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Accurate Computation of Nonlinear Advection

by Forrest M. Holly, Jr., Univ of Iowa, Dep of Civil &, Environmental Engineering, Iowa, City, IA, USA,
Keichi Toda, Univ of Iowa, Dep of Civil &, Environmental Engineering, Iowa, City, IA, USA,



Document Type: Proceeding Paper

Part of: Water for Resource Development

Abstract:

Advection, the transport of a quantity by the mean velocity, is a process which appears in virtually all equations of free-surface hydraulics. The demonstrated accuracy and efficiency of the Holly-Preissmann two-point fourth order computational method for linear contaminant advection suggest that the method may also be useful for the nonlinear momentum advection terms in the de St. Venant flow equations. Reformulation of the method to handle the more general nonlinear case is described. How the advection operator can be combined with other terms to form a hybrid characteristics/finite difference scheme, obviating the need for a split operator method as commonly employed is shown. Application of the method to linear and nonlinear test cases, including a phase and amplitude analysis for the linear case, are discussed. The need for further research is highlighted through description of several difficulties encountered in nonlinear trials.

Subject Headings: Advection | Nonlinear analysis | Hydraulic properties | Surface properties | Linear analysis | Free surfaces | Overland flow

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