Download or read book Simulation of Multispecies Gas Flows Using the Discontinuous Galerkin Method written by and published by . This book was released on 2012 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Truncation errors and computational cost are obstacles that still hinder large-scale applications of the Computational Fluid Dynamics method. The discontinuous Galerkin method is one of the high-order schemes utilized extensively in recent years, which is locally conservative, stable, and high-order accurate. Besides that, it can handle complex geometries and irregular meshes with hanging nodes. In this document, the nondimensional compressible Euler equations and Reynolds-Averaged Navier-Stokes equations are discretized by discontinuous Galerkin methods with a two-equations turbulence model on both structured and unstructured meshes. The traditional equation of state for an ideal gas model is substituted by a multispecies thermodynamics model in order to complete the governing equations. An approximate Riemann solver is used for computing the convective flux, and the diffusive flux is approximated with some internal penalty based schemes. The temporal discretization of the partial differential equations is either performed explicitly with the aid of Rung-Kutta methods or with semi-implicit methods. Inspired by the artificial viscosity diffusion based limiter for shock-capturing method, which has been extensively studied, a novel and robust technique based on the introduction of mass diffusion to the species governing equations to guarantee that the species mass fractions remain positive has been thoroughly investigated. This contact-surface-capturing method is conservative and a high order of accuracy can be maintained for the discontinuous Galerkin method. For each time step of the algorithm, any trouble cell is first caught by the contact-surface discontinuity detector. Then some amount of mass diffusions are added to the governing equations to change the gas mixtures and arrive at an equilibrium point satisfying some conditions. The species properties are reasonable without any oscillations. Computations are performed for many steady and unsteady flow problems. For general non-mixing fluid flows, the classical air-helium shock bubble interaction problem is the central test case for the high-order discontinuous Galerkin method with a mass diffusion based limiter chosen. The computed results are compared with experimental, exact, and empirical data to validate the fluid dynamic solver.
Download or read book An Application of Discontinuous Galerkin Methods to the Simulation of Kinetic Equations written by Patrick Steven Medina and published by . This book was released on 2012 with total page 64 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical modeling of the behavior of gas flows over sharp leading edges of air vehicles are challenging because they require the solution of model kinetic equations. These equations lead to stiff problems in regimes transitional from continuum to free molecular, therefore the development of methods that are high order and high resolution receive a lot of interest. For this thesis, the author develops an efficient algorithm for high-order, high-accuracy solutions to model kinetic equations of gas dynamics using multiple time stepping schemes and mesh refinement based on the discontinuous Galerkin (DG) approximation in both spatial and velocity variables. The author applies this method to the simulation of normal shock wave problem and heat transfer problem to demonstrate the methods' efficiently.
Download or read book Direct Numerical Simulation of Multi Phase Flows Using Extended Discontinuous Galerkin Methods written by Martin Smuda and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discontinuous Galerkin Method written by Vít Dolejší and published by Springer. This book was released on 2016-10-15 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of the book is the mathematical theory of the discontinuous Galerkin method (DGM), which is a relatively new technique for the numerical solution of partial differential equations. The book is concerned with the DGM developed for elliptic and parabolic equations and its applications to the numerical simulation of compressible flow. It deals with the theoretical as well as practical aspects of the DGM and treats the basic concepts and ideas of the DGM, as well as the latest significant findings and achievements in this area. The main benefit for readers and the book’s uniqueness lie in the fact that it is sufficiently detailed, extensive and mathematically precise, while at the same time providing a comprehensible guide through a wide spectrum of discontinuous Galerkin techniques and a survey of the latest efficient, accurate and robust discontinuous Galerkin schemes for the solution of compressible flow.
