Development of CIP-Reversed Weighted Residual Method for Water Flow with Free Water Surface and Arbitrary Topography (Algorithmic Improvements and Applications)

Abstract

A new numerical method for solving a flow with a free water surface and an arbitrary topography is described. The method is based on the constrained interpolation profile (CIP) scheme and the finite-element method (FEM). Although advection terms are accurately solved using the conventional CIP scheme, nonadvection terms are solved by FEM. To solve nonadvection terms, the reversed weighted residual method (RWRM) based on FEM is proposed. Using the RWRM, surface boundary conditions can be imposed on an arbitrarily curved water surface appropriately even if a simple Cartesian mesh system is employed and the surface is not fitted to the boundaries of a computational mesh. Furthermore, in this paper, an algorithmic improvement in the pressure acceleration phase is proposed. By using the improved numerical procedure, the computational cost due to a matrix-solution can be reduced efficiently. The improved CIP-RWRM solver is applied to 2-D solutions to examine its efficiency and accuracy. The computational results show good agreements with the results calculated by other numerical methods for a multiphase flow.

Residual circulation due to internal waves shoaling on a slope

“…First-order solutions of Boussinesq-type equations and a criterion for the applicability of the theory-The above Boussinesq-type equations were solved with a method similar to that described by Nakamura et al (2004). The configuration is shown in Fig.…”