2016/02/04 by Florent Renac, Renac, Florent
Engineering · Mathematics · #65M12 #65M60 #Acoustic Wave Phenomena Research #Aerodynamics and Acoustics in Jet Flows #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1602.01598
openalex publication_date 2016/02/04 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
We present an extension to high-order of a first-order Lagrange-projection\nlike method for the approximation of the Euler equations introduced in Coquel\n it et al. (Math. Comput., 79 (2010), pp.~1493--1533). The method is based on\na decomposition between acoustic and transport operators associated to an\nimplicit-explicit time integration, thus relaxing the constraint of acoustic\nwaves on the time step. We propose here to use a discontinuous Galerkin method\nfor the space approximation. Considering the isentropic Euler equations, we\nderive conditions to keep positivity of the mean value of density and satisfy\nan entropy inequality for the numerical solution in each element of the mesh at\nany approximation order in space. These results allow to design limiting\nprocedures to restore these properties at nodal values within elements.\nNumerical experiments support the conclusions of the analysis and highlight\nstability and robustness of the present method, though it allows the use of\nlarge time steps.\n