Multicomponent‐Flow Analyses by Multimode Method of Characteristics

For unsteady open‐channel flows having N interacting unknown variables, a system of $N$ mutually independent, partial differential equations can be used to describe the flow‐field. The system generally belongs to marching‐type problems and permits transformation into characteristic equations that are associated with $N$ distinct characteristic directions. Because characteristics can be considered “wave” or “disturbance” propagation, a fluvial system so described can be viewed as adequately definable using these $N$ component waves. A numerical algorithm to solve the $N$ families of characteristics can then be introduced for formulation of an $N‐\mathrm{component}$ flow‐simulation model. The multimode method of characteristics (MMOC), a new numerical scheme that has a combined capacity of several specified‐time‐interval (STI) schemes of the method of characteristics, makes numerical modeling of such $N‐\mathrm{component}$ riverine flows feasible and attainable. Merging different STI schemes yields different kinds of MMOC schemes, for which two kinds are displayed herein. With the MMOC, each characteristic is dynamically treated by an appropriate numerical mode, which should lead to an effective and suitable global simulation, covering various types of unsteady flow. The scheme is always linearly stable and its numerical accuracy can be systematically analyzed. By increasing the $N$ value, one can develop a progressively sophisticated model that addresses increasingly complex river‐mechanics problems.