Download or read book High order hybridized Discontinuous Galerkin Method for Geophysical Flows written by Shinhoo Kang and published by . This book was released on 2019 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: As computational research has grown, simulation has become a standard tool in many fields of academic and industrial areas. For example, computational fluid dynamics (CFD) tools in aerospace and research facilities are widely used to evaluate the aerodynamic performance of aircraft or wings. Weather forecasts are highly dependent on numerical weather prediction (NWP) model. However, it is still difficult to simulate the complex physical phenomena of a wide range of length and time scales with modern computational resources. In this study, we develop a robust, efficient and high-order accurate numerical methods and techniques to tackle the challenges. First, we use high-order spatial discretization using (hybridized) discontinuous Galerkin (DG) methods. The DG method combines the advantages of finite volume and finite element methods. As such, it is well-suited to problems with large gradients including shocks and with complex geometries, and large-scale simulations. However, DG typically has many degrees-of-freedoms. To mitigate the expense, we use hybridized DG (HDG) method that introduces new “trace unknowns” on the mesh skeleton (mortar interfaces) to eliminate the local “volume unknowns” with static condensation procedure and reduces globally coupled system when implicit time-stepping is required. Also, since the information between the elements is exchanged through the mesh skeleton, the mortar interfaces can be used as a glue to couple multi-phase regions, e.g., solid and fluid regions, or non-matching grids, e.g., a rotating mesh and a stationary mesh. That is the HDG method provides an efficient and flexible coupling environment compared to standard DG methods. Second, we develop an HDG-DG IMEX scheme for an efficient time integrating scheme. The idea is to divide the governing equations into stiff and nonstiff parts, implicitly treat the former with HDG methods, and explicitly treat the latter with DG methods. The HDG-DG IMEX scheme facilitates high-order temporal and spatial solutions, avoiding too small a time step. Numerical results show that the HDG-DG IMEX scheme is comparable to an explicit Runge-Kutta DG scheme in terms of accuracy while allowing for much larger timestep sizes. We also numerically observe that IMEX HDG-DG scheme can be used as a tool to suppress the high-frequency modes such as acoustic waves or fast gravity waves in atmospheric or ocean models. In short, IMEX HDG-DG methods are attractive for applications in which a fast and stable solution is important while permitting inaccurate processing of the fast modes. Third, we also develop an EXPONENTIAL DG scheme for an efficient time integrators. Similar to the IMEX method, the governing equations are separated into linear and nonlinear parts, then the two parts are spatially discretized with DG methods. Next, we analytically integrate the linear term and approximate the nonlinear term with respect to time. This method accurately handles the fast wave modes in the linear operator. To efficiently evaluate a matrix exponential, we employ the cutting-edge adaptive Krylov subspace method. Finally, we develop a sliding-mesh interface by combining nonconforming treatment and the arbitrary Lagrangian-Eulerian (ALE) scheme for simulating rotating flows, which are important to estimate the characteristics of a rotating wind turbine or understanding vortical structures shown in atmospheric or astronomical phenomena. To integrate the rotating motion of the domain, we use the ALE formulation to map the governing equation to the stationary reference domain and introduce mortar interfaces between the stationary mesh and the rotating mesh. The mortar structure on the sliding interface changes dynamically as the mesh rotates
Download or read book Towards High performance Discontinuous Galerkin Simulations of Reacting Flows Using Legion written by Kihiro Bando and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: High-fidelity scale-resolving computational fluid dynamics (CFD) simulations may provide a path towards predictive capabilities for many engineering-relevant applications, in particular those involving the interaction between multiple physics such as turbulent multi-component reacting flows. However, their routine use is hindered by their cost. The throughput of the fastest supercomputers is fortunately still increasing but this comes at the cost of specialized devices and hardware heterogeneity. Modern supercomputing thus imposes new requirements onto numerical algorithms and their implementation for leveraging the available compute while significantly complicating the design, development, and maintenance of massively parallel computational physics software. This dissertation focuses on addressing numerical and implementation challenges of CFD of multi-component reacting flows. It considers high-order discontinuous Galerkin (DG) discretization methods as a way towards a more efficient use of modern compute architectures for performing high-fidelity simulations of configurations involving complex geometries. Both the high accuracy requirement and the ability to accommodate unstructured meshes are key motivations for investigating this class of numerical schemes. The entire content of this manuscript is based on DG-Legion, a novel unstructured DG CFD solver for the compressible Navier-Stokes equations written on top of the Legion system for targeting distributed heterogeneous architectures. The main challenge related to the computer science aspect was to scale the code on GPU supercomputers. An explicit ghost formulation is proposed which results in performance competitive with state-of-the-art solvers based on the message-passing interface (MPI) system while the application code remains free of explicit communication and synchronization, i.e. it has sequential semantics. The contribution related to the numerics addresses two important questions. First, the issue of spurious pressure oscillations generated by fully-conservative schemes for thermally perfect mixtures is analyzed in detail. A generic framework is developed in order to generate systematic variations of the baseline scheme with improved properties. When applied to the problem at hand, several techniques that were previously proposed independently are recovered as special cases in a rigorous way. Finally, a hybrid strategy for preserving the positivity of DG solutions for the composition-describing scalars is introduced. The method based on the composition of subcell finite volume schemes and linear-scaling limiters leads to an overall positivity-preserving scheme in the inviscid limit, compatible with higher-order quadrature rules, and better preserving the subcell resolution compared to only using rescaling techniques.
Download or read book The Development of Efficient Techniques for Simulating Non continuum Gas Flows written by Craig Euler and published by . This book was released on 2013 with total page 77 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is concerned with the development of efficient techniques for simulating non-continuum flows using model kinetic equations. High order nodal discontinuous Galerkin (DG) discretization in velocity space of the Bhatnagar-Gross-Krook (BGK) and Ellipsoidal-Statistical Bhatnagar-Gross-Krook (ES-BGK) model kinetic equations are developed and implemented. The spatial and temporal discretization are implemented on the basis of the CLAWPACK software which is extended to solve the kinetic model equations. The author performs numerical simulations of the heat transfer and the normal shock wave problems. Accuracy of the numerical solutions in satisfying the conservation laws is assessed. The author confirms that the solutions exhibit the expected order of convergence. In the problem of the normal shock wave the obtained numerical solutions are compared to experimental data. In the second part of the thesis, the problem of spatially homogeneous relaxation is considered. For this problem, a new conservative BGK model with velocity dependent collision frequency is designed. With the new model, one achieves the correct relaxation rates for a selected group of moments. The correct rates are obtained by solving the Boltzmann equation deterministically at the initial time step.
