Adaptive simulation of free surface flows with discrete least squares meshless (DLSM) method using a posteriori error estimator

Abstract

Purpose

The purpose of this paper is to propose an adaptive refinement strategy based on a posteriori error estimate for the efficient simulation of free surface flows using discrete least squares meshless (DLSM) method.

Design/methodology/approach

A pressure projection method is employed to discretize the governing equations of mass and momentum conservation in a Lagrangian form. The semi‐discretized equations are then discretized in space using the DLSM method, in which the sum of squared residual of the governing equations and their boundary conditions are minimized with respect to the unknown nodal parameters.

Findings

Since the position of the free surface is of great significant in free surface problems, a posteriori error estimator which automatically associates higher error to the nodes near the free surface is proposed and used along with a node moving refinement strategy to simulate the free surface problems more efficiently. To test the ability and efficiency of the proposed adaptive simulation method, two test problems, namely dam break and evolution of a water bubble, are solved and the results are presented and compared to those of analytical and experimental results.

Originality/value

Error estimate and adaptive refinement have been mostly used in confined and steady‐state flow. Here in this paper, a new attempt has been made to use these concepts in moving boundary problem.

Citation

Shobeyri, G. and Afshar, M.H. (2012), "Adaptive simulation of free surface flows with discrete least squares meshless (DLSM) method using a posteriori error estimator", Engineering Computations, Vol. 29 No. 8, pp. 794-813. https://doi.org/10.1108/02644401211271591