Adjoint-Based Optimization of Flapping Kinematics in Viscous Flows

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106466/1/AIAA2013-2848.pd

Unsteady Output-Based Adaptation Using Continuous-in-Time Adjoints

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143081/1/6.2017-0529.pd

Output Error Control Using r-Adaptation

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143062/1/6.2017-4111.pd

Adaptive mesh refinement method for CFD applications

The main objective of this thesis is the development of an adaptive mesh refinement (AMR) algorithm for computational fluid dynamics simulations using hexahedral and tetrahedral meshes. This numerical methodology is applied in the context of large-eddy simulations (LES) of turbulent flows and direct numerical simulations (DNS) of interfacial flows, to bring new numerical research and physical insight. For the fluid dynamics simulations, the governing equations, the spatial discretization on unstructured grids and the numerical schemes for solving Navier-Stokes equations are presented. The equations follow a discretization by conservative finite-volume on collocated meshes. For the turbulent flows formulation, the spatial discretization preserves symmetry properties of the continuous differential operators and the time integration follows a self-adaptive strategy, which has been well tested on unstructured grids. Moreover, LES model consisting of a wall adapting local-eddy-viscosity within a variational multi-scale formulation is used for the applications showed in this thesis. For the two-phase flow formulation, a conservative level-set method is applied for capturing the interface between two fluids and is implemented with a variable density projection scheme to simulate incompressible two-phase flows on unstructured meshes. The AMR algorithm developed in this thesis is based on a quad/octree data structure and keeps a relation of 1:2 between levels of refinement. In the case of tetrahedral meshes, a geometrical criterion is followed to keep the quality metric of the mesh on a reasonable basis. The parallelization strategy consists mainly in the creation of mesh elements in each sub-domain and establishes a unique global identification number, to avoid duplicate elements. Load balance is assured at each AMR iteration to keep the parallel performance of the CFD code. Moreover, a mesh multiplication algorithm (MM) is reported to create large meshes, with different kind of mesh elements, but preserving the topology from a coarser original mesh. This thesis focuses on the study of turbulent flows and two-phase flows using an AMR framework. The cases studied for LES of turbulent flows applications are the flow around one and two separated square cylinders, and the flow around a simplified car model. In this context, a physics-based refinement criterion is developed, consisting of the residual velocity calculated from a multi-scale decomposition of the instantaneous velocity. This criteria ensures grid adaptation following the main vortical structures and giving enough mesh resolution on the zones of interest, i.e., flow separation, turbulent wakes, and vortex shedding. The cases studied for the two-phase flows are the DNS of 2D and 3D gravity-driven bubble, with a particular focus on the wobbling regime. A study of rising bubbles in the wobbling regime and the effect of dimensionless numbers on the dynamic behavior of the bubbles are presented. Moreover, the use of tetrahedral AMR is applied for the numerical simulation of gravity-driven bubbles in complex domains. On this topic, the methodology is validated on bubbles rising in cylindrical channels with different topology, where the study of these cases contributed to having new numerical research and physical insight in the development of a rising bubble with wall effects.El objetivo principal de esta tesis es el desarrollo de un algoritmo adaptativo de refinamiento de malla (AMR) para simulaciones de dinámica de fluidos computacional utilizando mallas hexaédricas y tetraédricas. Esta metodología numérica se aplica en el contexto de simulaciones Large-eddie (LES) de flujos turbulentos y simulaciones numéricas directas (DNS) de flujos interfaciales, para traer nuevas investigaciones numéricas y entendimiento físicas. Para las simulaciones de dinámica de fluidos, se presentan las ecuaciones governantes, la discretización espacial en mallas no estructuradas y los esquemas numéricos para resolver las ecuaciones de Navier-Stokes. Las ecuaciones siguen una discretización conservativa por volumenes finitos en mallas colocadas. Para la formulación de flujos turbulentos, la discretización espacial preserva las propiedades de simetría de los operadores diferenciales continuos y la integración de tiempo sigue una estrategia autoadaptativa, que ha sido bien probada en mallas no estructuradas. Además, para las aplicaciones que se muestran en esta tesis, se utiliza el modelo LES que consiste en una viscosidad local que se adapta a la pared dentro de una formulación multiescala variable. Para la formulación de flujo de dos fases, se aplica un método de conjunto de niveles conservador para capturar la interfaz entre dos fluidos y se implementa con un esquema de proyección de densidad variable para simular flujos de dos fases incompresibles en mallas no estructuradas. El algoritmo AMR desarrollado en esta tesis se basa en una estructura de datos de quad / octree y mantiene una relación de 1: 2 entre los niveles de refinamiento. En el caso de las mallas tetraédricas, se sigue un criterio geométrico para mantener la calidad de la malla en una base razonable. La estrategia de paralelización consiste principalmente en la creación de elementos de malla en cada subdominio y establece un número de identificación global único, para evitar elementos duplicados. El equilibrio de carga está asegurado en cada iteración de AMR para mantener el rendimiento paralelo del código CFD. Además, se ha desarrollado un algoritmo de multiplicación de malla (MM) para crear mallas grandes, con diferentes tipos de elementos de malla, pero preservando la topología de una malla original más pequeña. Esta tesis se centra en el estudio de flujos turbulentos y flujos de dos fases utilizando un marco AMR. Los casos estudiados para aplicaciones de LES de flujos turbulentos son el flujo alrededor de uno y dos cilindros separados de sección cuadrada, y el flujo alrededor de un modelo de automóvil simplificado. En este contexto, se desarrolla un criterio de refinamiento basado en la física, que consiste en la velocidad residual calculada a partir de una descomposición de escala múltiple de la velocidad instantánea. Este criterio garantiza la adaptación de la malla siguiendo las estructuras vorticales principales y proporcionando una resolución de malla suficiente en las zonas de interés, es decir, separación de flujo, estelas turbulentas y desprendimiento de vórtices. Los casos estudiados para los flujos de dos fases son el DNS de la burbuja impulsada por la gravedad en 2D y 3D, con un enfoque particular en el régimen de oscilación. Además, el uso de AMR tetraédrico se aplica para la simulación numérica de burbujas impulsadas por la gravedad en dominios complejos. En este tema, la metodología se valida en burbujas que ascienden en canales cilíndricos con topología diferente, donde el estudio de estos casos contribuyó a tener una nueva investigación numérica y una visión física en el desarrollo de una burbuja con efectos de pared

