393 research outputs found
Fully-coupled pressure-based finite-volume framework for the simulation of fluid flows at all speeds in complex geometries
A generalized finite-volume framework for the solution of fluid flows at all speeds in complex geometries and on unstructured meshes is presented. Starting from an existing pressure-based and fully-coupled formulation for the solution of incompressible flow equations, the additional implementation of pressure–density–energy coupling as well as shock-capturing leads to a novel solver framework which is capable of handling flows at all speeds, including quasi-incompressible, subsonic, transonic and supersonic flows. The proposed numerical framework features an implicit coupling of pressure and velocity, which improves the numerical stability in the presence of complex sources and/or equations of state, as well as an energy equation discretized in conservative form that ensures an accurate prediction of temperature and Mach number across strong shocks. The framework is verified and validated by a large number of test cases, demonstrating the accurate and robust prediction of steady-state and transient flows in the quasi-incompressible as well as subsonic, transonic and supersonic speed regimes on structured and unstructured meshes as well as in complex domains
Cut Cell Methods in Global Atmospheric Dynamics
In this thesis, we study next generation techniques for the numerical simulation of global atmospheric dynamics, which range from modeling and grid generation to discretization schemes. Based on a detailed dimensional analysis of the compressible three-dimensional Navier-Stokes equations for small- and large-scale motions in the atmosphere, we derive the compressible Euler equations, the dynamical core of meteorological models. We also provide an insight into multiscale modeling and present a new numerical way of deriving reduced atmospheric models and gaining consistency of the modeling and discretization errors. The main focus of this thesis is the grid generation of the atmosphere. With regard to newly available surveys of the Earth's surface and the ever increasing computing capacities, the atmospheric triangulation techniques have to be reconsidered. In particular, the widely-used terrain-following coordinates prove to be disadvantaguous for highly resolved grids, since both the pressure gradient force error and the hydrostatic inconsistency of this vertical ansatz seriously increase with finer resolution. After a detailed analysis of the standard methods for vertical atmospheric triangulations, we present the cut cell approach as capable alternative. We construct a special cut cell method with two stabilizing constraints and provide a comprehensive guideline for an implementation of cut cells into existing atmospheric codes. For the spatial discretization of the dynamical core, we choose the Finite Volume method because of its favorable characteristics concerning conservation properties and handling of hyperbolicity. We accompany the Finite Volume discretization by a new non-linear interpolation scheme of the velocity field, which is adapted to the geometry and rotation of the Earth. To fathom the capabilities of cut cell grids together with our discretization and new interpolation scheme, we finally present several three-dimensional simulation runs. We apply standard benchmarks like an advection test and the simulation of a Rossby-Haurwitz wave and construct a new test case of counterbalancing flow between high- and low-pressure areas, with which we expose the potential of cut cell methods and the influences of different effects of the Euler equations as well as the topography of the Earth
A Nitsche-based cut finite element method for a fluid--structure interaction problem
We present a new composite mesh finite element method for fluid--structure
interaction problems. The method is based on surrounding the structure by a
boundary-fitted fluid mesh which is embedded into a fixed background fluid
mesh. The embedding allows for an arbitrary overlap of the fluid meshes. The
coupling between the embedded and background fluid meshes is enforced using a
stabilized Nitsche formulation which allows us to establish stability and
optimal order \emph{a priori} error estimates,
see~\cite{MassingLarsonLoggEtAl2013}. We consider here a steady state
fluid--structure interaction problem where a hyperelastic structure interacts
with a viscous fluid modeled by the Stokes equations. We evaluate an iterative
solution procedure based on splitting and present three-dimensional numerical
examples.Comment: Revised version, 18 pages, 7 figures. Accepted for publication in
CAMCo
Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics
This article serves as a summary outlining the mathematical entropy analysis
of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD
equations as they are particularly useful for mathematically modeling a wide
variety of magnetized fluids. In order to be self-contained we first motivate
the physical properties of a magnetic fluid and how it should behave under the
laws of thermodynamics. Next, we introduce a mathematical model built from
hyperbolic partial differential equations (PDEs) that translate physical laws
into mathematical equations. After an overview of the continuous analysis, we
thoroughly describe the derivation of a numerical approximation of the ideal
MHD system that remains consistent to the continuous thermodynamic principles.
