2019/02/20 by Maria Colombo, Gianluca Crippa, Colombo, Maria +5 · 3 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1902.07513
openalex publication_date 2019/02/20 · openalex created_date 2022/07/29 · openalex updated_date 2026/08/01
We deal with the numerical investigation of the local limit of nonlocal\nconservation laws. Previous numerical experiments suggest convergence in the\nlocal limit. However, recent analytic results state that (i) in general\nconvergence does not hold because one can exhibit counterexamples; (ii)\nconvergence can be recovered provided viscosity is added to both the local and\nthe nonlocal equations. Motivated by these analytic results, we investigate the\nrole of numerical viscosity in the numerical study of the local limit of\nnonlocal conservation laws. In particular, we show that the numerical viscosity\nof Lax-Friedrichs type schemes jeopardizes the reliability of the numerical\nscheme and erroneously detects convergence in cases where convergence is ruled\nout by analytic results. We also test Godunov type schemes, less affected by\nnumerical viscosity, and show that in some cases they provide more reliable\nresults.\n