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NUMERICAL SIMULATION OF VORTEX BREAKDOWN ON A DELTA WING AT LOW SPEED

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Chinese Journal of Aeronautics 1996年第4期9卷 235-238页

作者： Zhu Ziqiang Jia Jianbo(Institute of Fluid Mechanics, Beijing University Of Aeronauticsand Astronautics, Beijing, China, 100083 ) Institute of Fluid Mechanics Beijing Univ. Aero. and Astronaut. Beijing 100083 China

The incompressible N-S equations are solved by using a pseudo-compressibility method. Computation is made for both 60°and 70°sharp edged delta wings. Thepredictions for position and angle attack of vortex breakdown are investigated. The effectof the leading edge sweep angle on vortex breakdown is also discussed. Numerical resultsshow that the present method is an effective tool for investigation of vortex breakdown atlow speed.

关键词： vortex breakdown incompressible flow navier-stokes equation pseudocompressibility method

SOME PROPERTIES OF THREE-DIMENSIONAL BELTRAMI FLOWS

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Acta Mechanica Sinica 1991年第4期7卷 289-294页

作者：是长春黄永念 Peking University Beijing 100871China

The investigation of Beltrami flows is important for the research on the mechanism of turbulent *** this paper the general solutions of the Beltrami flows are given,which depend explicitly on the solutions of three independent Helmholtz equations with scalar *** fields of Beltrami flows can then be obtained explicitly after the application of some curl operations on the solutions of Helmholtz equa- *** the basis of the exact solutions of Euler equations given above,we obtain one kind of exact solu- tions of non-steady navier-stokes equations which are also the Beltrami *** interesting examples of Beltrami flows other than'ABC flows','Kolmogolov flows','Rayleigh-Bernard flows','Q-flows' are *** detailed analytic results of these examples will be published in the near future.

关键词： Beltrami flow Euler equation navier-stokes equation exact solution

An analysis of the incompressible viscous flows problem by meshless method

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Chinese Physics B 2006年第10期15卷 2352-2356页

作者：熊渊博王浩 Department of Engineering Mechanics Hunan University Changsha 410082 China

Generally the incompressible viscous flow problem is described by the navier-stokes equation. Based on the weighted residual method the discrete formulation of element-free Galerkin is inferred in this paper. By the step-bystep computation in the field of time, and adopting the least-square estimation of the-same-order shift, this paper has calculated both velocity and pressure from the decoupling independent equations. Each time fraction Newton-Raphson iterative method is applied for the velocity and pressure. Finally, this paper puts the method into practice of the shear-drive cavity flow, verifying the validity, high accuracy and stability.

关键词： incompressible viscous flows element-free Galerkin method navier-stokes equation weighted residual method

Numerical Study of Pinching Liquid Filament Using VOF Method

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Chinese Journal of Chemical Engineering 2003年第5期11卷 542-549页

作者：洪若瑜 Department of Chemistry and Chemical Engineering Soochow UniversitySuzhou 215001China

Study on pinching liquid nlament in literature was reviewed. The breakup of liquid filaments under surface tension is governed by incompressible, two-dimensional (2-D), navier-stokes equations. Surface tension was expressed via a CSF (continuous surface force) modei that ensures robustness and accuracy. A new surface reconstruction scheme, alternative phase integration (API) scheme was proposed to solve the kinematic equation, and was compared with other three referential schemes. A general-purpose computer program has been developed for simulating transient, 2-D, incompressible fluid flows with free surface of complex topology. The transient behavior of breaking Newtonian liquid filaments under surface tension was simulated successfully using the developed program. The initial wave growth predicted using API-VOF (volume of fluid) scheme was in good agreement with Rayleigh's linear theory and one-dimensional (1-D) long-wave theory. Both long wave theory and two-dimensional (2-D) API-VOF modei on fine meshes show that as time goes on, these waves pinch off large droplets separated by smaller satellite ones that decrease in size with decreasing wavelength. Self-similar structure during the breakup was found using 1-D and 2-D models, and three breakups were predicted for a typical case. The criterion of filament breaking predicted by the 2-D modei is that the wavelength is longer than the circumference of a filament. The predicted sizes of main and satellite droplets were compared with published experimental measurements.