The derivation of the method and the theorems contained within serve as the
bulk of the review article. We demonstrate that the derived numerical
approximation retains the correct entropic properties of the continuous model
and show its applicability to a variety of standard numerical test cases for
MHD schemes. We close with our conclusions and a brief discussion on future
work in the area of entropy consistent numerical methods and the modeling of
plasmas
An adaptive, training-free reduced-order model for convection-dominated problems based on hybrid snapshots
The vast majority of reduced-order models (ROMs) first obtain a low
dimensional representation of the problem from high-dimensional model (HDM)
training data which is afterwards used to obtain a system of reduced
complexity. Unfortunately, convection-dominated problems generally have a
slowly decaying Kolmogorov n-width, which makes obtaining an accurate ROM built
solely from training data very challenging. The accuracy of a ROM can be
improved through enrichment with HDM solutions; however, due to the large
computational expense of HDM evaluations for complex problems, they can only be
used parsimoniously to obtain relevant computational savings. In this work, we
exploit the local spatial and temporal coherence often exhibited by these
problems to derive an accurate, cost-efficient approach that repeatedly
combines HDM and ROM evaluations without a separate training phase. Our
approach obtains solutions at a given time step by either fully solving the HDM
or by combining partial HDM and ROM solves. A dynamic sampling procedure
identifies regions that require the HDM solution for global accuracy and the
reminder of the flow is reconstructed using the ROM. Moreover, solutions
combining both HDM and ROM solves use spatial filtering to eliminate potential
spurious oscillations that may develop. We test the proposed method on inviscid
compressible flow problems and demonstrate speedups up to an order of
magnitude.Comment: 29 pages, 13 figure
Development and applications of the Finite Point Method to compressible aerodynamics problems
This work deals with the development and application of the Finite Point Method (FPM) to compressible aerodynamics problems. The research focuses mainly on investigating the capabilities of the meshless technique to address practical problems, one of the most outstanding issues in meshless methods.
The FPM spatial approximation is studied firstly, with emphasis on aspects of the methodology that can be improved to increase its robustness and accuracy. Suitable ranges for setting the relevant approximation parameters and the performance likely to be attained in practice are determined. An automatic procedure to adjust the approximation parameters is also proposed to simplify the application of the method, reducing problem- and user-dependence without affecting the flexibility of the meshless technique.
The discretization of the flow equations is carried out following wellestablished approaches, but drawing on the meshless character of the
methodology. In order to meet the requirements of practical applications, the procedures are designed and implemented placing emphasis on robustness and efficiency (a simplification of the basic FPM technique is proposed to this end). The flow solver is based on an upwind spatial discretization of the convective fluxes (using the approximate Riemann solver of Roe) and an explicit time integration scheme. Two additional artificial diffusion schemes are also proposed to suit those cases of study in which computational cost is a major concern. The performance of the flow solver is evaluated in order to determine the potential of the meshless approach. The accuracy, computational cost and parallel scalability of the method are studied in comparison with a conventional FEM-based technique.
Finally, practical applications and extensions of the flow solution scheme are presented. The examples provided are intended not only to show the
capabilities of the FPM, but also to exploit meshless advantages. Automatic hadaptive procedures, moving domain and fluid-structure interaction problems, as well as a preliminary approach to solve high-Reynolds viscous flows, are a sample of the topics explored.
All in all, the results obtained are satisfactorily accurate and competitive in terms of computational cost (if compared with a similar mesh-based
implementation). This indicates that meshless advantages can be exploited with efficiency and constitutes a good starting point towards more challenging applications.En este trabajo se aborda el desarrollo del Método de Puntos Finitos (MPF) y su aplicación a problemas de aerodinámica de flujos compresibles. El objetivo principal es investigar el potencial de la técnica sin malla para la solución de problemas prácticos, lo cual constituye una de las limitaciones más importantes de los métodos sin malla.
En primer lugar se estudia la aproximación espacial en el MPF, haciendo hincapié en aquéllos aspectos que pueden ser mejorados para incrementar la robustez y exactitud de la metodologÃa. Se determinan rangos adecuados para el ajuste de los parámetros de la aproximación y su comportamiento en situaciones prácticas. Se propone además un procedimiento de ajuste automático de estos parámetros a fin de simplificar la aplicación del método y reducir la dependencia de factores como el tipo de problema y la intervención del usuario, sin afectar la flexibilidad de la técnica sin malla.
A continuación se aborda el esquema de solución de las ecuaciones del flujo. La discretización de las mismas se lleva a cabo siguiendo métodos estándar, pero aprovechando las caracterÃsticas de la técnica sin malla. Con el objetivo de abordar problemas prácticos, se pone énfasis en la robustez y eficiencia de la implementación numérica (se propone además una simplificación del procedimiento de solución). El comportamiento del esquema se estudia en detalle para evaluar su potencial y se analiza su exactitud, coste computacional y escalabilidad, todo ello en comparación con un método convencional basado en Elementos Finitos.
