2021/06/15 by Eduardo Abreu, Abreu, Eduardo, Arthur Espírito Santo +5
Engineering · Mathematics · Physics and Astronomy · #35L45 #65M08 #76M10 #76M20 #76S05 #Advanced Mathematical Physics Problems #Computational Fluid Dynamics and Aerodynamics #Cosmology and Gravitation Theories #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2106.08363
openalex publication_date 2021/06/15 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
In this paper, we study both convergence and bounded variation properties of\na new fully discrete conservative Lagrangian--Eulerian scheme to the entropy\nsolution in the sense of Kruzhkov (scalar case) by using a weak asymptotic\nanalysis. We discuss theoretical developments on the conception of no-flow\ncurves for hyperbolic problems within scientific computing. The resulting\nalgorithms have been proven to be effective to study nonlinear wave formations\nand rarefaction interactions. We present experiments to a study based on the\nuse of the Wasserstein distance to show the effectiveness of the no-flow curves\napproach in the cases of shock interaction with an entropy wave related to the\ninviscid Burgers' model problem and to a 2x2 nonlocal traffic flow symmetric\nsystem of type Keyfitz--Kranzer.\n