Simple and robust h-adaptive shock-capturing method for flux reconstruction framework

Chinese Journal of Aeronautics - Tập 36 - Trang 348-365 - 2023
Lintao HUANG1, Zhenhua JIANG1, Shuai LOU2, Xin ZHANG1, Chao YAN1
1School of Aeronautic Science and Engineering, Beihang University, Beijing, 100191, China
2Research Office No.12, Beijing Institute of Astronautical Systems Engineering, Beijing 100076, China

Tài liệu tham khảo

Chen, 2021, A low-diffusion robust flux splitting scheme towards wide-ranging Mach number flows, Chin J Aeronaut, 34, 628, 10.1016/j.cja.2020.12.010 Qu, 2021, A hybrid multidimensional Riemann solver to couple self-similar method with MULTV method for complex flows, Chin J Aeronaut, 34, 29, 10.1016/j.cja.2020.11.003 Wang, 2022, Revisiting the space-time gradient method: A time-clocking perspective, high order difference time discretization and comparison with the harmonic balance method, Chin J Aeronaut, 35, 45, 10.1016/j.cja.2022.05.016 Zheng, 2022, Numerical simulation method of surge experiments on gas turbine engines, Chin J Aeronaut, 36, 107, 10.1016/j.cja.2022.08.007 Qiao, 2022, Far-field sonic boom prediction considering atmospheric turbulence effects: An improved approach, Chin J Aeronaut, 35, 208, 10.1016/j.cja.2022.01.013 Deng, 2020, Constructing higher order discontinuity-capturing schemes with upwind-biased interpolations and boundary variation diminishing algorithm, Comput Fluids, 200, 10.1016/j.compfluid.2020.104433 Lou, 2020, Effective high-order energy stable flux reconstruction methods for first-order hyperbolic linear and nonlinear systems, J Comput Phys, 414, 10.1016/j.jcp.2020.109475 Lu, 2021, Direct numerical simulation of roughness-induced transition controlled by two-dimensional wall blowing, J Fluid Mech, 920, A28, 10.1017/jfm.2021.448 Zhou, 2021, Direct numerical simulation of control of oblique breakdown in a supersonic boundary layer using a local cooling strip, Phys Fluids, 33, 10.1063/5.0059402 Wu, 2021, Very high order WENO schemes using efficient smoothness indicators, J Comput Phys, 432, 10.1016/j.jcp.2021.110158 Han, 2022, A novel high-order scheme for numerical simulation of wake flow over helicopter rotors in hover, Chin J Aeronaut, 35, 260, 10.1016/j.cja.2021.07.032 Wang, 2013, High-order CFD methods: current status and perspective, Int J Numer Methods Fluids, 72, 811, 10.1002/fld.3767 Zhang, 2017, On positivity-preserving high order discontinuous Galerkin schemes for compressible Navier-Stokes equations, J Comput Phys, 328, 301, 10.1016/j.jcp.2016.10.002 Huynh, 2007, A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods Hesthaven, 2007 Kopriva, 1996, A conservative staggered-grid Chebyshev multidomain method for compressible flows, J Comput Phys, 125, 244, 10.1006/jcph.1996.0091 Kopriva, 1996, A conservative staggered-grid Chebyshev multidomain method for compressible flows. II. A semi-structured method, J Comput Phys, 128, 475, 10.1006/jcph.1996.0225 Liang, 2013, A comparison of computational efficiencies of spectral difference method and correction procedure via reconstruction, J Comput Phys, 239, 138, 10.1016/j.jcp.2013.01.001 Wang, 2009, A unifying lifting collocation penalty formulation including the discontinuous Galerkin, spectral volume/difference methods for conservation laws on mixed grids, J Comput Phys, 228, 8161, 10.1016/j.jcp.2009.07.036 Leicht, 2011, 67 Yang, 2016, A high-order flux reconstruction method with adaptive mesh refinement and artificial diffusivity on unstructured moving/deforming mesh for shock capturing, Comput Fluids, 139, 17, 10.1016/j.compfluid.2016.03.025 Zhang, 2017, A high-order flux reconstruction/correction procedure via reconstruction method for shock capturing with space-time extension time stepping and adaptive mesh refinement Estivalezes, 1996, High-order positivity-preserving kinetic schemes for the compressible Euler equations, SIAM J Numer Anal, 33, 2050, 10.1137/S0036142994271009 Balsara, 2012, Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics, J Comput Phys, 231, 7504, 10.1016/j.jcp.2012.01.032 Hu, 2013, Positivity-preserving method for high-order conservative schemes solving compressible Euler equations, J Comput Phys, 242, 169, 10.1016/j.jcp.2013.01.024 Guo, 2015, Positivity preserving high-order local discontinuous Galerkin method for parabolic equations with blow-up solutions, J Comput Phys, 289, 181, 10.1016/j.jcp.2015.02.041 Vilar, 2016, Positivity-preserving cell-centered Lagrangian schemes for multi-material compressible flows: from first-order to high-orders. part I: The one-dimensional case, J Comput Phys, 312, 385, 10.1016/j.jcp.2016.02.027 Xiong, 2016, Parametrized positivity preserving flux limiters for the high order finite difference WENO scheme solving compressible Euler equations, J Sci Comput, 67, 1066, 10.1007/s10915-015-0118-0 Jiang ZH, Deng X, Yan C, et al. Positivity-preserving hybrid DG/FV method with subcell resolution for compressible Euler equations with stiff source terms. arXiv preprint: 2007.05867, 2020. Zhang, 2010, On maximum-principle-satisfying high order schemes for scalar conservation laws, J Comput Phys, 229, 3091, 10.1016/j.jcp.2009.12.030 