Session G10: CFD: Immersed Boundary Methods II

A Multi-resolution Fourier-Spectral and Finite-Volume Hybrid LGF Method For Solving External Flows

Lattice Green's Function (LGF), Immersed Boundary (IB) Method, and Adaptive Mesh Refinement (AMR) have been successfully combined to carry out high Reynolds number, high fidelity simulations of incompressible, external flows around bodies in a scalable and efficient manner. In this study, we extended this framework to solve fully 3D flows around nominally 2D bodies with infinite spans. Using properties of Fourier series, we developed an algorithm capable of handling multi-resolution meshes in all three spatial dimensions. Specifically, by manipulating Dirac Delta functions, we derived the evolution equations of the Fourier modes arising from Fourier expanding Navier-Stokes equations; by applying LGF of Fourier transformed Laplace operator, the algorithm solves a Poisson equation in an infinite domain with finite active grid cells; by employing the properties of truncated Fourier series, the algorithm can conduct AMR entirely in Fourier modes. Finally, we verified our algorithm using flow past cylinder at Re=300 by comparing our results to previous computations and validated the algorithm using corresponding experimental data. Currently, we are working on a flow stability algorithm based on this framework.   

High-order Immersed Boundary Method for Flux Reconstruction Method on Hierarchical Cartesian Grid

We propose new high-order Immersed Boundary Methods for a hierarchical Cartesian grid-based flow solver using the Flux Reconstruction (FR) method. The FR method is a high-order accuracy method for flow simulation. It can apply to unstructured grids suitable for analyzing a flow around complex geometries and can achieve high parallelization efficiency. Also, we can generate the hierarchical Cartesian grid automatically and robustly for complex geometries. However, the accuracy deteriorates near the wall in the Cartesian grid, although the interior domain is calculated using the high-order FR method. Therefore, we developed new high-order Immersed Boundary Methods using a high-order distribution of physical quantities from the FR method. Specifically, the curvature effect of the wall surface is investigated in detail. The accuracy is validated through basic inviscid flow simulations. As a result, we achieved the same accuracy as the order of the FR method (up to 4th-order) by polynomial extrapolation of the physical quantities from the fluid domain or by polynomial interpolation of the physical quantities considering the curvature of the wall surface.   

A new conceptual approach for immersed boundaries based on volume-filtering

We present a novel approach to solving for the flow around moving immersed solids in a conservative manner without the need for body-fitting meshes, termed Volume-Filtered Immersed Boundary (VF-IB) method. This approach is derived by volume-filtering the conservation equations which transforms boundary conditions at solid-fluid interfaces into body-forces that apply to the right-hand side of the filtered mass and momentum equations. This approach answers long-standing questions related to IBMs: 1) what is the significance of the internal flow within the IB obtained when solving the conservation equations everywhere in the domain, 2) what is the correct choice of Lagrangian marker volume and 3) how does the sharpness of the IB surface affect the solution. The VF-IB method is physically and mathematically rigorous and does not depend on any ad-hoc numerical considerations, allowing us to explicitly express the IB forcing terms without assuming any discretization scheme. We implement and show how to couple this method with a finite-volume fluid solver. We show how to perform interpolation and extrapolation procedures using symmetric, compact, and unitary filter kernels to get accurate forces at the solid-fluid interface. To validate the approach, and help answer the above listed questions, we solve several canonical test cases, with both static and moving IBs. The VF-IBM yields excellent agreement with experiments and body-fitted mesh simulations. Further, we discuss how the choice of filter kernel impacts the solution quality.

    

A High-Order Method for Multiphase Problems with Three-Phase Contact Lines

We present a highly accurate extended discontinuous Galerkin method (XDG) for the simulation of multiphase problems with three-phase contact lines, where two fluid phases interact with a third, solid phase. An example for such a configuration is a water droplet sitting on a soft solid surface, where the surface of the droplet pulls on the solid, deforming it at the three-phase contact line. We will briefly outline the basic concepts of the XDG method and then concentrate on its central component: implicit interfaces. We will detail the numerical coupling approach at fluid-fluid and fluid-solid interfaces and at the three-phase contact line. Finally, we will show results of the simulation of a fluid droplet sitting on a flexible substrate.   

An open-source fluid-structure interaction code for anyone and everyone

Modern computers and algorithms have led to powerful software simulations of complex fluid-structure interaction problems. Yet, many software packages are either proprietary or have a steep learning curve. We present an open-source fluid-structure interaction tool that is implemented in Julia. Julia’s features allow the code to be readable, maintainable, and extendable without sacrificing performance. The software package is designed to provide a high-level and idiomatic interface, rich with tutorials, that is easy for beginners to pick up while providing a powerful toolkit. The package is an implementation of a high-fidelity immersed boundary algorithm, and is capable of accurately simulating flows past a user’s choice of a combination of rigid or deforming bodies undergoing either stationary or moving prescribed kinematics. Functionality exists for performing both nonlinear simulations as well as performing global analysis techniques focusing on laminar flows, however, as a future effort, it will incorporate turbulence models. In all cases, users can easily retrieve key flow data (e.g., velocity, vorticity, pressure) and analyze them using our package’s functionality. We have prioritized extensively documenting the code so advanced users may modify the source to their liking.