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Article

A Hybrid Time Integration Scheme for the Discontinuous Galerkin Discretizations of Convection-Dominated Problems

School of Aeronautic Science and Engineering, Beihang University, Beijing 100191, China
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Energies 2020, 13(8), 1870; https://doi.org/10.3390/en13081870
Received: 27 February 2020 / Revised: 29 March 2020 / Accepted: 5 April 2020 / Published: 11 April 2020
Discontinuous Galerkin (DG) method is a popular high-order accurate method for solving unsteady convection-dominated problems. After spatially discretizing the problem with the DG method, a time integration scheme is necessary for evolving the result. Owing to the stability-based restriction, the time step for an explicit scheme is limited by the smallest element size within the mesh, making the calculation inefficient. In this paper, a hybrid scheme comprising a three-stage, third-order accurate, and strong stability preserving Runge–Kutta (SSP-RK3) scheme and the three-stage, third-order accurate, L-stable, and diagonally implicit Runge–Kutta (LDIRK3) scheme is proposed. By dealing with the coarse and the refined elements with the explicit and implicit schemes, respectively, the time step for the hybrid scheme is free from the limitation of the smallest element size, making the simulation much more efficient. Numerical tests and comparison studies were made to show the performance of the hybrid scheme. View Full-Text
Keywords: unsteady convection-dominated problem; time integration; discontinuous Galerkin; explicit scheme; implicit scheme unsteady convection-dominated problem; time integration; discontinuous Galerkin; explicit scheme; implicit scheme
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MDPI and ACS Style

Li, L.; Wu, S. A Hybrid Time Integration Scheme for the Discontinuous Galerkin Discretizations of Convection-Dominated Problems. Energies 2020, 13, 1870. https://doi.org/10.3390/en13081870

AMA Style

Li L, Wu S. A Hybrid Time Integration Scheme for the Discontinuous Galerkin Discretizations of Convection-Dominated Problems. Energies. 2020; 13(8):1870. https://doi.org/10.3390/en13081870

Chicago/Turabian Style

Li, Liang, and Songping Wu. 2020. "A Hybrid Time Integration Scheme for the Discontinuous Galerkin Discretizations of Convection-Dominated Problems" Energies 13, no. 8: 1870. https://doi.org/10.3390/en13081870

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