Srinivasan, 2018, A positivity-preserving high order discontinuous Galerkin scheme for convection–diffusion equations, J Comput Phys, 366, 120, 10.1016/j.jcp.2018.04.002 Zhang, 2010, On positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations on rectangular meshes, J Comput Phys, 229, 8918, 10.1016/j.jcp.2010.08.016 Zhang, 2012, Maximum-principle-satisfying and positivity-preserving high order discontinuous Galerkin schemes for conservation laws on triangular meshes, J Sci Comput, 50, 29, 10.1007/s10915-011-9472-8 Kawai, 2008, Localized artificial diffusivity scheme for discontinuity capturing on curvilinear meshes, J Comput Phys, 227, 9498, 10.1016/j.jcp.2008.06.034 Miyaji, 2011, On the compressible flow simulations with shocks by a flux reconstruction approach Premasuthan, 2014, Computation of flows with shocks using the spectral difference method with artificial viscosity, I: Basic formulation and application, Comput Fluids, 98, 111, 10.1016/j.compfluid.2013.12.013 Haga, 2019, On a robust and accurate localized artificial diffusivity scheme for the high-order flux-reconstruction method, J Comput Phys, 376, 534, 10.1016/j.jcp.2018.09.052 Toro, 2013 Vincent, 2011, A new class of high-order energy stable flux reconstruction schemes, J Sci Comput, 47, 50, 10.1007/s10915-010-9420-z Bank, 1983, The efficient implementation of local mesh refinement algorithms, Adaptive computational methods for partial differential equations, 1, 74 Stout QF, De Zeeuw DL, Gombosi TI, et al. Adaptive blocks: A high performance data structure. Proceedings of the 1997 ACM/IEEE conference on supercomputing. 1997.p.1–10. Popinet, 2003, Gerris: A tree-based adaptive solver for the incompressible Euler equations in complex geometries, J Comput Phys, 190, 572, 10.1016/S0021-9991(03)00298-5 Khokhlov, 1998, Fully threaded tree algorithms for adaptive refinement fluid dynamics simulations, J Comput Phys, 143, 519, 10.1006/jcph.1998.9998 MacNeice, 2000, A parallel adaptive mesh refinement community toolkit, Comput Phys Commun, 120, 330, 10.1016/S0010-4655(99)00501-9 Ji, 2010, A new adaptive mesh refinement data structure with an application to detonation, J Comput Phys, 229, 8981, 10.1016/j.jcp.2010.08.023 Bell, 1994, Three-dimensional adaptive mesh refinement for hyperbolic conservation laws, SIAM J Sci Comput, 15, 127, 10.1137/0915008 Houston, 2001, hp-adaptive discontinuous Galerkin finite element methods for first-order hyperbolic problems, SIAM J Sci Comput, 23, 1226, 10.1137/S1064827500378799 Hartmann, 2003, Adaptive discontinuous Galerkin finite element methods for nonlinear hyperbolic conservation laws, SIAM J Sci Comput, 24, 979, 10.1137/S1064827501389084 Shi, 2013, Adjoint based error estimation and hp-adaptation for the high-order CPR method Shi, 2015, Adjoint-based error estimation and mesh adaptation for the correction procedure via reconstruction method, J Comput Phys, 295, 261, 10.1016/j.jcp.2015.04.011 Liu, 2016, Positivity-preserving Runge-Kutta discontinuous Galerkin method on adaptive cartesian grid for strong moving shock, Numer Math-Theory Methods Appl, 9, 87, 10.4208/nmtma.2015.m1416 Krivodonova, 2004, Shock detection and limiting with discontinuous Galerkin methods for hyperbolic conservation laws, Appl Numer Math, 48, 323, 10.1016/j.apnum.2003.11.002 Kopera, 2014, Analysis of adaptive mesh refinement for IMEX discontinuous Galerkin solutions of the compressible Euler equations with application to atmospheric simulations, J Comput Phys, 275, 92, 10.1016/j.jcp.2014.06.026 Gottlieb, 2011 Zhang, 2011, Positivity-preserving high order discontinuous Galerkin schemes for compressible Euler equations with source terms, J Comput Phys, 230, 1238, 10.1016/j.jcp.2010.10.036 Wang, 2012, Robust high order discontinuous Galerkin schemes for two-dimensional gaseous detonations, J Comput Phys, 231, 653, 10.1016/j.jcp.2011.10.002 Du, 2019, High-order bound-preserving discontinuous Galerkin methods for stiff multispecies detonation, SIAM J Sci Comput, 41, B250, 10.1137/18M122265X Cheng, 2020, A quasi-conservative discontinuous Galerkin method for solving five equation model of compressible two-medium flows, J Sci Comput, 85, 1, 10.1007/s10915-020-01319-5 Cockburn, 1989, TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws III: One-dimensional systems, J Comput Phys, 84, 90, 10.1016/0021-9991(89)90183-6 Woodward, 1984, The numerical simulation of two-dimensional fluid flow with strong shocks, J Comput Phys, 54, 115, 10.1016/0021-9991(84)90142-6 Cockburn, 1998, The Runge-Kutta discontinuous Galerkin method for conservation laws V: Multidimensional systems, J Comput Phys, 141, 199, 10.1006/jcph.1998.5892 Jiang, 2016, Hybrid central-upwind finite volume schemes for solving the Euler and Navier-Stokes equations, Comput Math Appl, 72, 2241, 10.1016/j.camwa.2016.08.022 Daru, 2000, Evaluation of TVD high resolution schemes for unsteady viscous shocked flows, Comput Fluids, 30, 89, 10.1016/S0045-7930(00)00006-2 Daru, 2009, Numerical simulation of the viscous shock tube problem by using a high resolution monotonicity-preserving scheme, Comput Fluids, 38, 664, 10.1016/j.compfluid.2008.06.008