Download or read book Rarefied Gas Dynamics written by Ching Shen and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aerodynamics is a science engaged in the investigation of the motion of air and other gases and their interaction with bodies, and is one of the most important bases of the aeronautic and astronautic techniques. The continuous improvement of the configurations of the airplanes and the space vehicles aid the constant enhancement of their performances are closely related with the development of the aerodynamics. In the design of new flying vehicles the aerodynamics will play more and more important role. The undertakings of aeronautics and astronautics in our country have gained achievements of world interest, the aerodynamics community has made outstanding contributions for the development of these undertakings and the science of aerodynamics. To promote further the development of the aerodynamics, meet the challenge in the new century, summary the experience, cultivate the professional personnel and to serve better the cause of aeronautics and astronautics and the national economy, the present Series of Modern Aerodynamics is organized and published.
Download or read book Development of the Discontinuous Galerkin Method for High resolution Large Scale CFD and Acoustics in Industrial Geometries written by Koen Hillewaert and published by Presses univ. de Louvain. This book was released on 2013-02-10 with total page 173 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this work is the practical development of the discontinuous Galerkin method, arguably the most mature high-order discretisation, for the scale resolving simulations of turbomachinery flows.
Download or read book An Explicit Discontinuous Galerkin Method for Parallel Compressible Two Phase Flow Simulations written by Malte Hoffmann and published by . This book was released on 2017 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advances in Some Hypersonic Vehicles Technologies written by Ramesh K. Agarwal and published by BoD – Books on Demand. This book was released on 2018-03-14 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book describes the recent progress in some hypersonic technologies such as the aerodynamic modeling and numerical simulations of rarefied flows, boundary layer receptivity, coupled aerodynamics, and heat transfer problems, including fluid-thermal-structure interactions and launcher aerodynamic design as well as other miscellaneous topics, such as porous ceramic composite phase change control system and vehicle profile, following LQR design. Both the researchers and the students should find the material useful in their work.
Download or read book High Performance Computing in Science and Engineering 15 written by Wolfgang E. Nagel and published by Springer. This book was released on 2016-02-05 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the state-of-the-art in supercomputer simulation. It includes the latest findings from leading researchers using systems from the High Performance Computing Center Stuttgart (HLRS) in 2015. The reports cover all fields of computational science and engineering ranging from CFD to computational physics and from chemistry to computer science with a special emphasis on industrially relevant applications. Presenting findings of one of Europe’s leading systems, this volume covers a wide variety of applications that deliver a high level of sustained performance. The book covers the main methods in high-performance computing. Its outstanding results in achieving the best performance for production codes are of particular interest for both scientists and engineers. The book comes with a wealth of color illustrations and tables of results.
Download or read book Ground Water Reactive Transport Model Cover Page 03 REVISED eBooks End User License Agreement Website 04 Contents 05 Foreword czheng 06 Preface 07 Contributors 08 Chapter 1 Yeh et al HYDROGEOCHEMA 09 Chapter 2 Wheeler et al IPARS FINAL 10 Chapter 3 Xu et al revised TOUGHREACT 11 Chapter 4 Clement et al RT3D 12 Chapter 5 White et al STOMP ECKEChem 13 Chapter 6 Hammond et al PFLOTRAN 14 Chapter 7 Samper et al CORE2D V4 15 Chapter 8 Mayer et al MIN3P 16 Chapter 9 Hao et al NUFT 17 Index written by Fan Zhang and published by Bentham Science Publishers. This book was released on 2012 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ground water reactive transport models are useful to assess and quantify contaminant precipitation, absorption and migration in subsurface media. Many ground water reactive transport models available today are characterized by varying complexities, strengths, and weaknesses. Selecting accurate, efficient models can be a challenging task. This ebook addresses the needs, issues and challenges relevant to selecting a ground water reactive transport model to evaluate natural attenuation and alternative remediation schemes. It should serve as a handy guide for water resource managers seeking to ach.
Download or read book A Spectral Discontinuous Galerkin Method for Incompressible Flow with Applications to Turbulence written by Stephan-Marian Piatkowski and published by . This book was released on 2019* with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A High order Discontinuous Galerkin Method for Unsteady Compressible Flows with Immersed Boundaries written by Stephan Krämer-Eis and published by . This book was released on 2017-10-20 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Towards Industrialization of High Order Discontinuous Galerkin Methods for Turbulent Flows written by Thomas Bolemann and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Modeling of Microscale Gas Flows Using the Direct Simulation Monte Carlo Method written by and published by . This book was released on 2003 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
