MRT lattice Boltzmann method for 2D flows in curvilinear coordinates

Budinski, Ljubomir

doi:10.1016/j.compfluid.2014.03.007

Cited by 19 publications

(12 citation statements)

References 35 publications

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“…In this regime, the analytic profiles can be recovered using the H(2; 3) × H(2; 3) model (employing 3 × 3 = 9 velocities), which is just the equivalent of the widely-used D2Q9 model employed in Refs. [45,53]. However, the vielbein formaism allows only one node to be used in the ϕ direction, thus bringing an improvement in the computational efficiency of several orders of magnitude compared to the implementations presented in Refs.…”

Section: Low Mach Flowsmentioning

confidence: 99%

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Lattice Boltzmann models based on the vielbein formalism for the simulation of flows in curvilinear geometries

Busuioc

Ambruş

2019

Phys. Rev. E

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In this paper, we consider the Boltzmann equation with respect to orthonormal vielbein fields in conservative form. This formalism allows the use of arbitrary coordinate systems to describe the space geometry, as well as of an adapted coordinate system in the momentum space, which is linked to the physical space through the use of vielbeins. Taking advantage of the conservative form, we derive the macroscopic equations in a covariant tensor notation, and show that the hydrodynamic limit can be obtained via the Chapman-Enskog expansion in the Bhatnaghar-Gross-Krook (BGK) approximation for the collision term. We highlight that in this formalism, the component of the momentum which is perpendicular to some curved boundary can be isolated as a separate momentum coordinate, for which the half-range Gauss-Hermite quadrature can be applied. We illustrate the capabilities of this formalism by considering two applications. The first one is the circular Couette flow between rotating coaxial cylinders, for which benchmarking data is available for all degrees of rarefaction, from the hydrodynamic to the ballistic regime. The second application concerns the flow in a gradually expanding channel. We employ finite-difference lattice Boltzmann models based on half-range Gauss-Hermite quadratures for the implementation of diffuse reflection, together with the fifth order WENO and third-order TVD Runge-Kutta numerical methods for the advection and

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Section: Low Mach Flowsmentioning

confidence: 99%

“…The lattice Boltzmann implementations employed in Refs. [45,53] are validated only in the hydrodynamic regime at small Mach numbers and employ the D2Q9 model (employing 9 velocities). Our scheme is capable of recovering this regime also with 9 velocities.…”

Section: G Performance Analysismentioning

confidence: 99%

Lattice Boltzmann models based on the vielbein formalism for the simulation of flows in curvilinear geometries

Busuioc

Ambruş

2019

Phys. Rev. E

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“…If Smoothed Particle Hydrodynamics (SPH) based methods prove to offer satisfactory results in slowly varying flow as the standard grid-based methods, then it can reasonably be stated that future natural watercourses flow modelling techniques should build upon this method. The importance of numerical modelling of open channel flow in hydraulic engineering is reflected upon by a great number of developed numerical models and approaches [1,[5][6][7][8]. Various authors, aiming for the same goal (a more accurate and practical mechanism for predicting floods, flow domains, hydraulic effect on structures, etc.)…”

Section: Introductionmentioning

confidence: 99%

“…The first part is the advection step: (5) which is followed by the second, combined propagation and diffusion step: (6) Eqs. (6) and include the remaining parts of the mass and momentum conservation eqs. (2).…”

Section: Telemac-2d Codementioning

confidence: 99%

Different approaches to two-dimensional numerical modelling of natural watercourses

2018

JCE

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Different approaches to two-dimensional numerical modelling of natural watercoursesResults obtained by analysis of three different approaches to numerical modelling of open watercourses are presented in the paper. Two examples of flow, uniform flow on the physical model of a curve at the Tisza River and nonuniform flow at the Danube River, are analysed. Standard error analysis has revealed that results of the similar order of magnitude are obtained in implementation of two numerical methods in which computational grids are used, while the method in which computational grid is not used, i.e. the smoothed particle hydrodynamics method, requires further improvements to enable successful modelling of the gradually variable flow. Key words:2D flow, finite element method, finite difference method, smoothed particle hydrodynamics method Pregledni rad Zoltan Horvat, Mirjana Horvat, Nikola Rosić, Budo Zindović, Radomir Kapor Različiti pristupi dvodimenzionalnom numeričkom modeliranju prirodnih vodotoka U radu su prikazani rezultati analize tri različita pristupa numeričkom modeliranju otvorenih vodotoka. Analizirana su dva primjera strujanja, jednoliko strujanje na fizikalnom modelu krivine na rijeci Tisi i nejednoliko strujanje na rijeci Dunavu. Analiza standardne pogreške pokazala je da se upotrebom dviju numeričkih metoda u kojima se koriste računske mreže dobivaju rezultati istog reda točnosti, dok metoda u kojoj se ne koristi računska mreža, metoda hidrodinamike izglađenih čestica, zahtijeva daljnja poboljšanja kako bi se uspješno modeliralo postupno promjenjivo strujanje.

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“…One way to solve this problem is to use nonuniform lattices. In recent years, different methods have been developed to extend the LBM on a nonuniform mesh, including the interpolation-supplemented scheme (ISLBE) [16], grid refinement scheme [17][18][19], dynamically adaptive grids for shallow water simulations [20], and the MRT-LBM for transformed equations in a curvilinear coordinates system [21].…”

Section: Introductionmentioning

confidence: 99%

Application of a Steady Meandering River with Piers Using a Lattice Boltzmann Sub-Grid Model in Curvilinear Coordinate Grid

Chen

Zhao

Huang

2018

Water

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Abstract:A sub-grid multiple relaxation time (MRT) lattice Boltzmann model with curvilinear coordinates is applied to simulate an artificial meandering river. The method is based on the D2Q9 model and standard Smagorinsky sub-grid scale (SGS) model is introduced to simulate meandering flows. The interpolation supplemented lattice Boltzmann method (ISLBM) and the non-equilibrium extrapolation method are used for second-order accuracy and boundary conditions. The proposed model was validated by a meandering channel with a 180 • bend and applied to a steady curved river with piers. Excellent agreement between the simulated results and previous computational and experimental data was found, showing that MRT-LBM (MRT lattice Boltzmann method) coupled with a Smagorinsky sub-grid scale (SGS) model in a curvilinear coordinates grid is capable of simulating practical meandering flows.

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MRT lattice Boltzmann method for 2D flows in curvilinear coordinates

Cited by 19 publications

References 35 publications

Lattice Boltzmann models based on the vielbein formalism for the simulation of flows in curvilinear geometries

Lattice Boltzmann models based on the vielbein formalism for the simulation of flows in curvilinear geometries

Different approaches to two-dimensional numerical modelling of natural watercourses

Application of a Steady Meandering River with Piers Using a Lattice Boltzmann Sub-Grid Model in Curvilinear Coordinate Grid

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