Modified kinetic flux vector splitting (m-KFVS) method for compressible flows

Anil, N; Rajan, N.; Deshpande, S. M.

doi:10.1016/j.compfluid.2011.04.005

Cited by 3 publications

(5 citation statements)

References 53 publications

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“…Although the viscous term is necessary for stability, it artificially smears (or spreads) discontinuities in the solution thereby affecting how accurately shocks are captured. The front smearing, also known as numerical diffusion, is typical of most first-order monotone schemes including those that take into account the physics of propagating wave contributions such as flux vector splitting (FVS) methods [46,47], Kinetic-FVS [48,49], Godunov-type schemes [50][51][52][53][54] and other approximate Reimann solvers [55][56][57][58]. However, it is important to note that the later are significantly less diffusive relative to the LxF scheme.…”

Section: Monotone Schemesmentioning

confidence: 99%

Revisiting low-fidelity two-fluid models for gas–solids transport

Adeleke

Adewumi

Ityokumbul

2016

Journal of Computational Physics

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Two-phase gas-solids transport models are widely utilized for process design and automation in a broad range of industrial applications. Some of these applications include proppant transport in gaseous fracking fluids, air/gas drilling hydraulics, coal-gasification reactors and food processing units. Systems automation and real time process optimization stand to benefit a great deal from availability of efficient and accurate theoretical models for operations data processing. However, modeling two-phase pneumatic transport systems accurately requires a comprehensive understanding of gas-solids flow behavior. In this study we discuss the prevailing flow conditions and present a low-fidelity two-fluid model equation for particulate transport. The model equations are formulated in a manner that ensures the physical flux term remains conservative despite the inclusion of solids normal stress through the empirical formula for modulus of elasticity. A new set of RoePike averages are presented for the resulting strictly hyperbolic flux term in the system of equations, which was used to develop a Roe-type approximate Riemann solver. The resulting scheme is stable regardless of the choice of flux-limiter. The model is evaluated by the prediction of experimental results from both pneumatic riser and air-drilling hydraulics systems. We demonstrate the effect and impact of numerical formulation and choice of numerical scheme on model predictions. We illustrate the capability of a low-fidelity one-dimensional two-fluid model in predicting relevant flow parameters in two-phase particulate systems accurately even under flow regimes involving counter-current flow.

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Section: Monotone Schemesmentioning

confidence: 99%

Revisiting low-fidelity two-fluid models for gas–solids transport

Adeleke

Adewumi

Ityokumbul

2016

Journal of Computational Physics

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“…This is not surprising because the Boltzmann level scheme is nothing but a limited combination of CIR and Lax‐Wendroff schemes. Any other combination, eg, modified CIR and Lax‐Wendroff, with proper TVD criteria will give rise to a different limited scheme but this paper intends to explore kinetic version of conventional limiting procedures. Now, using property , scheme can be rewritten as

\begin{matrix} right U_{i}^{{(k)}^{n + 1}} & left = U_{i}^{{(k)}^{n}} - λ [({F X}_{i}^{{(k)}^{+^{n}}} - {F X}_{i - 1}^{{(k)}^{+^{n}}}) + ({F X}_{i + 1}^{{(k)}^{-^{n}}} - {F X}_{i}^{{(k)}^{-^{n}}})] & right \\ right & left - \frac{λ}{2} [Φ (R_{i}^{{(k)}^{+}}) ({F X}_{i + 1}^{{(k)}^{+^{n}}} - {F X}_{i}^{{(k)}^{+^{n}}}) - Φ (R_{i - 1}^{{(k)}^{+}}) ({F X}_{i}^{(k)})] \end{matrix}

…”

Section: Derivation Of Flks Scheme For 1d Euler Equationsmentioning

confidence: 99%

“…The "moment method strategy" used in the derivation of KFVS scheme is the key for the development of many schemes, 12,13,18,20,21,26 some of which are higher-order versions of KFVS. In this work, a new high-resolution scheme based on flux limiting 24 is formulated.…”

