Prediction–Correction Method for Parallelizing Implicit 2D Hydrodynamic Models. I: Scheme

Abstract

Parallel solutions of linear systems arising from velocity–pressure coupling in implicit two-dimensional (2D) hydrodynamic models are usually difficult and inefficient. Using domain decomposition, a prediction–correction parallelization method is proposed to solve such systems in parallel. It is proposed as a special method for parallelizing simulations of free-surface flows in alluvial rivers. Rather than solving a large-scale global linear system over the whole domain, the method solves sub linear systems for subdomains in two steps, prediction and correction. For free-surface flows in alluvial rivers, the gravity wave propagation over subdomains is divided into internal and external parts, moving within a subdomain and across its boundaries, respectively. The external part is assumed to be well solved at the prediction step; the whole wave propagation is then solved at the correction step using updated boundary values and initial estimates. A theoretical analysis is conducted to derive the computational errors at the prediction and correction steps of this method, resulting in the condition for its application. The method is tested on five meshes whose numbers of elements are 12,800–819,200. The grid scale, which is equal to or smaller than a common scale of real applications, provides grid-independent results. The method performs well for problems of various computational granularities. In solving linear systems with the different meshes, sequential runs were 41–96 times slower than parallel runs using 64 subdomains and 64 working cores.