The characteristic-Galerkin method for advection-dominated problems - An assessment. (English) Zbl 0611.76095
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.
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.
MSC:
76R50 | Diffusion |
76M99 | Basic methods in fluid mechanics |
86A05 | Hydrology, hydrography, oceanography |
Keywords:
one-dimensional convective diffusion equation; accuracy analysis; characteristic-based Galerkin method; advection-dominated problems; numerical propagation characteristics; explicit time-stepping scheme; linear basis functions; spatial discretization; classical Lax-Wendroff method; implicit Crank-Nicolson scheme; coastal hydrodynamic applications; pure advection; steep Gaussian profile; dispersion of a continuous source; oscillating flow; long-wave propagation; bottom frictional dissipation; rectangular channel; characteristic-based finite difference scheme; Hermitian cubic interpolating polynomialsReferences:
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