Volume 26, Issue 4
A Hybrid Method with TENO Based Discontinuity Indicator for Hyperbolic Conservation Laws

Commun. Comput. Phys., 26 (2019), pp. 973-1007.

Published online: 2019-07

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• Abstract

With the observation that the TENO weighting strategy can explicitly distinguish smooth scales from nonsmooth scales in spectral space, in this paper, a new discontinuity indicator is proposed based on the high-order TENO paradigm [Fu et al., JCP 305(2016): 333-359]. 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. Since the time-consuming characteristic decomposition and smoothness-indicator computation of TENO are avoided in smooth regions, the overall computational efficiency can be improved significantly. Moreover, the cut-off wavenumber separating smooth and nonsmooth scales is determined by the parameter CT. In contrast to the thresholds of other discontinuity indicators, which are typically defined in physical space, CT takes effects in wavespace rendering its high generality. A set of benchmark cases with widespread length-scales is simulated to assess the performance of the proposed discontinuity indicator and the resulting hybrid shock-capturing scheme. Compared to the monotonicity-preserving discontinuity indicator and the TVB discontinuity indicator, the proposed algorithm delivers better performance with a fixed set of parameters for all considered benchmarks.

• Keywords

TENO, high order scheme, shock-capturing scheme, nonlinear scheme, finite volume method, finite difference method.

35L65, 65M06, 76J20, 76N15, 76F05

linfu@stanford.edu (Lin Fu)

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@Article{CiCP-26-973, author = {Fu , Lin }, title = {A Hybrid Method with TENO Based Discontinuity Indicator for Hyperbolic Conservation Laws}, journal = {Communications in Computational Physics}, year = {2019}, volume = {26}, number = {4}, pages = {973--1007}, abstract = {

With the observation that the TENO weighting strategy can explicitly distinguish smooth scales from nonsmooth scales in spectral space, in this paper, a new discontinuity indicator is proposed based on the high-order TENO paradigm [Fu et al., JCP 305(2016): 333-359]. 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. Since the time-consuming characteristic decomposition and smoothness-indicator computation of TENO are avoided in smooth regions, the overall computational efficiency can be improved significantly. Moreover, the cut-off wavenumber separating smooth and nonsmooth scales is determined by the parameter CT. In contrast to the thresholds of other discontinuity indicators, which are typically defined in physical space, CT takes effects in wavespace rendering its high generality. A set of benchmark cases with widespread length-scales is simulated to assess the performance of the proposed discontinuity indicator and the resulting hybrid shock-capturing scheme. Compared to the monotonicity-preserving discontinuity indicator and the TVB discontinuity indicator, the proposed algorithm delivers better performance with a fixed set of parameters for all considered benchmarks.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2018-0176}, url = {http://global-sci.org/intro/article_detail/cicp/13226.html} }
TY - JOUR T1 - A Hybrid Method with TENO Based Discontinuity Indicator for Hyperbolic Conservation Laws AU - Fu , Lin JO - Communications in Computational Physics VL - 4 SP - 973 EP - 1007 PY - 2019 DA - 2019/07 SN - 26 DO - http://doi.org/10.4208/cicp.OA-2018-0176 UR - https://global-sci.org/intro/article_detail/cicp/13226.html KW - TENO, high order scheme, shock-capturing scheme, nonlinear scheme, finite volume method, finite difference method. AB -

With the observation that the TENO weighting strategy can explicitly distinguish smooth scales from nonsmooth scales in spectral space, in this paper, a new discontinuity indicator is proposed based on the high-order TENO paradigm [Fu et al., JCP 305(2016): 333-359]. 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. Since the time-consuming characteristic decomposition and smoothness-indicator computation of TENO are avoided in smooth regions, the overall computational efficiency can be improved significantly. Moreover, the cut-off wavenumber separating smooth and nonsmooth scales is determined by the parameter CT. In contrast to the thresholds of other discontinuity indicators, which are typically defined in physical space, CT takes effects in wavespace rendering its high generality. A set of benchmark cases with widespread length-scales is simulated to assess the performance of the proposed discontinuity indicator and the resulting hybrid shock-capturing scheme. Compared to the monotonicity-preserving discontinuity indicator and the TVB discontinuity indicator, the proposed algorithm delivers better performance with a fixed set of parameters for all considered benchmarks.

Lin Fu. (2019). A Hybrid Method with TENO Based Discontinuity Indicator for Hyperbolic Conservation Laws. Communications in Computational Physics. 26 (4). 973-1007. doi:10.4208/cicp.OA-2018-0176
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