关键词： navier-stokes equation control volume volume of fluid free surface liquid-filament breaking

A GPU-Accelerated Discontinuous Galerkin Method for Solving Two-Dimensional Laminar Flows

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Transactions of Nanjing University of Aeronautics and Astronautics 2022年第4期39卷 450-466页

作者： GAO Huanqin CHEN Hongquan ZHANG Jiale XU Shengguan GAO Yukun Key Laboratory of Non-steady Aerodynamics and Flow Control of MIIT College of Aerospace EngineeringNanjing University of Aeronautics and AstronauticsNanjing 210016P.R.China School of Mechanical Engineering Anhui University of TechnologyMaanshan 243002P.R.China

A graphics processing unit(GPU)-accelerated discontinuous Galerkin(DG)method is presented for solving two-dimensional laminar *** DG method is ported from central processing unit to GPU in a way of achieving GPU speedup through programming under the compute unified device architecture(CUDA)*** CUDA kernel subroutines are designed to meet with the requirement of high order computing of DG *** corresponding data structures are constructed in component-wised manners and the thread hierarchy is manipulated in cell-wised or edge-wised manners associated with related integrals involved in solving laminar navier-stokes equations,in which the inviscid and viscous flux terms are computed by the local lax-Friedrichs scheme and the second scheme of Bassi&Rebay,respectively.A strong stability preserving Runge-Kutta scheme is then used for time marching of numerical *** resulting GPU-accelerated DG method is first validated by the traditional Couette flow problems with different mesh sizes associated with different orders of approximation,which shows that the orders of convergence,as expected,can be *** numerical simulations of the typical flows over a circular cylinder or a NACA 0012 airfoil are then carried out,and the results are further compared with the analytical solutions or available experimental and numerical values reported in the literature,as well as with a performance analysis of the developed code in terms of GPU *** shows that the costs of computing time of the presented test cases are significantly reduced without losing accuracy,while impressive speedups up to 69.7 times are achieved by the present method in comparison to its CPU counterpart.

关键词： discontinuous Galerkin GPU compute unified device architecture(CUDA) navier-stokes equation laminar flows

Numerical Model of Internal Solitary Wave Evolution on ImpermeableVariable Seabed in A Stratified Two-Layer Fluid System

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China Ocean Engineering 2006年第2期20卷 303-313页

作者： Chen-Yuan CHEN John Rong-Chung HSU Cheng-Wu CHEN Ming-Hung CHENG Department of Madne Envirorunent and Engineering National Sun Yat-sen University Kaohsiung 80424 Taiwan China School of Civil and Resource Engineering University of Western Australia WA 6009 Australia Department of Logistics Management Shu-Te University Kaohsiung 82445 Taiwan China

In the present study a numerical model developed by Lynett and Liu （2002） is modified to include density difference in a stratified two-layer fluid in a three-dimensional internal wave domain. The internal solitary wave （ISW） in the model is assumed to be weakly nonlinear and weakly dispersive, and the viscosity effects at all boundaries are ignored. The governing equations based on the navier-stokes and Euler equations are solved for internal solitary wave propagation over variable seabed topography. Theoretical formulations are established, from which analytical solutions are obtained, in addition to numerical results. Wave profiles from previous experimental studies are compared with the numerical results from the present analytical solutions. Numerical models developed on the basis of the present analytical solutions are better than those developed by Lynett and Liu （2002）. The results of numerical modeling agree well with the experimental data.

关键词： navier-stokes equation nonlinearity frequency dispersion internal solitary wave numerical model

Hyperbolic Method to Explore Multiplicity Flow Solutions in a Four-Sided Lid-Driven Cavity

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American Journal of Computational Mathematics 2022年第3期12卷 314-323页

作者： Hubert Baty Observatoire Astronomique de Strasbourg CNRS Université de Strasbourg Strasbourg France

