Centered and Upwind Multigrid Turbulent Flow Simulations with Applications to Launch Vehicles

Bigarella, E. D. V.; Basso, Edson; Azevedo, João Luiz F.

doi:10.2514/6.2004-5384

Cited by 9 publications

(18 citation statements)

References 18 publications

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“…It is known that flux schemes may have influence in such flow solutions, as reported by Swanson, Radespiel and Turkel (1998), Zingg et al (1999), Allmaras (2002), and Bigarella (2002). The present group attributes such problems to nonphysical behavior of centered flux schemes, more precisely in the explicitly added artificial dissipation model, as reported in Bigarella, Moreira and Azevedo (2004). The present paper shows conclusive results that corroborate this assertive.…”

Section: Paper Received 27 July 2009 Paper Accepted 29 November 2011supporting

confidence: 79%

“…A dependency of the numerical solution with the computational mesh topology and refinement has also been observed. Although Bigarella (2002) reports this problem in a different context, namely a finite difference code, the same issue can also be found with the present finite volume formulation (Bigarella, Moreira and Azevedo, 2004). Moreover, Bigarella, Moreira and Azevedo (2004) also discuss a detailed analysis of mesh topology for such boundary layer flows.…”

Section: Subsonic Flat Platementioning

confidence: 79%

“…The dependency of the discretization accuracy on mesh cell type and topology is acknowledged in the literature, as discussed by Mavriplis (1997), Deconinck, Roe and Struijs (1993), Sidilkover (1994, Peroomian and Chakravarthy (1997), Deconinck and Degrez (1999), Jawahar and Kamath (2000), and Drikakis (2003). These references, in particular, present efforts towards the development of numerical schemes that are less sensitive to mesh topology, and that present native multidimensional "cell-transparent" behavior.…”

Section: Discretization Order Of Accuracymentioning

confidence: 99%

“…Furthermore, it has been observed, during the application of this method along with the multigrid scheme in highly stretched grids, that it may be beneficial to increase the K 4 value to K 4 = 1/64 (Bigarella and Azevedo, 2005).…”

Section: Matrix Switched Model (Matd)mentioning

confidence: 99%

“…An agglomeration full-multigrid scheme (FMG) is included in order to achieve better convergence rates for the simulations. More details on the theoretical and numerical formulations can be found in Bigarella, Basso and Azevedo (2004), and Bigarella and Azevedo (2005).…”

Section: Theoretical and Numerical Formulationsmentioning

confidence: 99%

See 4 more Smart Citations

A study of convective flux schemes for aerospace flows

Bigarella¹,

Azevedo²

2012

J. Braz. Soc. Mech. Sci. & Eng.

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Section: Paper Received 27 July 2009 Paper Accepted 29 November 2011supporting

confidence: 79%

Section: Subsonic Flat Platementioning

confidence: 79%

Section: Discretization Order Of Accuracymentioning

confidence: 99%

Section: Matrix Switched Model (Matd)mentioning

confidence: 99%

Section: Theoretical and Numerical Formulationsmentioning

confidence: 99%

See 3 more Smart Citations

A study of convective flux schemes for aerospace flows

Bigarella¹,

Azevedo²

2012

J. Braz. Soc. Mech. Sci. & Eng.

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Aeroelasticidade transônica de aerofólio com arqueamento variável

