A Computational Method for Eu's Generalized Hydrodynamic Equations of Rarefied and Microscale Gasdynamics

Myong, R.S.

doi:10.1006/jcph.2000.6678

Cited by 96 publications

(44 citation statements)

References 33 publications

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“…Furthermore, the hyperbolicity leads to discontinuous subshock solutions in the shock profile. A variant of the moment method has been proposed by Eu in [13] and is used, e.g., in [31] by Myong. Recently, a 10-moment system has been used by Suzuki and van Leer in [42].…”

Section: Introductionmentioning

confidence: 99%

Two‐Dimensional Bulk Microflow Simulations Based on Regularized Grad’s 13‐Moment Equations

Torrilhon¹

2006

Multiscale Model. Simul.

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Abstract.The newly derived fluid model named regularized 13-moment system (R13) is capable of describing rarefied/microflows with high accuracy due to special modeling of the nonequilibrium dissipation. Explicit two-dimensional equations are presented and discussed and a specialized numerical method derived. In two dimensions evolution equations for nine basic variables need to be solved, including directional temperatures, shear stress, and heat flux. The governing partial differential equations are given in balance law form with relaxation and parabolic dissipation. The numerical method is formulated as a practical and straightforward extension of standard finite volume methods. It focuses on bulk simulations with no boundary in order to provide a building block. As a microflow example the interaction of a shock front with a dense microbubble is considered in which the bubble's diameter is a few mean free paths. The results are compared to the solution of the Navier-Stokes-Fourier system demonstrating the relevance of the new R13 model.

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Section: Introductionmentioning

confidence: 99%

Two‐Dimensional Bulk Microflow Simulations Based on Regularized Grad’s 13‐Moment Equations

Torrilhon¹

2006

Multiscale Model. Simul.

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“…Despite the main concept of the aforementioned conditions was initially proposed by Navier [1], the first corresponding mathematical model was introduced by Maxwell in 1879 [7]; according to this approach the values of slip velocity and temperature are defined with the corresponding normal to the boundary surface gradients [3]. Since then, various studies have been conducted on the prediction of the attitude of rarefied gases,focusing on the utilization of two-or three-dimensional computational fields, structured or unstructured grids, various geometries, etc., [8,9,10,11,12,13]. Furthermore, significant efforts have been exerted for the development of higher-order spatial schemes to increase the accuracy of the final steady-state solution at the region of the solid wall boundaries [14,15,16,17].…”

Section: Introductionmentioning

confidence: 99%

Numerical Analysis of Rarefied Gas Flows Using the Academic CFD Code Galatea

Klothakis¹,

Lygidakis²,

Nikolos³

2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

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Abstract. During the last decades considerable efforts have been exerted for the development of micro air vehicles as well as microelectromechanical systems in general, for a wide range of applications. However, such systems involve microscale rarefied gas flows, which appear to be significantly different comparing to flows at macroscale and continuum regime; it is this the reason the Navier-Stokes equations fail to simulate such phenomena without further modification. To this end, the enhancement of the in-house academic Computational Fluid Dynamics solver Galatea to encounter such simulations is reported in this study. In case of rarefied gas flows and particularly for fluids in slip flow regime (Knudsen number greater than 0.01) the no-slip condition on solid wall surfaces is no longer valid; hence, velocity slip conditions as well as temperature jump ones have to be included instead. Furthermore, to increase accuracy at the same region the second-order accurate spatial slip model of Beskok and Karniadakis has been incorporated, which avoids the numerical difficulties, entailed by the evaluation of the second derivative of slip velocity when complex geometries along with unstructured hybrid grids are encountered. Due to oscillations that might appear, especially during the initial steps of the iterative procedure, a normalization scheme is additionally employed, to allow for the gradual increase of the corresponding slip/jump values. Galatea has been validated against a benchmark test case concerning rarefied laminar flow (inside the slip flow regime) over a wing with a NACA0012 airfoil in different angles of attack. The obtained results were compared with those of a reference solver, and with those obtained with the paralleld open-source kernel SPARTA, based on the Direct Simulation Monte-Carlo method. According to this last approach, the flow domain is divided into a finite number of computational cells, while the required sample macroscopic flow properties are retrieved assuming intermolecular collisions of the simulated particles inside such cells. An excellent agreement was achieved between the results obtained by Galatea and SPARTA as well.

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“…Due to the modelling successes, the interest in computations based on moment equations is vivid, e.g., in [1], [21], [24] and [33]. Computational methods for the R13-system have been proposed in [35] for the initial value problem and in [12] for the boundary value problem.…”

Section: Introductionmentioning

confidence: 99%

Boundary conditions for regularized 13-moment-equations for micro-channel-flows

Torrilhon

Struchtrup

2008

Journal of Computational Physics

153

138

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Boundary conditions are the major obstacle in simulations based on advanced continuum models of rarefied and micro-flows of gases. In this paper we present a theory how to combine the regularized 13-moment-equations derived from Boltzmann's equation with boundary conditions obtained from Maxwell's kinetic accommodation model. While for the linear case these kinetic boundary conditions suffice, we need additional conditions in the non-linear case. They are provided by the bulk solutions obtained after properly transforming the equations while keeping their asymptotic accuracy with respect to Boltzmann's equation.After finding a suitable set of boundary conditions and equations, a numerical method for generic shear flow problems is formulated. Several test simulations demonstrate the stable and oscillation-free performance of the new approach.

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A Computational Method for Eu's Generalized Hydrodynamic Equations of Rarefied and Microscale Gasdynamics

Cited by 96 publications

References 33 publications

Two‐Dimensional Bulk Microflow Simulations Based on Regularized Grad’s 13‐Moment Equations

Two‐Dimensional Bulk Microflow Simulations Based on Regularized Grad’s 13‐Moment Equations

Numerical Analysis of Rarefied Gas Flows Using the Academic CFD Code Galatea

Boundary conditions for regularized 13-moment-equations for micro-channel-flows

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