Modélisation des problèmes de grandes déformations multi-domaines par une approche Eulérienne monolithique massivement parallèle

Modeling of multi-domain problems is addressed in a Purely Eulerian framework. A single mesh is used all over the domain. The evolution of the different interacting bodies is described using numerical tools such as the Level Set method. The characteristics of the subdomains, considered as heterogeneities in the mesh, are determined using mixture laws.This work is one of the first attempts applying fully Eulerian Approach to Model large deformation problems. Therefore, the capacity of this approach is tested to determine necessary developments. The friction between the different objects is managed by adding a boundary layer implying the presence of a lubricant. Combined with an identification technique, a new quadratic mixture Law is introduced to determine the lubricant viscosity. Comparisons have been performed with Forge® and results were found satisfactory. To treat the contact problem between the different objects, a directional solver was developed. Despite the interesting results, it remains the topic of further improvements. The scalability of the approach in a massively parallel environment is tested as well. Several recommendations were proposed to ensure an optimal performance. The technique of a single mesh guarantees a very good scalability since the efficiency of parallelism depends of the partition of a single mesh (unlike the Lagrangian Methods). The proposed method presents undeniable capacities but remains far from being complete. Ideas for future Improvements are proposed accordingly.La modélisation des problèmes multi-domaine est abordée dans un cadre purement Eulérien. Un maillage unique, ne représentant plus la matière, est utilisé. Les différentes frontières et leur évolution sont décrites via des outils numériques tels que la méthode Level Set. Les caractéristiques locales de chaque sous domaines sont déterminées par des lois de mélange.Ce travail est une des premières tentations appliquant une approche Eulérienne pour modéliser de problèmes de grandes déformations. Dans un premier temps, la capacité de l'approche est testée afin de déterminer les développements nécessaires.Le frottement entre les différents objets est géré par un lubrifiant ajouté dans une couche limite. Combinée avec une technique d'identification, une nouvelle loi de mélange quadratique est introduite pour décrire la viscosité du lubrifiant. Des comparaisons ont été effectuées avec Forge® et les résultats sont trouvés satisfaisants. Pour traiter le contact entre les différents objets, un solveur directionnel a été développé. Malgré que les résultats soient intéressants, il reste le sujet de nouvelles améliorations. La scalabilité de l'approche dans un environnement massivement parallèle est testée aussi. Plusieurs recommandations ont été proposées pour s'assurer d'une performance optimale. La technique du maillage unique permet d'obtenir une très bonne scalabilité. L'efficacité du parallélisme ne dépend que de la partition d'un seul maillage (contrairement aux méthodes Lagrangiennes). La méthode proposée présente des capacités indéniables mais reste loin d'être complète. Des pistes d'amélioration sont proposées en conséquence

Methods for Optimal Output Prediction in Computational Fluid Dynamics.

