Order of accuracy study of unstructured grid finite volume upwind schemes

Azevedo, João Luiz F.; Silva, Luı́s Fernando Figueira da; Strauss, Daniel

doi:10.1590/s1678-58782010000100011

Cited by 6 publications

(3 citation statements)

References 19 publications

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“…For instance, the effect of the spatial discretization scheme, for the convective terms, is a very important aspect which has not been discussed at all in the present paper. A detailed discussion of numerical errors associated with the spatial discretization schemes can be seen in Azevedo, Figueira da Silva and Strauss (2010).…”

Section: Blunt Body Results Using the Hybrid Formulationmentioning

confidence: 99%

A new particle-like method for high-speed flows with chemical non-equilibrium

Guzzo¹,

Azevedo²

2010

JATM

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The present work is concerned with the numerical simulation of hypersonic blunt body flows with chemical non-equilibrium. New theoretical and numerical formulations for coupling the chemical reaction to the fluid dynamics are presented and validated. The fluid dynamics is defined for a stationary unstructured mesh and the chemical reaction process is defined for "finite quantities" moving through the stationary mesh. The fluid dynamics is modeled by the Euler equations and the chemical reaction rates by the Arrhenius law. Ideal gases are considered. The thermodynamical data are based on JANNAF tables and Burcat's database. The algorithm proposed by Liou, known as AUSM+, is implemented in a cell-centered based finite volume method and in an unstructured mesh context. Multidimensional limited MUSCL interpolation method is used to perform property reconstructions and to achieve second-order accuracy in space. The minmod limiter is used. The second order accuracy, five stage, Runge-Kutta time-stepping scheme is employed to perform the time march for the fluid dynamics. The numerical code VODE, which is part of the CHEMKIN-II package, is adopted to perform the time integration for the chemical reaction equations. The freestream reacting fluid is composed of H 2 and air at the stoichiometric ratio. The emphasis of the present paper is on the description of the new methodology for handling the coupling of chemical and fluid mechanic processes, and its validation by comparison with the standard time-splitting procedure. The configurations considered are the hypersonic flow over a wedge, in which the oblique detonation wave is induced by an oblique shock wave, and the hypersonic flow over a blunt body. Differences between the solutions obtained with each formulation are presented and discussed, including the effects of grid refinement in each case. The primary objective of such comparisons is the validation of the proposed methodology. Moreover, for the hypersonic flow over a blunt body, solutions obtained for two meshes are shown, compared and analyzed. The numerical solutions are also compared with experimental data.

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Section: Blunt Body Results Using the Hybrid Formulationmentioning

confidence: 99%

A new particle-like method for high-speed flows with chemical non-equilibrium

Guzzo¹,

Azevedo²

2010

JATM

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“…Some flux vector splitting schemes such as the van Leer [3] and Liou AUSM schemes [4] are implemented along with Roe's flux difference splitting scheme [5] and tested for second-order accuracy with a MUSCL reconstruction [6]. However, the nominally second-order schemes presented results with an order of accuracy smaller than the expected in the solutions for unstructured grids [7]. Aside from this fact, it is well known that total-variation-diminishing (TVD) schemes have their order of accuracy reduced to first order in the presence of discontinuities, due to the effect of limiters.…”

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Implicit High-Order Spectral Finite Volume Method for Inviscid Compressible Flows

et al. 2010

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The present work has the objective of demonstrating the capabilities of a spectral finite volume scheme implemented in a cell-centered finite volume context for unstructured meshes. The two-dimensional Euler equations are considered to represent the flows of interest. The spatial discretization scheme is developed to achieve high resolution for flow problems governed by hyperbolic conservation laws. Roe's flux difference splitting method is used as the numerical approximate Riemann solver. Several applications are performed in order to assess the method capability compared to data available in the literature and also compared to an weighted essentially nonoscillatory scheme. There is good agreement with the comparison data, and efficiency improvements over the weighted essentially nonoscillatory method are observed. The features of the present methodology include an implicit timemarching algorithm; second-, third-, and fourth-order spatial resolution; exact high-order domain boundary representation; and a hierarchical moment limiter to treat flow solution discontinuities.

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“…Alguns esquemas abordados na literatura, os esquemas upwind, como os métodos de separação de vetores de fluxo [Van Leer, 1982][Liou, 1996, foram propostos e testa-dos utilizando-se o esquema de reconstrução MUSCL [Anderson, 1963] linear, gerando discretizações com segunda ordem de precisão espacial. Porém, existe uma redução na ordem de precisão efetiva destes esquemas de segunda ordem de precisão nominal quando têm-se malhas não estruturadas [Azevedo et al, 2010]. Além disso, reconstruções do tipo MUSCL levam a esquemas de redução de variação total TVD, onde esquemas com essa propriedade mostram uma redução da ordem de precisão na presença de descontinuidades causadas pela utilização dos limitadores de fluxo [Boris andBook, 1973][van Leer, 1974].…”

Section: Considerações Iniciaisunclassified

Estruturas de dados topológicas aplicadas em simulações de escoamentos compressíveis utilizando volumes finitos e métodos de alta ordem

Barbosa¹

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Order of accuracy study of unstructured grid finite volume upwind schemes

Cited by 6 publications

References 19 publications

A new particle-like method for high-speed flows with chemical non-equilibrium

A new particle-like method for high-speed flows with chemical non-equilibrium

Implicit High-Order Spectral Finite Volume Method for Inviscid Compressible Flows

Estruturas de dados topológicas aplicadas em simulações de escoamentos compressíveis utilizando volumes finitos e métodos de alta ordem

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