Quadrature-based moment closures for non-equilibrium flows: Hard-sphere collisions and approach to equilibrium

Icardi, Matteo; Asinari, Pietro; Marchisio, Daniele; Izquierdo, Salvador; Fox, Rodney O.

doi:10.1016/j.jcp.2012.07.012

Cited by 7 publications

(4 citation statements)

References 46 publications

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“…where last step follows from (30), and proves consistency. Moreover, if we now assume that ∆t = M ∆z for some M > 0 then last equality yields that local truncation error is third order both in space and in time, and this proves the claim.…”

mentioning

confidence: 63%

“…A quadrature-based method for Richards' equation. Here the quadrature-based scheme is presented, on the heels of other recent papers on PDEs methods (see for instance [30]). In [39], an integral formulation of Richards' equation is obtained after applying the Gauss-Green theorem to (1).…”

mentioning

confidence: 99%

“…and ν z (t, z) = ∂ν ∂z (t, z). If we now evaluate (15) at the exact solution to (30) and resort to first order Taylor expansions, letting µ j t,i := µ(t j , z i ) and ν j i := ν(t j , z i ) and ν j z,i := ν z (t j , z i ) for suitable i, j, we get that…”

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confidence: 99%

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A quadrature-based scheme for numerical solutions to Kirchhoff transformed Richards' equation

Berardi

Difonzo

2022

JCD

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<p style='text-indent:20px;'>In this work we propose a new numerical scheme for solving Richards' equation within Gardner's framework and accomplishing mass conservation. In order to do so, we resort to Kirchhoff transformation of Richards' equation in mixed form, so to exploit specific Gardner model features, obtaining a linear second order partial differential equation. Then, leveraging the mass balance condition, we integrate both sides of the equation over a generic grid cell and discretize integrals using trapezoidal rule. This approach provides a linear non-homogeneous initial value problem with respect to the Kirchhoff transform variable, whose solution yields the sought numerical scheme. Such a scheme is proven to be <inline-formula><tex-math id="M1">\begin{document}$ l^{2} $\end{document}</tex-math></inline-formula>-stable and convergent to the exact solution under suitably conditions on step-sizes, retaining the order of convergence from the underlying quadrature formula.</p>

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confidence: 63%

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confidence: 99%

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A quadrature-based scheme for numerical solutions to Kirchhoff transformed Richards' equation

Berardi

Difonzo

2022

JCD

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“…Therefore, developing approximate and simplified kinetic models which can preserve the most relevant features of Boltzmann equation is currently an important and essential attempt [6][7][8][17][18][19][20][21][22][23]. Examples in this class are the discrete ordinate method [6][7][8]24], the unified gas kinetic scheme (UGKS) and the discrete UGKS [25][26][27][28][29][30][31][32], the regularized 13 (26) moment approach [33][34][35][36][37], the quadrature method of moments [38][39][40], the lattice Boltzmann kinetic method (LBKM) [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56]…”

Section: Introductionmentioning

confidence: 99%

Discrete Boltzmann trans-scale modeling of high-speed compressible flows

Gan

Zhang

et al. 2018

Phys. Rev. E

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We present a general framework for constructing trans-scale discrete Boltzmann models (DBMs) for high-speed compressible flows ranging from continuum to transition regime. This is achieved by designing a higher-order discrete equilibrium distribution function that satisfies additional nonhydrodynamic kinetic moments. To characterize the thermodynamic nonequilibrium (TNE) effects and estimate the condition under which the DBMs at various levels should be used, two measures are presented: (i) the relative TNE strength, describing the relative strength of the (N+1)th order TNE effects to the Nth order one; (ii) the TNE discrepancy between DBM simulation and relevant theoretical analysis. Whether or not the higher-order TNE effects should be taken into account in the modeling and which level of DBM should be adopted is best described by the relative TNE intensity and/or the discrepancy rather than by the value of the Knudsen number. As a model example, a two-dimensional DBM with 26 discrete velocities at Burnett level is formulated, verified, and validated.

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Quadrature-Based Moment Methods for Polydisperse Multiphase Flows

Fox

2014

Stochastic Methods in Fluid Mechanics

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Quadrature-based moment closures for non-equilibrium flows: Hard-sphere collisions and approach to equilibrium

Cited by 7 publications

References 46 publications

A quadrature-based scheme for numerical solutions to Kirchhoff transformed Richards' equation

A quadrature-based scheme for numerical solutions to Kirchhoff transformed Richards' equation

Discrete Boltzmann trans-scale modeling of high-speed compressible flows

Quadrature-Based Moment Methods for Polydisperse Multiphase Flows

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