recursive filtering. The filter parameters are then determined through a constrained multi-objective optimization, ensuring desirable spectral properties, including high-wavenumber attenuation, filter-width precision, filter stability and positivity, and minimized dispersion and commutation errors. The AD-LES of turbulent channel flow benchmarks using the new filter demonstrate a noticeable improvement in turbulent flow predictions on highly stretched boundary-layer-type grids, particularly in reducing the log-layer mean velocity profile mismatch, compared to simulations using conventional filters. The analyses show that this enhancement is mainly attributed to the sufficient level of attenuation near the Nyquist wavenumber achieved by the new filter in all spatial directions across various grid configurations, among others. The new filter was also successfully tested on unstructured prism grids for the 3D Taylor-Green vortex benchmark.