In this study, the hyperbolic method is adopted to explore the flow field states of incompressible flow in a four-sided lid-driven square cavity. In particular, we focus on the flow bifurcation obtained at the critical Reynolds number . In the hyperbolic method, the diffusive term is transformed into a hyperbolic one by introducing a diffusion flux term, which is the solution of an additional equation. A classical Riemann-like solver with a finite-volume discretization is thus employed for the full flux (split into advective and diffusive parts), in order to solve the steady-state incompressible navier-stokes equation. The incompressibility of the flow is treated via the artificial pseudo-compressibility method. It is shown that our numerical code is able to detect the bifurcation by the analysis of the residual term relaxation during the pseudo-time iteration procedure. Moreover, depending on the combination choice of slope limiters for the two spatial directions, our method is able to select the first or the second stable solution among the double flow field state obtained when the Reynolds number is higher than the critical value that is estimated to be 129.4 in our study.

关键词： Fluid Mechanics navier-stokes equation Fundamental Solutions

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Superrelativity

Open Journal of Fluid Dynamics 2016年第2期6卷 130-143页

作者： Peter Donald Rodgers University of Queensland Brisbane Australia

Did any physics experts expect SUPERRELATIVITY paper, a physics revolution producing the EINSTEIN-RODGERS RELATIVITY equation, producing the HAWKING-RODGERS BLACK HOLE RADIUS, and producing the STEFAN-BOLTZMANN-SCHWARZSCHILD-HAWKING-RODGERS BLACK HOLE RADIATION POWER LAW, as the author gave a solution to The Clay Mathematics Institute’s very difficult problem about the navier-stokes equations? The Clay Mathematics Institute in May 2000 offered that great $million prize to the first person providing a solution for a specific statement of the problem: “Prove or give a counter-example of the following statement: In three space dimensions and time, given an initial velocity field, there exists a vector velocity and a scalar pressure field, which are both smooth and globally defined, that solve the navier-stokes equations.” Did I, the creator of this paper, expect SUPERRELATIVITY to become a sophisticated conversion of my unified field theory ideas and mathematics into a precious fluid dynamics paper to help mathematicians, engineers and astro-physicists? [1]. Yes, but I did not expect such superb equations that can be used in medicine or in outer space! In this paper, complicated equations for multi-massed systems become simpler equations for fluid dynamic systems. That simplicity is what is great about the navier-stokes equations. Can I delve deeply into adding novel formulae into the famous Schwarzschild’s equation? Surprisingly, yes I do! Questioning the concept of reversibility of events with time, I suggest possible 3-dimensional and 4-dimensional co-ordinate systems that seem better than what Albert Einstein used, and I suggest possible modifications to Maxwell’s equations. In SUPERRELATIVITY, I propose that an error exists in Albert Einstein’s Special Relativity equations, and that error is significant because it leads to turbulence in the universe’s fluids including those in our human bodies. Further, in SUPERRELATIVITY, after I create Schwarzschild-based equati

关键词： Superrelativity Relativity navier-stokes equation Physics Albert Einstein Stephen Hawking Black Hole Clay Mathematics Institute

Finite Element Simulation of an Unimolecular Thermal Decomposition inside a Reactor

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Journal of Applied Mathematics and Physics 2016年第2期4卷 328-340页

作者： Mohamed M. Mousa Department of Mathematics College of Sciences and Human Studies at Howtat Sudair Majmaah University Al Majmaah Saudi Arabia Department of Basic Science Faculty of Engineering Benha University Benha Egypt

This numerical study investigates the steady state unimolecular thermal decomposition of a chemical dissolved in water inside a parallel-plate reactor containing four heated circular rods using a penalty Galerkin finite element approach. The reactant fluid enters from the left inlet and exits from the right outlet of the reactor. All solid walls of the reactor are assumed to be thermodynamically isolated. The aim of the investigation is to illustrate the effects of the energy expelled during the reaction, temperature of the heated rods and fluid inlet velocity on the thermal field and concentration of the heat sensitive chemical. The simulation is conducted for different values of inlet velocity and rods temperature taking into consideration and neglecting the reaction energy. From the results, it is concluded that the thermal field and decomposition process of the chemical are significantly influenced by fluid velocity, rods temperature and the reaction type.

关键词： Finite Elements Heat and Mass Transfer Chemically Reacting Flows navier-stokes equation