Finalmente se presentan distintas aplicaciones y extensiones de la metodologÃa desarrollada. Los ejemplos numéricos pretenden demostrar las
capacidades del método y también aprovechar las ventajas de la metodologÃa sin malla en áreas en que la misma puede ser de especial interés. Los problemas tratados incluyen, entre otras caracterÃsticas, el refinamiento automático de la discretización, la presencia de fronteras móviles e
interacción fluido-estructura, como asà también una aplicación preliminar a flujos compresibles de alto número de Reynolds. Los resultados obtenidos muestran una exactitud satisfactoria. Además, en comparación con una técnica similar basada en Elementos Finitos, demuestran ser competitivos en términos del coste computacional. Esto indica que las ventajas de la metodologÃa sin malla pueden ser explotadas con eficiencia, lo cual constituye un buen punto de partida para el desarrollo de ulteriores aplicaciones.Postprint (published version
Development and applications of the finite point method to compressible aerodynamics problems
This work deals with the development and application of the Finite Point
Method (FPM) to compressible aerodynamics problems. The research focuses
mainly on investigating the capabilities of the meshless technique to address
practical problems, one of the most outstanding issues in meshless methods.
The FPM spatial approximation is studied firstly, with emphasis on aspects of
the methodology that can be improved to increase its robustness and accuracy.
Suitable ranges for setting the relevant approximation parameters and the
performance likely to be attained in practice are determined. An automatic
procedure to adjust the approximation parameters is also proposed to simplify
the application of the method, reducing problem- and user-dependence
without affecting the flexibility of the meshless technique.
The discretization of the flow equations is carried out following wellestablished
approaches, but drawing on the meshless character of the methodology. In order to meet the requirements of practical applications, the procedures are designed and implemented placing emphasis on robustness and efficiency (a simplification of the basic FPM technique is proposed to this end). The flow solver is based on an upwind spatial discretization of the convective fluxes (using the approximate Riemann solver of Roe) and an explicit time integration scheme. Two additional artificial diffusion schemes are also proposed to suit those cases of study in which computational cost is a major concern. The performance of the flow solver is evaluated in order to determine the potential of the meshless approach. The accuracy, computational cost and parallel scalability of the method are studied in
comparison with a conventional FEM-based technique.
Finally, practical applications and extensions of the flow solution scheme are
presented. The examples provided are intended not only to show the
capabilities of the FPM, but also to exploit meshless advantages. Automatic hadaptive procedures, moving domain and fluid-structure interaction problems,
as well as a preliminary approach to solve high-Reynolds viscous flows, are a
sample of the topics explored.
All in all, the results obtained are satisfactorily accurate and competitive in
terms of computational cost (if compared with a similar mesh-based
implementation). This indicates that meshless advantages can be exploited
with efficiency and constitutes a good starting point towards more challenging
applications
Modeling A Reciprocating Compressor Using A Two-Way Coupled Fluid And Solid Solver With Automatic Grid Generation And Adaptive Mesh Refinement
Computational fluid dynamics has been increasingly used in the design and analysis of reciprocating compressors over the last several years. One of the major challenges in the use of such tools is the creation of the numerical grid on which the modeled equations are solved. Since these compressors typically consist of many interconnected and moving parts, manual creation of the grid can be labor-intensive. Furthermore, it is necessary that the choice of grid yields a sufficiently resolved solution, so that the numerical error is significantly less than the modeling error. In this work, a small displacement refrigeration compressor is modeled using a numerical grid created with an automatic meshing approach. The grid is then automatically adapted to the flow based on the local flow field variables at each time step. This cut-cell based grid matches the supplied fluid volume exactly and permits general motion of all bounding surfaces. An explicit two-way coupled approach is used to account for the fluid-structure interaction between the deforming reed valves and the flow. The fluid is solved using a finite-volume approach, whereas the solid is solved using a finite-element model. The model is validated in comparison to measured mass flow rate, pressure, temperature, and valve lift for two different operation conditions and two different working fluids, namely R-404a and R-449a. The numerical accuracy of the calculations is demonstrated through an automated grid convergence study, and the effect of the grid and time-step resolution on the pressure pulsations and valve lift is shown. While computations on a relatively coarse grid yield power, mass flow rate, and pressure oscillation frequency comparable to measurements, a finer mesh is required inside the cylinder and in the discharge muffler to predict adequately the amplitude of the pressure fluctuations
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