In a Computational Fluid Dynamics (CFD) simulation, not all data is of equal importance. Instead, the goal of the user is often to compute certain critical "outputs" -- such as lift and drag -- accurately. While in recent years CFD simulations have become routine, ensuring accuracy in these outputs is still surprisingly difficult. Unacceptable levels of output error arise even in industry-standard simulations, such as the steady flow around commercial aircraft. This problem is only exacerbated when simulating more complex, unsteady flows. In this thesis, we present a mesh adaptation strategy for unsteady problems that can automatically reduce errors in outputs of interest. This strategy applies to problems in which the computational domain deforms in time -- such as flapping-flight simulations -- and relies on an unsteady adjoint to identify regions of the mesh contributing most to the output error. This error is then driven down via refinement of the critical regions in both space and time. Here, we demonstrate this strategy on a series of flapping-wing problems in two and three dimensions, using high-order discontinuous Galerkin (DG) methods for both spatial and temporal discretizations. Compared to other methods, results indicate that this strategy can deliver a desired level of output accuracy with significant reductions in computational cost. After concluding our work on mesh adaptation, we take a step back and investigate another idea for obtaining output accuracy: adapting the numerical method itself. In particular, we show how the test space of discontinuous finite element methods can be "optimized" to achieve accuracy in certain outputs or regions. In this work, we compute test functions that ensure accuracy specifically along domain boundaries. These regions -- which are vital to both scalar outputs (such as lift and drag) and distributions (such as pressure and skin friction) -- are often the most important from an engineering standpoint.PhDAerospace EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/133418/1/kastsm_1.pd

Airfoil Shape Optimization Using Output-Based Adapted Meshes

Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/143055/1/6.2017-3102.pd

Progress in particle-based multiscale and hybrid methods for flow applications

This work focuses on the review of particle-based multiscale and hybrid methods that have surfaced in the field of fluid mechanics over the last 20 years. We consider five established particle methods: molecular dynamics, direct simulation Monte Carlo, lattice Boltzmann method, dissipative particle dynamics and smoothed-particle hydrodynamics. A general description is given on each particle method in conjunction with multiscale and hybrid applications. An analysis on the length scale separation revealed that current multiscale methods only bridge across scales which are of the order of O(102)−O(103) and that further work on complex geometries and parallel code optimisation is needed to increase the separation. Similarities between methods are highlighted and combinations discussed. Advantages, disadvantages and applications of each particle method have been tabulated as a reference

Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications

The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system

Adaptive mesh refinement method for CFD applications

The main objective of this thesis is the development of an adaptive mesh refinement (AMR) algorithm for computational fluid dynamics simulations using hexahedral and tetrahedral meshes. This numerical methodology is applied in the context of large-eddy simulations (LES) of turbulent flows and direct numerical simulations (DNS) of interfacial flows, to bring new numerical research and physical insight. For the fluid dynamics simulations, the governing equations, the spatial discretization on unstructured grids and the numerical schemes for solving Navier-Stokes equations are presented. The equations follow a discretization by conservative finite-volume on collocated meshes. For the turbulent flows formulation, the spatial discretization preserves symmetry properties of the continuous differential operators and the time integration follows a self-adaptive strategy, which has been well tested on unstructured grids. Moreover, LES model consisting of a wall adapting local-eddy-viscosity within a variational multi-scale formulation is used for the applications showed in this thesis. For the two-phase flow formulation, a conservative level-set method is applied for capturing the interface between two fluids and is implemented with a variable density projection scheme to simulate incompressible two-phase flows on unstructured meshes. The AMR algorithm developed in this thesis is based on a quad/octree data structure and keeps a relation of 1:2 between levels of refinement. In the case of tetrahedral meshes, a geometrical criterion is followed to keep the quality metric of the mesh on a reasonable basis. The parallelization strategy consists mainly in the creation of mesh elements in each sub-domain and establishes a unique global identification number, to avoid duplicate elements. Load balance is assured at each AMR iteration to keep the parallel performance of the CFD code. Moreover, a mesh multiplication algorithm (MM) is reported to create large meshes, with different kind of mesh elements, but preserving the topology from a coarser original mesh. This thesis focuses on the study of turbulent flows and two-phase flows using an AMR framework. The cases studied for LES of turbulent flows applications are the flow around one and two separated square cylinders, and the flow around a simplified car model. In this context, a physics-based refinement criterion is developed, consisting of the residual velocity calculated from a multi-scale decomposition of the instantaneous velocity. This criteria ensures grid adaptation following the main vortical structures and giving enough mesh resolution on the zones of interest, i.e., flow separation, turbulent wakes, and vortex shedding. The cases studied for the two-phase flows are the DNS of 2D and 3D gravity-driven bubble, with a particular focus on the wobbling regime. A study of rising bubbles in the wobbling regime and the effect of dimensionless numbers on the dynamic behavior of the bubbles are presented. Moreover, the use of tetrahedral AMR is applied for the numerical simulation of gravity-driven bubbles in complex domains. On this topic, the methodology is validated on bubbles rising in cylindrical channels with different topology, where the study of these cases contributed to having new numerical research and physical insight in the development of a rising bubble with wall effects.El objetivo principal de esta tesis es el desarrollo de un algoritmo adaptativo de refinamiento de malla (AMR) para simulaciones de dinámica de fluidos computacional utilizando mallas hexaédricas y tetraédricas. Esta metodología numérica se aplica en el contexto de simulaciones Large-eddie (LES) de flujos turbulentos y simulaciones numéricas directas (DNS) de flujos interfaciales, para traer nuevas investigaciones numéricas y entendimiento físicas. Para las simulaciones de dinámica de fluidos, se presentan las ecuaciones governantes, la discretización espacial en mallas no estructuradas y los esquemas numéricos para resolver las ecuaciones de Navier-Stokes. Las ecuaciones siguen una discretización conservativa por volumenes finitos en mallas colocadas. Para la formulación de flujos turbulentos, la discretización espacial preserva las propiedades de simetría de los operadores diferenciales continuos y la integración de tiempo sigue una estrategia autoadaptativa, que ha sido bien probada en mallas no estructuradas. Además, para las aplicaciones que se muestran en esta tesis, se utiliza el modelo LES que consiste en una viscosidad local que se adapta a la pared dentro de una formulación multiescala variable. Para la formulación de flujo de dos fases, se aplica un método de conjunto de niveles conservador para capturar la interfaz entre dos fluidos y se implementa con un esquema de proyección de densidad variable para simular flujos de dos fases incompresibles en mallas no estructuradas. El algoritmo AMR desarrollado en esta tesis se basa en una estructura de datos de quad / octree y mantiene una relación de 1: 2 entre los niveles de refinamiento. En el caso de las mallas tetraédricas, se sigue un criterio geométrico para mantener la calidad de la malla en una base razonable. La estrategia de paralelización consiste principalmente en la creación de elementos de malla en cada subdominio y establece un número de identificación global único, para evitar elementos duplicados. El equilibrio de carga está asegurado en cada iteración de AMR para mantener el rendimiento paralelo del código CFD. Además, se ha desarrollado un algoritmo de multiplicación de malla (MM) para crear mallas grandes, con diferentes tipos de elementos de malla, pero preservando la topología de una malla original más pequeña. Esta tesis se centra en el estudio de flujos turbulentos y flujos de dos fases utilizando un marco AMR. Los casos estudiados para aplicaciones de LES de flujos turbulentos son el flujo alrededor de uno y dos cilindros separados de sección cuadrada, y el flujo alrededor de un modelo de automóvil simplificado. En este contexto, se desarrolla un criterio de refinamiento basado en la física, que consiste en la velocidad residual calculada a partir de una descomposición de escala múltiple de la velocidad instantánea. Este criterio garantiza la adaptación de la malla siguiendo las estructuras vorticales principales y proporcionando una resolución de malla suficiente en las zonas de interés, es decir, separación de flujo, estelas turbulentas y desprendimiento de vórtices. Los casos estudiados para los flujos de dos fases son el DNS de la burbuja impulsada por la gravedad en 2D y 3D, con un enfoque particular en el régimen de oscilación. Además, el uso de AMR tetraédrico se aplica para la simulación numérica de burbujas impulsadas por la gravedad en dominios complejos. En este tema, la metodología se valida en burbujas que ascienden en canales cilíndricos con topología diferente, donde el estudio de estos casos contribuyó a tener una nueva investigación numérica y una visión física en el desarrollo de una burbuja con efectos de pared.Postprint (published version