Kinetic flux vector splitting for euler equations

Mandal, J.C.; Deshpande, S. M.

doi:10.1016/0045-7930(94)90050-7

Cited by 224 publications

(137 citation statements)

References 6 publications

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“…First examples of gas-kinetic schemes can be found in 30 and 28 . In these schemes, in contrast to the commonly used Roe or AUSM fluxes, a local kinetic problem around the cell interfaces is reconstructed in order to calculate the numerical fluxes in the finite volume method.…”

Section: The Bgk-ns Methods and The Unified Gas-kinetic Schemementioning

confidence: 99%

Kinetic Models and Gas Kinetic Schemes for Hybrid Simulation of Partially Rarefied Flows

Colonia

Steijl

Barakos

2015

AIAA Atmospheric Flight Mechanics Conference

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Approaches to predict flow fields that display rarefaction effects incur a cost in computational time and memory considerably higher than methods commonly employed for continuum flows. For this reason, to simulate flow fields where continuum and rarefied regimes coexist, hybrid techniques have been introduced. In the present work analytically defined Gas-Kinetic schemes based on the Shakhov and Rykov models, for monoatomic and diatomic gas flows, respectively, are proposed and evaluated with the aim to be used in the context of hybrid simulations. This should reduce the region where more expensive methods are needed by extending the validity of the continuum formulation. Moreover, since for rarefied gas flows at high velocities it is necessary to take into account the non-equilibrium among the internal degrees of freedom, the extension of the approach to employ diatomic gas models with rotational relaxation is a mandatory first step towards realistic simulations. Compared to previous works of Xu and co-workers the presented scheme is defined directly on the basis of kinetic models which involve a Prandtl number correction. Moreover, the methods are defined fully analytically instead of making use of Taylor expansion for the evaluation of the required derivatives. The scheme has been tested for various test cases and Mach numbers proving to produce reliable predictions in agreement with other approaches for near-continuum flows. Finally, the performance of the scheme, in terms of memory and computational time, compared to discrete velocity methods makes it a compelling alternative in place of more complex methods for hybrid simulations of weakly rarefied flows.

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Section: The Bgk-ns Methods and The Unified Gas-kinetic Schemementioning

confidence: 99%

Kinetic Models and Gas Kinetic Schemes for Hybrid Simulation of Partially Rarefied Flows

Colonia

Steijl

Barakos

2015

AIAA Atmospheric Flight Mechanics Conference

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“…Details about the boundary conditions can be found in the work of Mandal and Deshpande (1994) and Ramesh and Deshpande (2001). …”

Section: Boundary Conditionmentioning

confidence: 99%

Implicit scheme for meshless compressible Euler solver

Singh

Ramesh

Balakrishnan

2015

Engineering Applications of Computational Fluid Mechanics

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In this paper, an implicit scheme is presented for a meshless compressible Euler solver based on the Least Square Kinetic Upwind Method (LSKUM). The Jameson and Yoon's split flux Jacobians formulation is very popular in finite volume methodology, which leads to a scalar diagonal dominant matrix for an efficient implicit procedure . However, this approach leads to a block diagonal matrix when applied to the LSKUM meshless method. The above split flux Jacobian formulation, along with a matrix-free approach, has been adopted to obtain a diagonally dominant, robust and cheap implicit time integration scheme. The efficacy of the scheme is demonstrated by computing 2D flow past a NACA 0012 airfoil under subsonic, transonic and supersonic flow conditions. The results obtained are compared with available experiments and other reliable computational fluid dynamics (CFD) results. The present implicit formulation shows good convergence acceleration over the RK4 explicit procedure. Further, the accuracy and robustness of the scheme in 3D is demonstrated by computing the flow past an ONERA M6 wing and a clipped delta wing with aileron deflection. The computed results show good agreement with wind tunnel experiments and other CFD computations.

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“…For the equilibrium part, this is nothing but the kinetic flux vector splitting introduced by Mandal and Deshpande in [28] for the Euler equations of gas dynamics. We can also use the flux vector splitting of Perthame [31] where the physical equilibrium is replaced in the splitting of Ψ by a compactly supported square-shaped distribution.…”

Section: Micro-macro Model For the General Hydrodynamic Scaling (Sectmentioning

confidence: 99%

“…This ensures that both left and right Maxwellian are well represented on the velocity grid. A second order scheme is used with the kinetic flux vector splitting of [28] for the macroscopic terms with an implicit time disctetization of the collision operator. For the three tests, the kinetic zone is separated from the fluid zone by two left and a right buffer zones of length 1/30.…”

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confidence: 99%

Diffusion approximation

Gass¹,

Harris²

2001

Encyclopedia of Operations Research and Management Science

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Abstract.This paper presents a general methodology to design macroscopic fluid models that take into account localized kinetic upscaling effects. The fluid models are solved in the whole domain together with a localized kinetic upscaling that corrects the fluid model wherever it is necessary. This upscaling is obtained by solving a kinetic equation on the non-equilibrium part of the distribution function. This equation is solved only locally and is related to the fluid equation through a downscaling effect. The method does not need to find an interface condition as do usual domain decomposition methods to match fluid and kinetic representations. We show our approach applies to problems that have a hydrodynamic time scale as well as to problems with diffusion time scale. Simple numerical schemes are proposed to discretized our models, and several numerical examples are used to validate the method.

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Kinetic flux vector splitting for euler equations

Cited by 224 publications

References 6 publications

Kinetic Models and Gas Kinetic Schemes for Hybrid Simulation of Partially Rarefied Flows

Kinetic Models and Gas Kinetic Schemes for Hybrid Simulation of Partially Rarefied Flows

Implicit scheme for meshless compressible Euler solver

Diffusion approximation

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