Explicit Computation of Discontinuous Channel Flow

Abstract

An explicit finite element model for free‐surface flow is developed and shown to be second and fourth‐order accurate with respect to the time and space increments, respectively. The method utilizes a Taylor series expansion for integration in time coupled with the classical Galerkin variational principle. The resulting algebraic equations are linear and can be solved sequentially in the form of smaller uncoupled systems. This results in significantly lower computational and storage requirements while maintaining satisfactory accuracy. Stability limits are established for the method by means of Fourier analysis and the associated phase and amplitude portraits demonstrate a highly selective dissipative character. This makes the method suitable for computation of discontinuous flow, while the explicit nature of the method allows an equally accurate computation of supercritical flow. Following an order of accuracy analysis, the method is extended to two‐space dimensions and several computational examples are presented that show the scheme's performance under various flow conditions. On the basis of these results the method is judged to be more efficient for problems requiring high accuracy near flow discontinuities than, implicit methods with similar properties.