Development of highly accurate interpolation method for mesh-free flow simulations II. Application of CIVA method to incompressible flow simulations

Abstract

This is the second report on the development of a highly accurate interpolation method, which is called cubic interpolation with volume/area (CIVA) co-ordinates, for mesh-free flow simulations. In this paper, the method of determining the c-parameter of CIVA using a constant curvature condition is first considered for the two- and three-dimensional cases. A computation of a three-dimensional passive scalar advection problem is performed for accuracy verification and for comparison with widely used methods. Then, an application algorithm of the CIVA method respecting incompressible fluid simulation is presented. As the incompressible condition based on Lagrangian approaches causes problems, in this paper we consider the condition based on the conventional Eulerian approach. The CIVA-based incompressible flow simulation algorithm enables a highly accurate simulation of many kinds of problems that have complicated geometries and involve complicated phenomena. To confirm the facts, numerical analyzes are executed for some benchmark problems, namely flow in a square cavity, free surface sloshing and moving boundary problems in complex geometries. The results show that the method achieves high accuracy and has high flexibility, even for the flows involving high Reynolds number, complicated geometries, moving boundaries and free surfaces. Copyright © 2000 John Wiley & Sons, Ltd.