High order shock-capturing TENO (targeted ENO) schemes

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Recently, I propose low-dissipation finite-volume method based on a new TENO shock-capturing scheme:

https://www.sciencedirect.com/sc ... i/S0010465518303576

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The five-point and six-point TENO schemes are further improved to the performance limit of optimal linear schemes

https://www.researchgate.net/pub ... daptive_dissipation

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I propose "A hybrid method with TENO based discontinuity indicator for hyperbolic conservation laws" :

https://www.researchgate.net/pub ... c_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.

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One review about High-order TENO Schemes for Hyperbolic Conservation Laws can be found in

https://www.researchgate.net/pub ... c_Conservation_Laws

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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/sc ... i/S0045793018308399

e.g.

TENO scheme

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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/pub ... ive_Mesh_Refinement

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The Mach number 2000 jets computed by the latest high-order shock-capturing TENO schemes:

https://www.researchgate.net/pub ... mics_and_turbulence

https://www.sciencedirect.com/sc ... i/S0010465519302000

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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

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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

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A new hypersonic flow solver from Center for Turbulence Research at Stanford University is published. The solver is based on the sixth-order low-dissipation TENO6-A scheme for shock-capturing and the code is open-source:

https://www.researchgate.net/pub ... _aerothermodynamics

https://www.sciencedirect.com/sc ... i/S0010465520300837

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Thanks to the work of Arash Hamzehloo and his team, the TENO schemes are demonstrated to perform significantly better than WENO for compressible wall-bounded turbulence:

https://onlinelibrary.wiley.com/doi/abs/10.1002/fld.4879

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Glad to give an invited seminar talk on the high-order TENO schemes for general hyperbolic conservation laws and turbulent flows

High-order TENO schemes for general hyperbolic conservation laws and turbulent flows

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周华 发表于 2020-7-1 13:21
讲的很好，很受启发

感谢 周老师 的支持！

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Open-source codes based on the high-order TENO schemes for complex fluids:

OpenSBLI solver

Based on TENO5, TENO6 and TENO8

A framework for the automated derivation and parallel execution of finite difference solvers on a range of computer architectures.

Lusher, David J., Satya P. Jammy, and Neil D. Sandham. “OpenSBLI: Automated code-generation for heterogeneous computing architectures applied to compressible fluid dynamics on structured grids.” arXiv preprint arXiv:2007.14933 (2020).

Code repository, https://github.com/LMNS3d/opensbli

HTR solver

Based on TENO6-A

An open-source exascale-oriented task-based multi-GPU high-order code for hypersonic aerothermodynamics

Renzo, Mario Di; Fu, Lin; Urzay, Javier; “HTR solver: An open-source exascale-oriented task-based multi-GPU high-order code for hypersonic aerothermodynamics,” Computer Physics Communications, (2020): 107262.

TENO scheme and HTR solver have supported the DOE PSAAP 3 (Predictive Science Academic Alliance Program) project at Stanford University, link for psaap 3 at stanford.

Code repository, https://data.mendeley.com/datasets/9zsxjtzfr7/1

ALPACA solver

Based on TENO5

A MPI-parallelized C++ code framework to simulate compressible multiphase flow physics

Hoppe, Nils; Adami, Stefan; Adams, Nikolaus A. ; “A modular massively parallel computing environment for three-dimensional multiresolution simulations of compressible flows,” arXiv:2012.04385, (2020).

Code repository, https://gitlab.lrz.de/nanoshock/ALPACA

MPI-AMRVAC solver

Based on TENO5-A

MPI-AMRVAC: A Parallel Adaptive Mesh Refinement Framework

van der Holst, Bar, et al. “MPI-AMRVAC: MPI-adaptive mesh refinement-versatile advection code,” Astrophysics Source Code Library (2012): ascl-1208.

Code repository, https://github.com/amrvac/amrvac

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We are moving towards the next generation high-order low-dissipation TENO schemes for solving nonlinear PDEs, see our latest paper on Journal of Computational Physics:

A novel high-order low-dissipation TENO-THINC scheme for hyperbolic conservation laws

https://www.researchgate.net/pub ... c_conservation_laws

https://www.sciencedirect.com/sc ... 21007944?via%3Dihub