EQSWP: Extended Unsteady‐Flow Double‐Sweep Equation Solver

Abstract

An extension of the double‐sweep technique is presented for solving systems of algebraic equations arising from implicit schemes of the box type for unsteady open‐channel flow. The new technique handles coefficient matrices with a nonzero column of coefficients as well as with coefficients clustered around the diagonal. This arises, for example, when the time step is unknown, or when the spatial location of node points depends upon an unknown distance, such as surge‐front location. Subcritical and zero‐intertia flow, which inherently are governed by a boundary condition at each end of a reach, have typically been treated by a double‐sweep technique. This strategy is preserved with the proposed method, even with a nonzero column of coefficients in the matrix of governing equations. Kinematic‐wave flow and superficial flow are traditionally considered a problem with a marching solution—with boundary conditions picked up at the upstream boundary, and flow variables determined directly in one forward sweep through the computational cells. With the nonzero column of coefficients however, a double‐sweep computational strategy is proposed.