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2021 | Book

AMR Enabled Quadtree Discretization of Incompressible Navier–Stokes Equations with Moving Boundaries Read chapter Read first chapter

Cartesian CFD Methods for Complex Applications

Editors: Prof. Dr. Ralf Deiterding, Dr. Margarete Oliveira Domingues, Prof. Dr. Kai Schneider

Publisher: Springer International Publishing

Book Series : SEMA SIMAI Springer Series

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

This volume collects the most important contributions from four minisymposia from ICIAM 2019. The papers highlight cutting-edge applications of Cartesian CFD methods and describe the employed algorithms and numerical schemes. An emphasis is laid on complex multi-physics applications like magnetohydrodynamics, combustion, aerodynamics with fluid-structure interaction, solved with various discretizations, e.g. finite difference, finite volume, multiresolution or lattice Boltzmann CFD schemes. Software design aspects and parallelization challenges are also considered. The book is addressed to graduate students and scientists in the fields of applied mathematics and computational engineering.

Table of Contents

Frontmatter
AMR Enabled Quadtree Discretization of Incompressible Navier–Stokes Equations with Moving Boundaries
Abstract
We present a versatile finite-volume method for the simulation of incompressible flows past moving bodies. The Navier–Stokes equations are discretized on AMR enabled quadtree grids, where the dynamic in time refinement is adapted to the evolution of the fluid–solid system. The immersed bodies are modeled through a second-order volume penalization method, and the interface is tracked using a level-set description. We highlight on two dimensional test cases that the uniform grids accuracy can be recovered using quadtree grids with less degrees of freedom.
Michel Bergmann, Antoine Fondanèche, Angelo Iollo
Fluid–Structure Interaction Using Volume Penalization and Mass-Spring Models with Application to Flapping Bumblebee Flight
Abstract
Wing flexibility plays an essential role in the aerodynamic performance of insects due to the considerable deformation of their wings during flight under the impact of inertial and aerodynamic forces. These forces come from the complex wing kinematics of insects. In this study, both wing structural dynamics and flapping wing motion are taken into account to investigate the effect of wing deformation on the aerodynamic efficiency of a bumblebee in tethered flight. A fluid–structure interaction solver, coupling a mass-spring model for the flexible wing with a pseudo-spectral code solving the incompressible Navier–Stokes equations, is implemented for this purpose. We first consider a tethered bumblebee flying in laminar flow with flexible wings. Compared to the rigid model, flexible wings generate smaller aerodynamic forces but require much less power. Finally, the bumblebee model is put into a turbulent flow to investigate its influence on the force production of flexible wings.
Hung Truong, Thomas Engels, Dmitry Kolomenskiy, Kai Schneider
No-Slip and Free-Slip Divergence-Free Wavelets for the Simulation of Incompressible Viscous Flows
Abstract
This work concerns divergence-free wavelet-based methods for the numerical resolution of Navier–Stokes equations. It generalizes to higher dimension the approach of Kadri-Harouna and Perrier (Multiscale Model. Simul. 13:399–422; 2015) that reformulates the projection method using the Helmholtz–Hodge decomposition in wavelet domain. The solution is searched in a finite dimensional free-slip divergence-free wavelet space, with time-dependent wavelet coefficients. We prove and verify the convergence of a first-order time numerical scheme for the Helmholtz–Hodge-based projection method. Numerical simulations on the 3D lid-driven cavity flow show the accuracy and efficiency of the method.
Souleymane Kadri Harouna, Valérie Perrier
An Immersed Boundary Method on Cartesian Adaptive Grids for the Simulation of Compressible Flows
Abstract
In this article, we present an immersed boundary method (IBM) for the simulation of compressible flows encountered in aerodynamics. The immersed boundary methods allow the mesh not to conform to obstacles, whose influence is taken into account by modifying the governing equations locally (either by a source term within the equation or by imposing the flow variables or fluxes locally, similarly to a boundary condition).
A main feature of the approach we propose is that it relies on structured Cartesian grids in combination with a dedicated HPC Cartesian solver, taking advantage of not only their low memory and CPU time requirements but also the automation of the mesh generation and adaptation. Turbulent flow simulations are performed with Reynolds-Averaged Navier–Stokes equations or with Large-Eddy Simulation approach, in combination with a wall function at high Reynolds number, in order to mitigate the cell count resulting from the isotropic nature of Cartesian cells.
The objective of this paper is to demonstrate the capability of the present immersed boundary method on Cartesian adaptive grids to capture compressible flow features. Results obtained are in good agreement with classical body-fitted approaches but with a significant reduction of the time of the whole process, that is, a day for RANS simulations, including the mesh generation.
S. Péron, T. Renaud, C. Benoit, I. Mary
Magnetohydrodynamics Adaptive Solvers in the AMROC Framework for Space Plasma Applications
Abstract
Plasma disturbances affect satellites and spacecraft and can cause serious problems to telecommunications and sensitive sensor systems on Earth. Considering the huge scale of the plasma phenomena, data collection at individual locations is not sufficient to cover this entire relevant environment. Therefore, computational plasma modelling has become a significant issue for space sciences, particularly for the near-Earth magnetosphere. However, the simulations of these disturbances present many physical as well as numerical and computational challenges. In this work, we discuss our recent magnetohydrodynamic solver, realised within the MPI-parallel AMROC (Adaptive Mesh Refinement in Object-oriented C++) framework, in which particular physical models and automatic mesh generation procedures have been implemented. A performance analysis using a selection of significant space applications validates the solvers capabilities and confirms the technical importance of our approach.
Müller Moreira Lopes, Margarete Oliveira Domingues, Ralf Deiterding, Odim Mendes
Verification of the WALE Large Eddy Simulation Model for Adaptive Lattice Boltzmann Methods Implemented in the AMROC Framework
Abstract
We detail the verification of the WALE large eddy simulation turbulence model for application in cell-based lattice Boltzmann methods, as implemented in our generic Cartesian structured adaptive mesh refinement framework AMROC. We demonstrate how to effectively apply the test case of decaying homogeneous isotropic turbulence to verify the core WALE implementation against higher resolved direct numerical simulations and the constant-coefficient Smagorinsky turbulence model. Both standard and regularised single relaxation collision models are analysed systematically. While our results confirm the established observation that the standard collision model yields less dissipative energy spectra, novel quantitative evidence is given that this positive behaviour comes at the cost of unphysical perturbations in high wavenumbers. In order to allow unaltered application of the finite-difference stencils intrinsic to the WALE approach in real-world flow situations, a new method is presented for ensuring consistent boundary conditions in microscopic distribution functions as well as in macroscopic variables. The benefit of the proposed technique is shown for dynamically adaptive simulations of flow around a sphere at Reynolds number 1000 and compared to a large eddy simulation using the constant-coefficient Smagorinsky model.
Christos Gkoudesnes, Ralf Deiterding
Metadata
Title
Cartesian CFD Methods for Complex Applications
Editors
Prof. Dr. Ralf Deiterding
Dr. Margarete Oliveira Domingues
Prof. Dr. Kai Schneider
Copyright Year
2021
Electronic ISBN
978-3-030-61761-5
Print ISBN
978-3-030-61760-8
DOI
https://doi.org/10.1007/978-3-030-61761-5

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