Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence
Abstract
:1. Introduction
- How does a central scheme augmented with a relaxation filter compare with the performance of the conventional upwind-biased approach to numerical dissipation in ILES?
- What reduction in computational expense can we expect through the utilization of this new explicit filtering framework?
- Can we quantify the effect of the free modeling parameters that accompany low-pass spatial filters on the statistical and instantaneous features of our solution field?
- What parameters dominate the dissipative nature of a WENO-ILES scheme for our test cases?
2. Governing Equations
3. Numerical Methods
3.1. Finite Volume Framework
3.2. Upwind-Biased ILES Schemes
3.2.1. WENO Reconstructions
3.2.2. Riemann Solvers
3.2.3. Rusanov Scheme
3.2.4. Roe Scheme
3.2.5. HLL Scheme
3.2.6. AUSM Scheme
3.3. Central Reconstruction Schemes
3.3.1. Relaxation Filtering
3.3.2. Shock Filtering
4. Results
4.1. Problem Definitions
4.2. MPI Methodology
4.3. Dual Shear Layer (DSL) Problem
4.4. Riemann Shock Interaction (RSI) Problem
5. Conclusions
- It can be stated with a certain degree of confidence that the central schemes implemented with relaxation filters perform in a comparable manner to the WENO-Riemann solver combinations tested here and that the standard and modified relaxation filters represent a viable alternative to the ILES framework for the test cases investigated here. Not only are they seen to capture small scale features and their nonlinear interactions accurately, they also appear to perform well when it comes to capturing shocks. However, WENO based ILES schemes are attractive, because they do not require any ad-hoc tuning or filtering parameters.
- We note a significant reduction in computational complexity due to the relative simplicity of the numerical algorithm for the relaxation filtering framework. In addition, the computational expense of this framework is seen to be much lower in comparison to the different WENO based ILES solvers. We find that the relaxation filtering (or explicit filtering) approach is approximately four times faster than the WENO reconstruction based ILES approaches.
- The free modeling parameters associated with the proposed numerical framework perform as expected with a changing transfer function shape corresponding to a modification of the dissipative behavior of the numerical method. This also allows us to actively control the dissipation in the numerical method through model free parameters and for the standard and shock relaxation filtering approach respectively.
- We have performed a thorough investigation of the WENO-Riemann solver based ILES schemes where it is verified that the AUSM Riemann solver is the least dissipative whereas the Rusanov solver is the most. The flux reconstruction scheme does have an effect on the dissipative behavior of the ILES methodology when it comes to the expressions for the calculation of the smoothness indicators (i.e., WENO-JS and WENO-Z), but for the dissipative Riemann solvers (Rusanov and HLL) only. The WENO-JS scheme is seen to be more dissipative than the WENO-Z scheme for these two solvers and more or less identical for the less dissipative AUSM and Roe solvers. It is seen that p does not have a major effect on the dissipative effect of the scheme for this investigation. However, less dissipative results are obtained for lower p values.
Acknowledgments
Author Contributions
Conflicts of Interest
References
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CPU Time (in Hours) | |||
---|---|---|---|
Solver | |||
Rusanov | 4.05 × 10 | 2.02 × 10 | 0.90 |
Roe | 5.29 × 10 | 6.14 × 10 | 1.39 |
HLL | 6.75 × 10 | 5.57 × 10 | 1.02 |
AUSM | 3.68 × 10 | 7.79 × 10 | 1.15 |
Relaxation filtering (standard) | 1.73 × 10 | 2.18 × 10 | 0.32 |
Relaxation filtering (modified) | 2.21 × 10 | 2.88 × 10 | 0.38 |
Shock filtering | 2.28 × 10 | 1.86 × 10 | 0.35 |
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Maulik, R.; San, O. Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence. Fluids 2017, 2, 14. https://doi.org/10.3390/fluids2020014
Maulik R, San O. Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence. Fluids. 2017; 2(2):14. https://doi.org/10.3390/fluids2020014
Chicago/Turabian StyleMaulik, Romit, and Omer San. 2017. "Resolution and Energy Dissipation Characteristics of Implicit LES and Explicit Filtering Models for Compressible Turbulence" Fluids 2, no. 2: 14. https://doi.org/10.3390/fluids2020014