A High Resolution Differential Filter for Large Eddy Simulation on Unstructured Grids for High-Order Methods

The applicability of a high resolution low-pass differential spatial filter for unstructured grids was investigated for typical high-order one-dimensional Finite Element methods. The goal was to investigate the accuracy and stability of the filter when applied on high-order elements. The one-dimensional differential filter was discretized based on Lagrange and Hierarchical Legendre base functions. Manufactured solutions were used to demonstrate the performance of the filter on two one-dimensional test cases for elements of order up to six. The results suggest that the proposed filter is effective for explicit filtering in Large Eddy Simulations using high-order methods.