Lattice Boltzmann method for viscoplastic fluid flow based on regularization of ghost moments
| Autor: | Alan Lugarini, Paulo Cesar Philippi, Admilson T. Franco |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Physics
010304 chemical physics Augmented Lagrangian method Applied Mathematics Mechanical Engineering General Chemical Engineering Constitutive equation Mathematical analysis Lattice Boltzmann methods Laminar flow Nonlinear Sciences::Cellular Automata and Lattice Gases Condensed Matter Physics Hagen–Poiseuille equation 01 natural sciences 010305 fluids & plasmas Physics::Fluid Dynamics 0103 physical sciences Fluid dynamics General Materials Science Boundary value problem Numerical stability |
| Zdroj: | Journal of Non-Newtonian Fluid Mechanics. 286:104413 |
| ISSN: | 0377-0257 |
| Popis: | In the Lattice Boltzmann Method (LBM) the viscosity is inversely proportional to the relaxation frequency. Hence, it should be possible to represent the singularity of some viscoplastic models by setting the relaxation frequency to zero. In the present paper we take full advantage of the LBM capabilities to propose an efficient and stable numerical scheme for viscoplastic fluid flow simulations invoking the exact Bingham constitutive equation. This scheme is expected to suit the need for more accurate viscoplastic simulations because it does compute the “infinite viscosity”, therefore dismissing the need for any viscosity regularization. Although allowing for a wide range of relaxation frequencies varying in space and time, we demonstrate that the present implementation does not degrade the standard LBM's error order. Numerical stability was promoted by of regularization of ghost moments for the lattice Boltzmann equation with force term. Since the locality of the LBM is preserved, so is the scheme's ability to be highly scalable in large computer clusters. We outline the method and the theory behind it through a detailed Chapman–Enskog expansion. Three laminar test cases are analyzed: parallel channel Poiseuille flow, square duct Poiseuille flow and lid-driven cavity flow. We show conformity with the standard LBM's error order for different wall boundary conditions and yield stress levels. Comparisons are made with other numerical studies employing augmented Lagrangian and viscosity regularization methods. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect