Introduction

Hirsch, Charles

doi:10.1016/b978-075066594-0/50039-4

Cited by 82 publications

(109 citation statements)

References 4 publications

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“…In the present method, the Jacobian matrix of a flux vector A D @F=@U is diagonalized in every grid index direction as follows [10,12] …”

Section: Density-based Methodsmentioning

confidence: 99%

“…The viscous part of the fluxes is centrally differenced. In the present applications, a thin-layer form is employed [10,12]. In the pressure-correction algorithm, its linearized form is used in the implicit stage, whereas in the density-based methods, the viscous terms are taken into account approximately by modifying the wave speeds [29].…”

Section: Finite-volume Formmentioning

confidence: 99%

“…At first sight, the textbooks directed at these two fields also look different [8,[10][11][12]. Both disciplines have been extended on the other hand: An artificial compressibility method [13] and preconditioning [14] have been used to extend the density-based methods to a low-Mach number regime, and in the pressure-based community, there has been a long-term quest for a method for all flow speeds.…”

Section: Introductionmentioning

confidence: 99%

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Application of pressure‐ and density‐based methods for different flow speeds

Miettinen

Siikonen

2015

Numerical Methods in Fluids

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SUMMARYIn this paper, pressure-based and density-based methods are studied at different flow speeds. The methods are intended for steady flows, and the goal is to find as general an approach as possible to cover different Mach number regimes. The solution methods are based on a finite-volume approach. Various forms of inviscid fluxes are applied and connected with either a pressure-based or density-based implicit solution. For this purpose, a new pressure-correction method is developed that can be applied for incompressible and for compressible flows. Another option is a standard density-based approximate factorization method. In both cases, a convergence is accelerated with a Full Approximation Scheme (FAS) multigrid approach. Sample problems in the range of Ma D 0 : : : 6 are simulated using different approaches, and their efficiency and accuracy are compared. On the basis of the quality of the solutions, recommendations are made.

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“…In the present method, the Jacobian matrix of a flux vector A D @F=@U is diagonalized in every grid index direction as follows [10,12] …”

Section: Density-based Methodsmentioning

confidence: 99%

Section: Finite-volume Formmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Application of pressure‐ and density‐based methods for different flow speeds

Miettinen

Siikonen

2015

Numerical Methods in Fluids

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“…Discretization is performed in a cell-centered finite-volume manner [20]. The AUSM-DV method [21] is employed for numerical fluxes with the second-order MUSCL method [22].…”

Section: Shock Wave Propagation Induced By Gas Heatingmentioning

confidence: 99%

Asymmetric Shock Wave Generation in a Microwave Rocket Using a Magnetic Field

Takahashi

2017

J. Phys.: Conf. Ser.

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Abstract.A plasma pattern is reproduced by coupling simulations between a particle-incell with Monte Carlo collisions model and a finite-difference time-domain simulation for an electromagnetic wave propagation when an external magnetic field is applied to the breakdown volume inside a microwave-rocket nozzle. The propagation speed and energy-absorption rate of the plasma are estimated based on the breakdown simulation, and these are utilized to reproduce shock wave propagation, which provides impulsive thrust for the microwave rocket. The shock wave propagation is numerically reproduced by solving the compressible Euler equation with an energy source of the microwave heating. The shock wave is asymmetrically generated inside the nozzle when the electron cyclotron resonance region has a lateral offset, which generates lateral and angular impulses for postural control of the vehicle. It is possible to develop an integrated device to maintain beaming flight of the microwave rocket, achieving both axial thrust improvement and postural control, by controlling the spatial distribution of the external magnetic field. IntroductionIt is necessary to develop innovative launch schemes to promote utilization of small satellites because the launch timings and orbits of small satellites are restricted in conventional launch schemes when sharing a chemical rocket with a main satellite. A microwave propulsion system has been proposed to realize frequent and flexible launches of small satellites while reducing the launch cost through repetitive launches of inexpensive vehicles [1][2][3][4][5]. Intense microwaves are radiated from a ground-based oscillator to a thruster equipped with a parabolic mirror, and the incident beam is focused by the mirror to induce air breakdown by the strong fields in the focal region. A dense plasma is generated by the gas breakdown and propagates toward the nozzle exit while forming strong shock waves because the energy absorbed by the plasma is transferred to neutral particles through the collision process. The vehicle obtains an impulsive thrust from interactions between the thruster wall and the shock waves. Chemical fuel aboard the vehicle can be removed or reduced because ambient air acts as the fuel, which decreases the launch cost.Pressure dependencies of the breakdown structure and the thrust performance of a microwave rocket were assessed previously by placing a parabolic thruster in a vacuum chamber [2,3,6]. A discrete plasma was formed at atmospheric pressure because a standing wave was induced in front of the plasma due to waves reflected by the overcritical plasma. On the other hand, the breakdown pattern became diffusive at lower pressures because rapid electron diffusion smeared out the plasma pattern. The propagation speed of the ionization front was found to increase with

