2021/09/21 by Mario Ricchiuto, Davide Torlo, Ricchiuto, Mario +1 · 3 citations
Engineering · Mathematics · #35C07 #65M99 #Advanced Numerical Methods in Computational Mathematics #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2109.10183
openalex publication_date 2021/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Testing the order of accuracy of (very) high order methods for shallow water (and Euler) equations is a delicate operation and the test cases are the crucial starting point of this operation. We provide a short derivation of vortex-like analytical solutions in 2 dimensions for the shallow water equations (and, hence, Euler equations) that can be used to test the order of accuracy of numerical methods. These solutions have different smoothness in their derivatives (up to \mathcal C^∞) and can be used accordingly to the order of accuracy of the scheme to test.