An Oscillation-Free Bound-Preserving Discontinuous Galerkin Method for Multi-component Chemically Reacting Flows
This paper develops an oscillation-free discontinuous Galerkin (OFDG) method for solving the multi-component chemically reacting flows. Two common governing equations are considered: reactive Euler equations and Navier–Stokes equations. Based on our recently developed high-order bound-preserving dis...
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| Vydáno v: | Journal of scientific computing Ročník 95; číslo 3; s. 90 |
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| Abstract | This paper develops an oscillation-free discontinuous Galerkin (OFDG) method for solving the multi-component chemically reacting flows. Two common governing equations are considered: reactive Euler equations and Navier–Stokes equations. Based on our recently developed high-order bound-preserving discontinuous Galerkin method in Du and Yang (J Comput Phys 469:111548, 2022), we add an extra damping term into this scheme to control the spurious oscillations. With the careful construction of the damping term, the proposed method not only achieves non-oscillatory property without sacrificing any order of accuracy but also preserves the conservative property which is the key ingredient of the bound-preserving technique developed in Du and Yang (2022). Therefore, the proposed OFDG method is well-compatible with the bound-preserving limiter in Du and Yang (2022). Similar to Liu et al. (SIAM J Sci Comput 44:A230–A259, 2022), the conservative modified exponential Runge–Kutta method is used to relax the restriction of time step sizes and preserve the conservative property of the fully discrete schemes. Numerical experiments, including one- and two-dimensional space, demonstrate the proposed method has desired properties. |
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| AbstractList | This paper develops an oscillation-free discontinuous Galerkin (OFDG) method for solving the multi-component chemically reacting flows. Two common governing equations are considered: reactive Euler equations and Navier–Stokes equations. Based on our recently developed high-order bound-preserving discontinuous Galerkin method in Du and Yang (J Comput Phys 469:111548, 2022), we add an extra damping term into this scheme to control the spurious oscillations. With the careful construction of the damping term, the proposed method not only achieves non-oscillatory property without sacrificing any order of accuracy but also preserves the conservative property which is the key ingredient of the bound-preserving technique developed in Du and Yang (2022). Therefore, the proposed OFDG method is well-compatible with the bound-preserving limiter in Du and Yang (2022). Similar to Liu et al. (SIAM J Sci Comput 44:A230–A259, 2022), the conservative modified exponential Runge–Kutta method is used to relax the restriction of time step sizes and preserve the conservative property of the fully discrete schemes. Numerical experiments, including one- and two-dimensional space, demonstrate the proposed method has desired properties. |
| ArticleNumber | 90 |
| Author | Liu, Yong Yang, Yang Du, Jie |
| Author_xml | – sequence: 1 givenname: Jie surname: Du fullname: Du, Jie organization: Yau Mathematical Sciences Center, Tsinghua University, Yanqi Lake Beijing Institute of Mathematical Sciences and Applications – sequence: 2 givenname: Yong surname: Liu fullname: Liu, Yong email: yongliu@lsec.cc.ac.cn organization: LSEC, Institute of Computational Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences – sequence: 3 givenname: Yang surname: Yang fullname: Yang, Yang organization: Department of Mathematical Sciences, Michigan Technological University |
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| Cites_doi | 10.1006/jcph.1998.5892 10.1016/j.jcp.2012.09.022 10.1007/s10915-018-0852-1 10.1016/j.jcp.2016.06.052 10.1016/j.jcp.2019.06.040 10.1016/0010-2180(81)90027-4 10.1016/0021-9991(89)90183-6 10.1016/j.jcp.2022.111548 10.1016/0010-2180(82)90015-3 10.1137/20M1354192 10.1016/j.jcp.2007.05.011 10.1002/fld.1134 10.1016/j.jcp.2017.03.022 10.1016/j.jcp.2020.109826 10.1080/00268976700100731 10.1007/s42967-020-00117-y 10.1137/18M122265X 10.1007/s10409-017-0664-9 10.1016/j.jcp.2011.07.031 10.1016/j.jcp.2018.01.051 10.1007/s00211-013-0558-0 10.1016/j.jcp.2010.08.016 10.1002/0471461296 10.1016/j.jcp.2014.03.029 10.1016/j.jcp.2013.04.012 10.1051/m2an/1991250303371 10.1016/j.jcp.2012.04.048 10.1137/21M140835X 10.1063/1.1747673 10.1007/s10915-018-0881-9 10.6028/NBS.NSRDS.37 |
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| Keywords | Conservative time integration 92E20 65M60 Oscillation-free discontinuous Galerkin method Multi-component chemically reacting flows Bound-preserving |
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| References_xml | – reference: HouimRWKuoKKA ghost fluid method for compressible reacting flows with phase changeJ. Comput. Phys.20132358659002013JCoPh.235..865H30176261:CAS:528:DC%2BC38XhslCku7bL10.1016/j.jcp.2012.09.022 – reference: LvYIhmeMDiscontinuous Galerkin method for multicomponent chemically reacting flows and combustionJ. Comput. Phys.20142701051372014JCoPh.270..105L32093781:CAS:528:DC%2BC2cXoslyjsrY%3D10.1016/j.jcp.2014.03.029 – reference: MaPLvYIhmeMAn entropy-stable hybrid scheme for simulations of transcritical real-fluid flowsJ. Comput. Phys.20173403303572017JCoPh.340..330M36358411:CAS:528:DC%2BC2sXltlajtrs%3D10.1016/j.jcp.2017.03.022 – reference: CockburnBShuC-WThe Runge–Kutta discontinuous Galerkin method for conservation laws V: multidimensional systemsJ. Comput. Phys.19981411992241998JCoPh.141..199C161965210.1006/jcph.1998.5892 – reference: WilkeCRA viscosity equation for gas mixturesJ. Chem. 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| SubjectTerms | Algorithms Approximation Chemical reactions Computational Mathematics and Numerical Analysis Damping Euler-Lagrange equation Galerkin method Heat Mathematical analysis Mathematical and Computational Engineering Mathematical and Computational Physics Mathematics Mathematics and Statistics Methods Partial differential equations Reacting flow Runge-Kutta method Theoretical Viscosity |
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| Title | An Oscillation-Free Bound-Preserving Discontinuous Galerkin Method for Multi-component Chemically Reacting Flows |
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