coolboy 发表于 2018-9-28 22:11
Thanks for sharing the information.
What is your opinion on the scheme by Colella and Woodward (Pie ...
Well. Piecewise Parabolic Method has been popular for many long time, particular for astrophysical simulations.
However, this type of schemes may still need some sort of adhoc operator for dicontinuity capturing,
e.g. see Eq.(3.2) in
https://cloudfront.escholarship.org/dist/prd/content/qt5sr307f1/qt5sr307f1.pdf
As far as I know, the ENO family scheme may be the state-of-the-art in terms of high-order accuracy, and sharp shock-capturing capability. The main drawback of previous version , e.g. WENO, is that they are typically very dissipative either.
This problem is greatly fixed by the concept of TENO.
Thanks a lot.
Recently, I propose low-dissipation finite-volume method based on a new TENO shock-capturing scheme:
https://www.sciencedirect.com/science/article/pii/S0010465518303576
The five-point and six-point TENO schemes are further improved to the performance limit of optimal linear schemes
https://www.researchgate.net/publication/328749415_Improved_five-point_and_six-point_TENO_schemes_for_hyperbolic_conservation_laws_with_adaptive_dissipation
I propose "A hybrid method with TENO based discontinuity indicator for hyperbolic conservation laws" :
https://www.researchgate.net/publication/329829078_A_hybrid_method_with_TENO_based_discontinuity_indicator_for_hyperbolic_conservation_laws
which reduces the computational costs of TENO scheme significantly.
1. With the observation that the TENO weighting strategy can explicitly distinguish smooth scales from nonsmooth scales in spectral space, in this paper, a new troubled-cell indicator is proposed based on the high-order TENO paradigm.
2. The cut-off wavenumber separating smooth and nonsmooth scales is determined by the parameter C_T. In contrast to the thresholds of other troubled-cell indicators, which are typically defined in physical space, C_T takes effects in wavespace rendering its high generality.
3. The local flow structures are classified as smooth or nonsmooth scales, and the hybrid numerical discretization scheme is applied correspondingly, i.e. the high-order upwind linear scheme without characteristic decomposition is employed for resolving smooth scales while the nonlinear low-dissipation TENO scheme is adopted to capture discontinuities.
4. A set of benchmark cases with widespread length-scales is simulated to assess the performance of the proposed troubled-cell indicator and the resulting hybrid shockcapturing scheme.
5. The parameter is not tuning for all simulations.
One review about High-order TENO Schemes for Hyperbolic Conservation Laws can be found in
https://www.researchgate.net/publication/331431219_Reviewing_of_High-order_TENO_Schemes_for_Hyperbolic_Conservation_Laws
不错，学习一下
Thanks to the work of Nico Fleischmann, the low-dissipation property of TENO schemes is demonstrated with extreme resolution simulations and the symmetry breaking issue has been addressed:
https://www.sciencedirect.com/science/article/abs/pii/S0045793018308399
e.g.
The low dissipation TENO6 scheme for Rotor Wake simulations
Thanks to the work of Constantin Oehrle, the low-dissipation TENO6 scheme has been implemented in the DLR block structured finite-volume Reynolds-averaged Navier-Stokes (RANS) CFD code FLOWer. The performance is impressive (in their paper called WENO6 scheme):
https://www.researchgate.net/publication/333420703_Higher-order_Simulations_of_a_Compound_Helicopter_using_Adaptive_Mesh_Refinement
:D
:D
学习学习
The Mach number 2000 jets computed by the latest high-order shock-capturing TENO schemes:
https://www.researchgate.net/publication/333787111_A_very-high-order_TENO_scheme_for_all-speed_gas_dynamics_and_turbulence
https://www.sciencedirect.com/science/article/pii/S0010465519302000
I am happy that the high-order TENO shocking-capturing schemes have appeared in a well-known CFD book:
Computational Methods for Fluid Dynamics
https://www.springer.com/gp/book/9783319996912
Open-source code OpenSBLI with TENO5, TENO6 and TENO8 scheme
Thanks to the work of Satya P. Jammy and David J. Lusher, the TENO5, TENO6 and TENO8 scheme have been implemented in the open-source code OpenSBLI , you are free to download and use
https://github.com/LMNS3d/opensbli