2020/02/19 by Hugo Carrillo, Carlos Parés, Carrillo, Hugo +3
Earth and Planetary Sciences · Engineering · #Meteorological Phenomena and Simulations #Computational Fluid Dynamics and Aerodynamics #Fluid Dynamics and Turbulent Flows
paper · pdf · doi:10.48550/arxiv.2002.08426
The goal of this work is to introduce new families of shock-capturing\nhigh-order numerical methods for systems of conservation laws that combine Fast\nWENO (FWENO) and Optimal WENO (OWENO) reconstructions with Approximate Taylor\nmethods for the time discretization. FWENO reconstructions are based on\nsmoothness indicators that require a lower number of calculations than the\nstandard ones. OWENO reconstructions are based on a definition of the nonlinear\nweights that allows one to unconditionally attain the optimal order of accuracy\nregardless of the order of critical points. Approximate Taylor methods update\nthe numerical solutions by using a Taylor expansion in time in which, instead\nof using the Cauchy-Kovalevskaya procedure, the time derivatives are computed\nby combining spatial and temporal numerical differentiation with Taylor\nexpansions in a recursive way. These new methods are compared between them and\nagainst methods based on standard WENO implementations and/or SSP-RK time\ndiscretization. A number of test cases are considered ranging from scalar\nlinear 1d problems to nonlinear systems of conservation laws in 2d.\n