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

Abstract

AbstractParallel 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 comp...