Silva¹

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Primeiramente a Deus por todas as bênçãos que Ele me concedeu, pelo seu amor, sua graça e força. Pela sua orientação e por sua presença constante em minha vida. Ao Prof. Assoc. Flávio Donizeti Marques pela orientação, confiança, paciência e sobretudo pela dedicação com que se envolveu neste projeto tornando possível a realização das atividades deste trabalho. Ao Prof. Dr. João L. F. Azevedo e ao grupo do CTA/IAE, em São José dos Campos, por cooperarem diretamente nas atividades do trabalho fornecendo o código CFD e as informações necessárias para utilização e desenvolvimento deste. Ao Prof. Paulo Greco pela estimada ajuda durante o projeto. A todos os amigos, professores e funcionários do Departamento de Engenharia dos Materiais Aeronáutica e Automobilística pela ajuda, paciência e sabedoria, em especial: Claudio, Mauricio, Vinícius, Glauco, Edson, Elizangela... A minha mãe Cristina, meu pai Edmilson e minha irmã Talita pelo amor, apoio, compreensão, carinho e paciência ao longo de todos esses anos. A minha namorada Mariane pela ajuda e incentivo em momentos difíceis. Aos amigos e irmãos da república Dracovolans Mateus Bonamigo, Marcus Vinicius, Thiago Macedo e Luiz Homero pela colaboração, incentivo e auxilio. Ao amigo Diego pela revisão do trabalho. v vi Agradecimentos Aos Irmãos do L&H pelos momentos que compartilhamos e que compreenderam a importância deste trabalho em minha vida, em especial o Pastor Marco, Fernando, Kátia, Walter, Rodrigo e Renato. Ao CNPq pelo apoio financeiro. E por fim a todos aqueles que de alguma forma contribuíram para que este trabalho se tornasse realidade, meu MUITO OBRIGADO. "Porque dEle, por meio dEle e para Ele são todas as coisas. A Ele, pois, a glória eternamente. Amem" (Romanos 11:36).

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Centered and Upwind Multigrid Turbulent Flow Simulations of Launch Vehicle Configurations

Bigarella

Azevedo

Scalabrin

2007

Journal of Spacecraft and Rockets

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The paper discusses results obtained with a finite-volume code that simulates viscous, turbulent flows for 3-D, adaptive, unstructured meshes. The implementation uses a cell-centered, face-based data structure. A fully explicit, second-order accurate, five-stage, Runge-Kutta time stepping scheme is used to perform the time marching of the flow equations. Spatial discretization of the Reynolds-averaged Navier-Stokes equations can be performed with second-order centered or upwind schemes. Automatic grid refinement routines are considered to adapt the original mesh. A sensor based on density gradients selects the volumes to be refined. The code is able to handle tetrahedra, hexahedra, wedges, and pyramids. A full multigrid scheme is available to accelerate convergence to steady state. Coarse grid levels are constructed through an agglomeration procedure. One-and two-equation turbulence models are implemented to include the turbulent effects into the numerical formulation. The mentioned features integrated in one single code allow the Brazilian aerospace program to simulate complex flow conditions for sounding rockets and satellite launch vehicles with accuracy and reasonable computational resources. Good agreement with theoretical or experimental results is obtained with the present numerical tool. Nomenclature a = speed of sound C = convective operator Cp = pressure coefficient D = artificial dissipation operator d = minimum distance to the wall e = total energy per unit volume e i = internal energy f = source term of the multigrid method k = specific turbulent kinetic energy p = static pressure P e = inviscid flux vector P v = viscous flux vector Q = vector of conserved properties q = heat flux vector RHS = right-hand side operator S = absolute value of the mean strain-rate tensor S = area vector S ij = mean strain-rate tensor component T = static temperature u, v, w = Cartesian velocity components V = viscous operator v = Cartesian velocity vector x, y, z = Cartesian coordinates = angle of attack 1 . . . 5 = Runge-Kutta control parameters = ratio of specific heats t = time step = von Karman constant = dynamic viscosity coefficient = kinematic viscosity coefficient = modified Spalart-Allmaras eddy-viscosity coefficient = density = viscous stress tensor = gradient ratio for limiter computation = control volume limiter ! = turbulent dissipation = absolute value of the mean rotation tensor ij = mean rotation tensor component Subscripts f, k = face index i, m = grid control volume indices ' = laminar property L, R = interface left and right properties t = turbulent property 1 = freestream property Superscripts (m) = current grid of the multigrid method n = time instant * = dimensional property

show abstract

Centered and Upwind Multigrid Turbulent Flow Simulations with Applications to Launch Vehicles

Cited by 9 publications

References 18 publications

A study of convective flux schemes for aerospace flows

A study of convective flux schemes for aerospace flows

Aeroelasticidade transônica de aerofólio com arqueamento variável

Centered and Upwind Multigrid Turbulent Flow Simulations of Launch Vehicle Configurations

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