TY - JOUR
T1 - Oscillation-Eliminating Discontinuous Galerkin Methods for Multicomponent Chemically Reacting Flows
AU - Du , Jie
AU - Fan , Chuan
AU - Wu , Kailiang
JO - Annals of Applied Mathematics
VL - 4
SP - 412
EP - 444
PY - 2025
DA - 2025/01
SN - 40
DO - http://doi.org/10.4208/aam.OA-2024-0029
UR - https://global-sci.org/intro/article_detail/aam/23778.html
KW - Oscillation elimination discontinuous Galerkin (OEDG) method, modal filter, bound-preserving, multicomponent chemically reacting flows.
AB - <p style="text-align: justify;">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 efficient. 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&nbsp;equations for chemically reacting flows. These results highlight the method’s
capability to handle complex flow dynamics while maintaining stability and
high-order accuracy.</p>