A stress tensor discontinuity-based immersed boundary-lattice Boltzmann method. (30th August 2018)

• Record Type: Journal Article
• Authors: Suzuki, Kosuke; Yoshino, Masato
• Is Part Of: Computers & fluids. Volume 172(2018)
• Page Start: 593
• Page End: 608
• Publication Date: 2018-08-30
• Subjects: Immersed boundary method -- Lattice Boltzmann method -- Moving-boundary flow -- Stress tensor discontinuity; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2018.03.027
• Languages: English
• ISSNs: 0045-7930

Abstract

Highlights: A stress tensor discontinuity-based immersed boundary-lattice Boltzmann method is proposed. The body force is equivalent to the discontinuity of the stress tensor across the boundary. The discontinuity of the stress tensor is calculated by desired particle distribution functions. The stress tensor on boundary Lagrangian points can be calculated. The total fluid force can be obtained without calculating the internal mass effect. Abstract: We propose an immersed boundary-lattice Boltzmann method using the discontinuity of the stress tensor. In the immersed boundary method, the body force which is applied to enforce the no-slip boundary condition is equivalent to the discontinuity of the stress tensor across the boundary. In the proposed method, the boundary is expressed by Lagrangian points independently of the background lattice points, and the discontinuity of the stress tensor is calculated on these points from desired particle distribution functions which satisfy the no-slip boundary condition based on the bounce-back scheme. By using this method, we can obtain the force locally acting on the boundary from the stress tensor of one side of the fluids divided by the boundary, and there is no need to consider the internal mass effect in calculating the total force and torque acting on the boundary. To our best knowledge, the present method is the first one which enables us to calculate the stress tensor on the boundary in the class of the diffusive interface method. In order to validate the present method, we apply it to simulations of typical moving-boundary problems, i.e., a Taylor–Couette flow, an oscillating circular cylinder in a stationary fluid, the sedimentation of an elliptical cylinder, and the sedimentation of a sphere. As a result, the present method has the first-order spatial accuracy and has a good agreement with other numerical and experimental results. In addition, we discuss two problems of the present method, i.e., penetration and spurious oscillation of local force, and a possible remedy for them.