Computational Fluid Dynamics Review 2010

Hafez, M.; Oshima, Koichi; Kwak, Dochan

doi:10.1142/7799

Cited by 8 publications

(9 citation statements)

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“…where C T k = C k are symmetric matrices and v k being the velocity field. The latter analysis by Godunov and Romenski in nineties in a series of papers [32,43,30,42,42,87,21,41] of various equations (ideal MHD equations, nonlinear elasticity, electrodynamics of slowly moving medium, superfluid flow, superconductivity) studied in the books of Landau and Lifshitz [62,61] reveals that for a proper understanding of the structure of the continuum mechanics models it is important to distinguish the Lagrangian and Eulerian frames of reference, and that the original Godunov structure (4) is, in fact, rather inherent to the conservation laws written in the Lagrangian frame, while their Eulerian counterparts are inherently non-conservative time evolutions and have more complicated structure (10).…”

Section: Shtc Framework Symmetric Hyperbolic Equations Well-posednementioning

confidence: 99%

Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

Peshkov

Pavelka

Romenski

et al. 2018

Continuum Mech. Thermodyn.

205

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SpoilerContinuum mechanics with dislocations, with the Cattaneo type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov type system of the first order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time reversible part of the governing equations is mathematically expressed in the former formulation as degeneracy of the Hamiltonian structure and in the latter formulation as the existence of a companion conservation law. In both formulations the time irreversible part represents gradient dynamics. The Godunov type formulation brings the mathematical rigor (the well-posedness of the Cauchy initial value problem) and the possibility to discretize while keeping the physical content of the governing equations (the Godunov finite volume discretization).

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Section: Shtc Framework Symmetric Hyperbolic Equations Well-posednementioning

confidence: 99%

Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

Peshkov

Pavelka

Romenski

et al. 2018

Continuum Mech. Thermodyn.

205

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“…Existence of the Lagrangian coordinates ξ a is a mathematical idealization and their practical use for general fluid-like motion is usually very problematic. Therefore, our unified approach to fluids and solids [28,16] relies on the reformulation of governing equations (6) in the Eulerian frame and later, on the replacement of the integrable (global) deformation field ξ a µ by the nonintegrable (local) distortion field A a µ which can be seen as a local basis tetrad (or non-holonomic basis tetrad). Therefore, in this section, we formulate equations of motion in the Eulerian frame which are obtained from the Lagrangian governing equations (6) by changing the unknowns ξ a → x µ , see details in [27].…”

Section: Eulerian Equations Of Motionmentioning

confidence: 99%

“…The lack of formulations of macroscopic equations for irreversible dynamics of viscous heatconducting and resistive media compatible with the causality principle of Einstein's special relativity and the Euler-Lagrange structure of general relativity (GR) is a long lasting problem [1,2,3]. In this paper, we propose a possible solution to this problem in the framework of Symmetric Hyperbolic and Thermodynamically Compatible (SHTC) equations [4,5,6,7,8,9]. Such an approach is not relying on postulates of equilibrium irreversible thermodynamics but treats irreversible processes from the non-equilibrium standpoint.…”

mentioning

confidence: 99%

A new continuum model for general relativistic viscous heat-conducting media

Romenski

Peshkov

Dumbser

et al. 2020

Phil. Trans. R. Soc. A.

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The lack of formulation of macroscopic equations for irreversible dynamics of viscous heat-conducting media compatible with the causality principle of Einstein’s special relativity and the Euler–Lagrange structure of general relativity is a long-lasting problem. In this paper, we propose a possible solution to this problem in the framework of SHTC equations. The approach does not rely on postulates of equilibrium irreversible thermodynamics but treats irreversible processes from the non-equilibrium point of view. Thus, each transfer process is characterized by a characteristic velocity of perturbation propagation in the non-equilibrium state, as well as by an intrinsic time/length scale of the dissipative dynamics. The resulting system of governing equations is formulated as a first-order system of hyperbolic equations with relaxation-type irreversible terms. Via a formal asymptotic analysis, we demonstrate that classical transport coefficients such as viscosity, heat conductivity, etc., are recovered in leading terms of our theory as effective transport coefficients. Some numerical examples are presented in order to demonstrate the viability of the approach. This article is part of the theme issue ‘Fundamental aspects of nonequilibrium thermodynamics’.

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“…The visualization of acoustic energy flow in real-life acoustic 3D space fields can be explain many particulars energetic effects (scattering, vortex flow, shielding area, etc. ), concerning the areas in which it is difficult to make numerical modeling and analysis with the CFD-FSI-CAA methods [1][2][3].…”

Section: Sound Intensity and Flow Visualizationsmentioning

confidence: 99%

“…The simultaneous obtainment of the aerodynamic and acoustic field from the compressible Navier-Stokes equations in made possible by the use of very accurate algorithms and of quiet boundary conditions [3]. This can provide further insights into the noise-generation mechanism.…”

Section: Some Remarks About Numerical Aeroacoustic Modelingmentioning

confidence: 99%

An Acoustics Intensity Based Investigation οf the Energy Flow Over the Barriers

Weyna

2010

Acta Phys. Pol. A

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Many of theoretical research of the acoustics fields provides useful information about pressure fields, but none currently offers a full mapping of the acoustic energy flow (vectorial effects) in front and back of any scattering systems working in 3D real environmental conditions. Interference, diffraction and scattering of waves made the real field very complex and difficult to the theoretical modelling. This is one of the reasons why the experimental investigations of acoustic fields using sound intensity (SI) technique are so effective and serviceable methods. The visualization of acoustic energy flow in real-life acoustic 3D space fields can explain many particulars energetic effects (perturbations and vortex flow, effects of scattering in direct and near field, etc.), concerning the areas in which it is difficult to make numerical modeling and analysis with the CFD-FSI-CAA simulation methods. The sound intensity image represents a more accurate and efficient information compare to the spatial sound fields modelled. The article presents the application of SI technique to graphic presentation of spatial distribution the acoustic energy flow over the barriers of various geometrical shapes structures located in a three-dimensional space. As the results of research, the graphic analysis of the sound intensity flux in 2D and 3D space is show. Visualisation of research results is shown in the form of intensity streamlines in space and as a shape of flow wave or isosurface in three-dimensional space. Numerous examples illustrate the application of the SI measurement for practical problems at the vibroacoustical diagnostic and noise abatement, as well as to the validation of results of CFD/CAA numerical modelling. The differences, if appearance, mainly result from the fact that theoretical forecasting uses far too big simplifications or that it is impossible to obtain proper data on real physical features of the tested area and structures.

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Computational Fluid Dynamics Review 2010

Cited by 8 publications

References 0 publications

Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

Continuum mechanics and thermodynamics in the Hamilton and the Godunov-type formulations

A new continuum model for general relativistic viscous heat-conducting media

An Acoustics Intensity Based Investigation οf the Energy Flow Over the Barriers

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