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NUMERICAL SIMULATION OF UNSTEADY-STATE UNDEREXPANDED JET USING discontinuous galerkin finite element method

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Transactions of Nanjing University of Aeronautics and Astronautics 2008年第2期25卷 89-93页

作者：陈二云李志刚马大为乐贵高赵改平任杰南京理工大学机械工程学院上海理工大学医疗器械学院

A discontinuous galerkin finite element method （DG-FEM） is developed for solving the axisymmetric Euler equations based on two-dimensional conservation laws. The method is used to simulate the unsteady-state underexpanded axisymmetric jet. Several flow property distributions along the jet axis, including density, pres- sure and Mach number are obtained and the qualitative flowfield structures of interest are well captured using the proposed method, including shock waves, slipstreams, traveling vortex ring and multiple Mach disks. Two Mach disk locations agree well with computational and experimental measurement results. It indicates that the method is robust and efficient for solving the unsteady-state underexpanded axisymmetric jet.

关键词： jets computational fluid dynamics multiple Mach disks vortex ring discontinuous galerkin finite element method

A multithreaded parallel upwind sweep algorithm for the S_(N) transport equations discretized with discontinuous finite elements

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Nuclear Science and Techniques 2023年第12期34卷 229-241页

作者： Zhi‑Wei Zong Mao‑Song Cheng Ying‑Chi Yu Zhi‑Min Dai Shanghai Institute of Applied Physics Chinese Academy of SciencesShanghai 201800China University of Chinese Academy of Sciences Beijing 100049China

The complex structure and strong heterogeneity of advanced nuclear reactor systems pose challenges for high-fidelity neutron-shielding calculations. Unstructured meshes exhibit strong geometric adaptability and can overcome the deficiencies of conventionally structured meshes in complex geometry modeling. A multithreaded parallel upwind sweep algorithm for S_(N) transport was proposed to achieve a more accurate geometric description and improve the computational efficiency. The spatial variables were discretized using the standard discontinuous galerkin finite-element method. The angular flux transmission between neighboring meshes was handled using an upwind scheme. In addition, a combination of a mesh transport sweep and angular iterations was realized using a multithreaded parallel technique. The algorithm was implemented in the 2D/3D S_(N) transport code ThorSNIPE, and numerical evaluations were conducted using three typical benchmark problems:IAEA, Kobayashi-3i, and VENUS-3. These numerical results indicate that the multithreaded parallel upwind sweep algorithm can achieve high computational efficiency. ThorSNIPE, with a multithreaded parallel upwind sweep algorithm, has good reliability, stability, and high efficiency, making it suitable for complex shielding calculations.

关键词： Shielding calculation Discrete ordinates method discontinuous galerkin finite element method Unstructured meshes

discontinuous galerkin CALCULATIONS FOR A NONLINEAR PDE MODEL OF DNA TRANSCRIPTION WITH SHORT, TRANSIENT AND FREQUENT PAUSING

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Journal of Computational Mathematics 2014年第6期32卷 601-629页

作者： Lisa Davis Tomas Gedeon Department of Mathematical Sciences Montana State University P.O. Box 172400 Bozeman MT 59717

A discontinuous galerkin finite element method is used to approximate solutions to a classical traffic flow PDE. This PDE is used to model the biological process of transcription; the process of transferring genetic information from DNA either to mRNA or to rRNA. The transcription process is punctuated by short, frequent RNAP pauses which are incorporated into the model as traffic lights. These pauses cause a delay in the average transcription process. The DG solution of the nonlinear model is used to calculate the delay and to determine the effect of the pauses on the average transcription time. Numerical error measurements between the DG solution and the true solution （derived by the method of characteristics） are given for a simple model problem. It shows an excellent agreement in a neighborhood away from the shocks as well as C9（Ax） convergence for the delay calculation. Preliminary parameter studies indicate that in a system with multiple pauses both the location and time duration of the pauses can significantly affect the average delay experienced by an RNAP.

