ALE finite volume method for free-surface Bingham plastic fluids with general curvilinear coordinates

• Published in: IOP conference series. Materials Science and Engineering Vol. 10; no. 1; p. 012022
• Main Authors: Nagai, Katsuaki, Ushijima, Satoru
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.06.2010
• Subjects: ALE (numerical method); Bingham plastics; Computational fluid dynamics; Containers; Finite volume method; Fluid flow; Fluids; Free surfaces; Liquid surfaces; Mathematical analysis; Mathematical models; Navier-Stokes equations; Newtonian fluids; Non Newtonian fluids; Numerical prediction; Spherical coordinates; Strain rate; Stress tensors; Tensors
• ISSN: 1757-899X; 1757-8981; 1757-899X
• DOI: 10.1088/1757-899X/10/1/012022

A numerical prediction method has been proposed to predict Bingham plastic fluids with free-surface in a two-dimensional container. Since the linear relationships between stress tensors and strain rate tensors are not assumed for non-Newtonian fluids, the liquid motions are described with Cauchy momentum equations rather than Navier-Stokes equations. The profile of a liquid surface is represented with the two-dimensional curvilinear coordinates which are represented in each computational step on the basis of the arbitrary Lagrangian-Eulerian (ALE) method. Since the volumes of the fluid cells are transiently changed in the physical space, the geometric conservation law is applied to the finite volume discretizations. As a result, it has been shown that the present method enables us to predict reasonably the Bingham plastic fluids with free-surface in a container.