Numerical Alternatives in Transient Stream Response

Abstract

A fundamental problem in the numerical prediction of transient stream response is identified as grid resolution. As it is unrealistic to expect predictive performance beyond the Nyquist limit, a successful algorithm must involve a compromise between adequate resolution and acceptable computational effort. Difficulties are rarely encountered in the numerical estimation of the hydrodynamic response, but serious numerical dispersion and solution oscillations frequently corrupt numerical estimates of the mass transport response. The numerical solution difficulties are traced to the discrete approximation to the convective term in an Eulerian framework, regardless of the numerical method adopted. The impact of grid resolution is quantified by Fourier response factor computations and numerical experiments for typical algorithms. Higher order nodal continuity and moving coordinate systems are identified as appropriate solution techniques for the mass transport response, the moving coordinate system approach being shown to be particularly attractive.