Immersed boundary methods for numerical simulation of confined fluid and plasma turbulence in complex geometries: a review

Immersed boundary methods for computing confined fluid and plasma flows in complex geometries are reviewed. The mathematical principle of the volume penalization technique is described and simple examples for imposing Dirichlet and Neumann boundary conditions in one dimension are given. Applications for fluid and plasma turbulence in two and three space dimensions illustrate the applicability and the efficiency of the method in computing flows in complex geometries, for example in toroidal geometries with asymmetric poloidal cross-sections.Comment: in Journal of Plasma Physics, 201

Physical mechanisms governing drag reduction in turbulent Taylor-Couette flow with finite-size deformable bubbles

The phenomenon of drag reduction induced by injection of bubbles into a turbulent carrier fluid has been known for a long time; the governing control parameters and underlying physics is however not well understood. In this paper, we use three dimensional numerical simulations to uncover the effect of deformability of bubbles injected in a turbulent Taylor-Couette flow on the overall drag experienced by the system. We consider two different Reynolds numbers for the carrier flow, i.e. $Re_i=5\times 10^3$ and $Re_i=2\times 10^4$; the deformability of the bubbles is controlled through the Weber number which is varied in the range $We=0.01 - 2.0$. Our numerical simulations show that increasing the deformability of bubbles i.e., $We$ leads to an increase in drag reduction. We look at the different physical effects contributing to drag reduction and analyse their individual contributions with increasing bubble deformability. Profiles of local angular velocity flux show that in the presence of bubbles, turbulence is enhanced near the inner cylinder while attenuated in the bulk and near the outer cylinder. We connect the increase in drag reduction to the decrease in dissipation in the wake of highly deformed bubbles near the inner cylinder

A comparative study of immersed-boundary interpolation methods for a flow around a stationary cylinder at low Reynolds number

The accuracy and computational efficiency of various interpolation methods for the implementation of non grid-confirming boundaries is assessed. The aim of the research is to select an interpolation method that is both efficient and sufficiently accurate to be used in the simulation of vortex induced vibration of the flow around a deformable cylinder. Results are presented of an immersed boundary implementation in which the velocities near nonconfirming boundaries were interpolated in the normal direction to the walls. The flow field is solved on a Cartesian grid using a finite volume method with a staggered variable arrangement. The Strouhal number and Drag coefficient for various cases are reported. The results show a good agreement with the literature. Also, the drag coefficient and Strouhal number results for five different interpolation methods were compared it was shown that for a stationary cylinder at low Reynolds number, the interpolation method could affect the drag coefficient by a maximum 2% and the Strouhal number by maximum of 3%. In addition, the bi-liner interpolation method took about 2% more computational time per vortex shedding cycle in companion to the other methods

Buoyancy-driven flow and fluid-structure interaction with moving boundaries

We deploy the residual-based variational multi-scale (VMS) method in the sense of large-eddy simulation (LES) in finite element method to buoyancy-driven flow in enclosures and consider an extensive range of Rayleigh number from laminar ($10^3$) to turbulent ($10^{10}$) in a 2D benchmark Rayleigh--B\\u27enard problem. 3D simulations for a laminar and a turbulent case are performed and comparisons including mean profiles as well as fluctuation profiles with other numerical and experimental results are successfully carried out. A weakly imposed boundary conditions method is employed for both velocity and temperature, and it produces reasonable results with a much coarser mesh compared with the traditional imposition of boundary conditions. This suggests that the VMS framework with the weak imposition of boundary conditions is a computationally efficient approach to model buoyancy-driven flows in complex indoor environments. In addition to the flow fields, we deploy the immersogeometric analysis (IMGA) method in the sense of the immersed boundary method (IBM) for objects moving in fluids onto an unstructured framework. The finite element formulation is stabilized by the VMS method in an unstructured background mesh. Weak imposition of boundary conditions is used to impose no-slip boundary condition on the immersed boundary. Adaptively refined quadrature rules are used to better capture the geometry of the immersed boundary and accurately integrate the background elements that intersect the immersed boundary. Treatment for the freshly-cleared nodes is considered. We assess the accuracy of the moving IMGA framework by analyzing object motion in a variety of flow structures, including freely dropping cylinder/sphere in viscous fluids and particle focusing in (un)obstructed channels. We show the quantities of interests are in good agreements with other analytical, numerical and experimental solutions. Advantages of this moving IMGA framework in computational cost and efficiency are indicated by the comparison with the body-fitted method using a commercial computational fluid dynamic (CFD) software. The framework of moving IMGA is capable to be deployed in applications of particle control and manipulation in microfluidic channels. The moving IMGA on the unstructured framework is further deployed to a scalable, adaptively refined, octree-based finite element approach for a better computational performance to track object motion. This enables using a parallel, hierarchically refined octree mesh as the background mesh, with a variationally consistent IMGA formulation on this background mesh. We integrate the unstructured framework of moving IMGA to the octree-based framework. We show good scaling results of the coupled framework on Stampede2, TACC. This illustrates the potential of the moving IMGA on the coupled framework to efficiently track complex particles in flows