Section: Derivation Of Flks Scheme For 1d Euler Equationsmentioning

confidence: 99%

“…Several higher‐order versions of KFVS, as already mentioned, reduce the truncation error and probably indirectly improve the pseudocollision effect to tackle the dissipation by obtaining a smaller relaxation time than the CFL time step. Ramesh and Deshpande and Anil et al have formulated modified KFVS schemes which are less dissipative than KFVS. The modified KFVS (m‐KFVS) performs as good as a second‐order scheme while still using stencil for first‐order scheme and hence is very efficient.…”

Section: Introductionmentioning

confidence: 99%

“…Ramesh and Deshpande and Anil et al have formulated modified KFVS schemes which are less dissipative than KFVS. The modified KFVS (m‐KFVS) performs as good as a second‐order scheme while still using stencil for first‐order scheme and hence is very efficient. The dissipation control parameter used in m‐KFVS has been devised using some physical arguments and the scheme performs well in subsonic, supersonic, and hypersonic flow regimes.…”

Section: Introductionmentioning

confidence: 99%

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A new flux‐limiting approach–based kinetic scheme for the Euler equations of gas dynamics

Kumar

Dass

2019

Numerical Methods in Fluids

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Summary This paper proposes a new kinetic‐theory‐based high‐resolution scheme for the Euler equations of gas dynamics. The scheme uses the well‐known connection that the Euler equations are suitable moments of the collisionless Boltzmann equation of kinetic theory. The collisionless Boltzmann equation is discretized using Sweby's flux‐limited method and the moment of this Boltzmann level formulation gives a Euler level scheme. It is demonstrated how conventional limiters and an extremum‐preserving limiter can be adapted for use in the scheme to achieve a desired effect. A simple total variation diminishing criteria relaxing parameter results in improving the resolution of the discontinuities in a significant way. A 1D scheme is formulated first and an extension to 2D on Cartesian meshes is carried out next. Accuracy analysis suggests that the scheme achieves between first‐ and second‐order accuracy as is expected for any second‐order flux‐limited method. The simplicity and the explicit form of the conservative numerical fluxes add to the efficiency of the scheme. Several standard 1D and 2D test problems are solved to demonstrate the robustness and accuracy.

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The Contribution of the Bhatnagar–gross–krook Model to the Development of Rarefied Gas Dynamics in the Early Years of the Space Age

Narasimha

2013

Int. J. Mod. Phys. C

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The advent of the space age in 1957 was accompanied by a sudden surge of interest in rarefied gas dynamics (RGD). The well-known difficulties associated with solving the Boltzmann equation that governs RGD made progress slow but the Bhatnagar–Gross–Krook (BGK) model, proposed three years before Sputnik, turned out to have been an uncannily timely, attractive and fruitful option, both for gaining insights into the Boltzmann equation and for estimating various technologically useful flow parameters. This paper gives a view of how BGK contributed to the growth of RGD during the first decade of the space age. Early efforts intended to probe the limits of the BGK model showed that, in and near both the continuum Euler limit and the collisionless Knudsen limit, BGK could provide useful answers. Attempts were therefore made to tackle more ambitious nonlinear nonequilibrium problems. The most challenging of these was the structure of a plane shock wave. The first exact numerical solutions of the BGK equation for the shock appeared during 1962 to 1964, and yielded deep insights into the character of transitional nonequilibrium flows that had resisted all attempts at solution through the Boltzmann equation. In particular, a BGK weak shock was found to be amenable to an asymptotic analysis. The results highlighted the importance of accounting separately for fast-molecule dynamics, most strikingly manifested as tails in the distribution function, both in velocity and in physical space — tails are strange versions or combinations of collisionless and collision-generated flows. However, by the mid-1960s Monte-Carlo methods of solving the full Boltzmann equation were getting to be mature and reliable and interest in the BGK waned in the following years. Interestingly, it has seen a minor revival in recent years as a tool for developing more effective algorithms in continuum computational fluid dynamics, but the insights derived from the BGK for strongly nonequilibrium flows should be of lasting value.

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Modified kinetic flux vector splitting (m-KFVS) method for compressible flows

Cited by 3 publications

References 53 publications

Revisiting low-fidelity two-fluid models for gas–solids transport

Revisiting low-fidelity two-fluid models for gas–solids transport

A new flux‐limiting approach–based kinetic scheme for the Euler equations of gas dynamics

The Contribution of the Bhatnagar–gross–krook Model to the Development of Rarefied Gas Dynamics in the Early Years of the Space Age

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