The characteristic-Galerkin method for advection-dominated problems - An assessment
We present results of an accuracy analysis of a recent characteristic- based Galerkin method suited for advection-dominated problems. The analysis shows that the numerical propagation characteristics of the explicit time-stepping scheme which uses linear basis functions for spatial discretization are superior to those of the related classical Lax-Wendroff method and the implicit Crank-Nicolson scheme. The model is subjected to three analytical test problems which embrace many essential realistic features of environmental and coastal hydrodynamic applications: pure advection of a steep Gaussian profile, dispersion of a continuous source in an oscillating flow, and long-wave propagation with bottom frictional dissipation in a rectangular channel. The numerical results demonstrate that the accuracy achieved with the present scheme is excellent and comparable to that of a characteristic- based finite difference scheme which uses Hermitian cubic interpolating polynomials. The results reported herein suggest strongly further use and testing of this robust model in engineering practice.
one-dimensional convective diffusion equation
characteristic-based finite difference scheme
Hermitian cubic interpolating polynomials
scientific article; zbMATH DE number 3988990