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“…Os autores acreditavam, que a instabilidade seria conseqüência das oscilações provocadas pelo comportamento assintótico da solução numérica que este método possui. Este fato foi brevemente discutido em [113] e bem discutido em [69,169]. No entanto, nos trabalhos de Oishi et al [114,115], não foi realizado um estudo teórico para comprovar as suspeitas dos autores.…”

Section: Esquemas Implícitos Na Metodologia Gensmacunclassified

Análise e implementação de métodos implícitos e de projeção para escoamentos com superfície livre.

Oishi¹

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Finalmente, e acima de tudo, a Deus pela minha vida.iii iv ResumoNo contexto do método MAC e baseado em esquemas de diferenças nitas, este trabalho apresenta três estudos: i) uma análise de estabilidade, ii) o desenvolvimento de técnicas implícitas e, iii) a construção de métodos de projeção para escoamentos com superfície livre.Na análise de estabilidade, o principal resultado mostra que o método de Crank-Nicolson torna-se condicionalmente estável quando aplicado para uma malha deslocada com a discretização explícita das condições de contorno do tipo Dirichlet. Entretanto, o mesmo método com condições de contorno implícitas é incondicionalmente estável.Para obter métodos mais estáveis, formulações implícitas são desenvolvidas para a equação da pressão na superfície livre, derivada da condição de tensão normal. Esta estratégia resulta no acoplamento dos campos de velocidade e pressão, o que exige a introdução de novos métodos de projeção.Os métodos de projeção assim desenvolvidos resultam em novas metodologias para escoamentos com superfície livre que são apropriados para o tratamento de problemas com baixo número de Reynolds. Além disso, mostra-se que os métodos propostos podem ser aplicados para uidos viscoelásticos. Novas estratégias são derivadas para obter métodos de projeção de segunda ordem de precisão para escoamentos com superfícies livres.Além dos resultados teóricos sobre a estabilidade de esquemas numéricos, técnicas implícitas e métodos de projeção, testes computacionais são realizados e comparados para consolidação da teoria apresentada. Os resultados numéricos são obtidos no sistema FREEFLOW.A eciência e robustez das técnicas desenvolvidas neste trabalho são demonstradas na solução de problemas tridimensionais complexos com superfície livre e baixo número de Reynolds, incluindo os problemas do jato oscilante e do inchamento do extrudado. In the context of the MAC method and based on nite dierence schemes, this work presents three studies: i) a stability analysis, ii) the development of implicit techniques, and iii) the construction of projection methods for free surface ows.In the stability analysis, the main result shows a precise stability restriction on the CrankNicolson method when one uses a staggered grid with Dirichlet explicit boundary conditions. However, the same method with implicit boundary conditions becomes unconditionally stable.In order to obtain more stable methods, implicit formulations are applied for the pressure equation at the free surface, which is derived from the normal stress condition. This approach results in a coupling of the velocity and pressure elds; hence new projection methods for free surface ows need to be developed.The developed projection methods result in new methodologies for low Reynolds number free surface ows. It is also shown that the proposed methods can be applied for viscoelastic uids. New strategies are derived for obtaining second-order accurate projection methods for free surface ows.In addition to the theoretical results on the stability of numeri...

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Introduction

Cited by 82 publications

References 4 publications

Application of pressure‐ and density‐based methods for different flow speeds

Application of pressure‐ and density‐based methods for different flow speeds

Asymmetric Shock Wave Generation in a Microwave Rocket Using a Magnetic Field

Análise e implementação de métodos implícitos e de projeção para escoamentos com superfície livre.

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