A NEW BOUNDARY CONDITION FOR RATE-TYPE NON-NEWTONIAN DIFFUSIVE MODELS AND THE STABLE MAC SCHEME

• 来源期刊: 计算数学（英文版）
• 关键词: Boundary Conditions Diffusive Complex Fluids models Positivity preserving schemes Stability of the MAC schemes
• 年，卷（期）: 2018,（4）
• 页码范围: 605-626
• 页数: 22页
• 语种: 英文
• DOI: 10.4208/jcm.1703-m2015-0359

摘要

We present a new Dirichlet boundary condition for the rate-type non-Newtonian diffusive constitutive models.The newly proposed boundary condition is compared with two such well-known and popularly used boundary conditions as the pure Neumann condition [1] and the Dirichlet condition by Sureshkumar and Beris [2].Our condition is demonstrated to be more stable and robust in a number of numerical test cases.A new Dirichlet boundary condition is implemented in the framework of the finite difference Marker and Cell (MAC) method.In this paper,we also present an energy-stable finite difference MAC scheme that preserves the positivity for the conformation tensor and show how the addition of the diffusion helps the energy-stability in a finite difference MAC scheme-setting.