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| Oscillation-Eliminating DiscontinuousGalerkin Methods for MulticomponentChemically Reacting Flows |
| Jie Du,Chuan Fan,Kailiang Wu |
| (School of Mathematical Sciences, Key Laboratory of MEA (Ministry of
Education) & Shanghai Key Laboratory of PMMP, East China
Normal University, Shanghai 200241, China;Department of Mathematics and Shenzhen International Center for
Mathematics, Southern University of Science and Technology, Shenzhen,
Guangdong 518055, China) |
| DOI： |
| Abstract: |
| This paper proposes a robust and efficient oscillation-eliminating
discontinuous Galerkin (OEDG) method for solving multicomponent chemically
reacting flows, which is an extension and application of the recent work [M. Peng,
Z. Sun, and K. Wu, Math. Comput., 2024, doi.org/10.1090/mcom/3998]. Following recently developed high-order bound-preserving discontinuous Galerkin
method in [J. Du and Y. Yang, J. Comput. Phys., 469 (2022), 111548], we
incorporate an OE procedure after each Runge-–Kutta time stage to suppress
spurious oscillations. The OE procedure is defined by the solution operator of
a damping equation, which can be analytically solved without requiring discretization, making its implementation straightforward, non-intrusive, and effi-
cient. Through careful design of the damping coefficients, the proposed OEDG
method not only achieves the essentially non-oscillatory (ENO) property without compromising accuracy but also preserves the conservative property—an
indispensable aspect of the bound-preserving technique introduced in [J. Du
and Y. Yang, J. Comput. Phys., 469 (2022), 111548]. The effectiveness and
robustness of the OEDG method are demonstrated through a series of one- and
two-dimensional numerical tests on the compressible Euler and Navier–Stokes
equations for chemically reacting flows. These results highlight the method’s
capability to handle complex flow dynamics while maintaining stability and
high-order accuracy |
| Key words: Oscillation elimination discontinuous Galerkin (OEDG) method, modal filter, bound-preserving, multicomponent chemically reacting flows |