关键词： discontinuous galerkin finite element method Transcription LWR traffic flowmodel.

discontinuous-galerkin-Based Analysis of Traffic Flow Model Connected with Multi-Agent Traffic Model

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Computer Modeling in Engineering & Sciences 2021年第9期128卷 949-965页

作者： Rina Okuyama Naoto Mitsume Hideki Fujii Hideaki Uchida The University of Tokyo 7-3-1 HongoBunkyo-kuTokyo113-8656Japan University of Tsukuba 1-1-1 TennodaiTsukuba CityIbaraki305-8577Japan

As the number of automobiles continues to increase year after year,the associated problem of traffic congestion has become a serious societal *** to mitigate this problem have considered methods for optimizing traffic volumes in wide-area road networks,and traffic-flow simulation has become a focus of interest as a technique for advance characterization of such *** of models commonly used for traffic-flow simulations include microscopic models based on discrete vehicle representations,macroscopic models that describe entire traffic-flow systems in terms of average vehicle densities and velocities,and mesoscopic models and hybrid(or multiscale)models incorporating both microscopic and macroscopic *** traffic-flow simulations are designed to model traffic systems under a variety of conditions,their underlyingmodelsmust be capable of rapidly capturing the consequences of minor variations in operating *** other words,the computation speed of macroscopic models and the precise representation of microscopic models are needed ***,in this study we propose a multiscale model that combines a microscopic model—for detailed analysis of subregions containing traffic congestion bottlenecks or other localized phenomena of interest-with a macroscopic model enabling simulation of wide target areas at a modest computational *** addition,to ensure analytical stability with robustness in the presence of discontinuities,we discretize our macroscopic model using a discontinuous galerkin finite element method(DGFEM),while to conjoin microscopic and macroscopic models,we use a generating/absorbing sponge layer,a technique widely used for numerical analysis of long-wavelength phenomena in shallow water,to enable traffic-flow simulations with stable input and output regions.

关键词： discontinuous galerkin finite element method multiscale modeling traffic flow

A NEW DIRECT discontinuous galerkin method WITH SYMMETRIC STRUCTURE FOR NONLINEAR DIFFUSION EQUATIONS

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Journal of Computational Mathematics 2013年第6期31卷 638-662页

作者： Chad Vidden Jue Yan Department of Mathematics Iowa State University Ames IA USA

In this paper we continue the study of discontinuous galerkin finite element methods for nonlinear diffusion equations following the direct discontinuous galerkin （DDG） meth- ods for diffusion problems [17] and the direct discontinuous galerkin （DDG） methods for diffusion with interface corrections [18]. We introduce a numerical flux for the test func- tion, and obtain a new direct discontinuous galerkin method with symmetric structure. Second order derivative jump terms are included in the numerical flux formula and explicit guidelines for choosing the numerical flux are given. The constructed scheme has a sym- metric property and an optimal L2 （L2） error estimate is obtained. Numerical examples are carried out to demonstrate the optimal （k ＋ 1）th order of accuracy for the method with pk polynomial approximations for both linear and nonlinear problems, under one-dimensional and two-dimensional settings.

关键词： discontinuous galerkin finite element method Diffusion equation Stability,Convergence.

Semi-Implicit Interior Penalty discontinuous galerkin methods for Viscous Compressible Flows

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Communications in Computational Physics 2008年第7期4卷 231-274页

作者： Vit Dolejsi Charles University Prague Faculty of Mathematics and PhysicsSokolovska 8318675 PragueCzech Republic.

We deal with the numerical solution of the Navier-Stokes equations describing a motion of viscous compressible *** order to obtain a sufficiently stable higher order scheme with respect to the time and space coordinates,we develop a combination of the discontinuous galerkin finite element(DGFE)method for the space discretization and the backward difference formulae(BDF)for the time *** the resulting discrete problem leads to a system of nonlinear algebraic equations at each time step,we employ suitable linearizations of inviscid as well as viscous fluxes which give a linear algebraic problem at each time ***,the resulting BDF-DGFE scheme is applied to steady as well as unsteady flows and achieved results are compared with reference data.

关键词： Compressible Navier-Stokes equations discontinuous galerkin finite element method backward difference formulae linearization.