Steady-State Anderson Accelerated Coupling of Lattice Boltzmann and Navier–Stokes Solvers

Atanasov, Atanas; Uekérmann, Benjamin; Mejía, Carlos A. Pachajoa; Bungartz, Hans‐Joachim; Neumann, Philipp

doi:10.3390/computation4040038

Cited by 5 publications

(3 citation statements)

References 30 publications

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“…The AA algorithm has been widely used in many fields due to its ease of application, fast convergence, good performance in high-dimensional environments, and large computational savings. These application areas include plasma physics (Willert et al, 2014), nonlinear radiation diffusion equations (An et al, 2017), flow problems (Atanasov et al, 2016), geometry (Brezinski et al, 2018), computer graphics (Ouyang et al, 2020), wave propagation (Yang et al, 2020(Yang et al, , 2021, robot localization (Pavlov et al, 2018), K-means clustering (Zhang et al, 2018), computer vision (Scieur et al, 2018, and reinforcement learning (Geist and Scherrer, 2018).…”

Section: Introductionmentioning

confidence: 99%

Least-squares reverse time migration in frequency domain based on Anderson acceleration with QR factorization

Huang,

Qu,

Dong

et al. 2024

Preprint

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Least-squares reverse time migration (LSRTM) has become a popular research topic and has been practically applied in recent years. LSRTM can generate preferable images with high signal-to-noise ratio (SNR), high resolution and balanced amplitude. However, LSRTM is still under the great computational pressure in processing field data. Anderson acceleration (AA) is widely popular for its ease of implementation and reduced computational effort. The QR factorization can be applied to AA to improve computational efficiency. We propose to use AA with QR factorization (AA-QR) for LSRTM in frequency domain to speed up the convergence and save computational cost. Through the numerical experiments using the sunken model, the salt model, and the Marmousi model, we find that the suitable memory size for AA-QR is 10 and the step length of AA-QR can be referred to 5 times 1st iteration step length of steepest descent (SD) method. Compared with SD method, conjugate gradient (CG) method, the limited-momory Broyden–Fletcher–Goldfarb–Shanno (LBFGS) method and AA, AA-QR can converges faster and has better imaging quality. Under noisy condition, AA-QR also can converge well and obtain high-resolution images. AA-QR can be used as an alternative to LBFGS when LSRTM chooses the gradient update algorithm.

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Section: Introductionmentioning

confidence: 99%

Least-squares reverse time migration in frequency domain based on Anderson acceleration with QR factorization

Huang,

Qu,

Dong

et al. 2024

Preprint

View full text Add to dashboard Cite

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“…They include analysis and design optimization of a variety of Stokes flows through capillaries, porous media flows, heat transfer problems under stationary conditions, and since the LB methods are explicit marching in nature, efficient solution techniques need to devised to accelerate their convergence (see e.g. [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43]). A recent review of the literature in the LB approach for such problems can be found in [41,42].…”

Section: Introductionmentioning

confidence: 99%

Galilean-invariant preconditioned central-moment lattice Boltzmann method without cubic velocity errors for efficient steady flow simulations

Hajabdollahi

Premnath

2018

Phys. Rev. E

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Lattice Boltzmann (LB) models used for the computation of fluid flows represented by the Navier-Stokes (NS) equations on standard lattices can lead to non-Galilean-invariant (GI) viscous stress involving cubic velocity errors. This arises from the dependence of their third-order diagonal moments on the first-order moments for standard lattices, and strategies have recently been introduced to restore Galilean invariance without such errors using a modified collision operator involving corrections to either the relaxation times or the moment equilibria. Convergence acceleration in the simulation of steady flows can be achieved by solving the preconditioned NS equations, which contain a preconditioning parameter that can be used to tune the effective sound speed, and thereby alleviating the numerical stiffness. In the present paper, we present a GI formulation of the preconditioned cascaded central-moment LB method used to solve the preconditioned NS equations, which is free of cubic velocity errors on a standard lattice, for steady flows. A Chapman-Enskog analysis reveals the structure of the spurious non-GI defect terms and it is demonstrated that the anisotropy of the resulting viscous stress is dependent on the preconditioning parameter, in addition to the fluid velocity. It is shown that partial correction to eliminate the cubic velocity defects is achieved by scaling the cubic velocity terms in the off-diagonal third-order moment equilibria with the square of the preconditioning parameter. Furthermore, we develop additional corrections based on the extended moment equilibria involving gradient terms with coefficients dependent locally on the fluid velocity and the preconditioning parameter. Such parameter dependent corrections eliminate the remaining truncation errors arising from the degeneracy of the diagonal third-order moments and fully restore Galilean invariance without cubic defects for the preconditioned LB scheme on a standard lattice. Several conclusions are drawn from the analysis of the structure of the non-GI errors and the associated corrections, with particular emphasis on their dependence on the preconditioning parameter. The GI preconditioned central-moment LB method is validated for a number of complex flow benchmark problems and its effectiveness to achieve convergence acceleration and improvement in accuracy is demonstrated.

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“…However, in conventional computational code, it would still be difficult to take the filtration process into consideration, because we must set the complex boundary conditions at the very concave and convex filter substrate. Quite recently, a lattice Boltzmann method (LBM) has been widely used for alternative fluid simulation [7][8][9][10][11][12][13]. Many research papers have been published, especially for simulations in porous media [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Effect of Pore Structure on Soot Deposition in Diesel Particulate Filter

Yamamoto

Sakai

2016

Computation

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Nowadays, in the after-treatment of diesel exhaust gas, a diesel particulate filter (DPF) has been used to trap nano-particles of the diesel soot. However, as there are more particles inside the filter, the pressure which corresponds to the filter backpressure increases, which worsens the fuel consumption rate, together with the abatement of the available torque. Thus, a filter with lower backpressure would be needed. To achieve this, it is necessary to utilize the information on the phenomena including both the soot transport and its removal inside the DPF, and optimize the filter substrate structure. In this paper, to obtain useful information for optimization of the filter structure, we tested seven filters with different porosities and pore sizes. The porosity and pore size were changed systematically. To consider the soot filtration, the particle-laden flow was simulated by a lattice Boltzmann method (LBM). Then, the flow field and the pressure change were discussed during the filtration process.

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Steady-State Anderson Accelerated Coupling of Lattice Boltzmann and Navier–Stokes Solvers

Cited by 5 publications

References 30 publications

Least-squares reverse time migration in frequency domain based on Anderson acceleration with QR factorization

Least-squares reverse time migration in frequency domain based on Anderson acceleration with QR factorization

Galilean-invariant preconditioned central-moment lattice Boltzmann method without cubic velocity errors for efficient steady flow simulations

Effect of Pore Structure on Soot Deposition in Diesel Particulate Filter

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