Numerical Simulation of Melting with Natural Convection Based on Lattice Boltzmann Method and Performed with CUDA Enabled GPU

Gong, Wei; Johannes, Kévyn; Kuznik, Frédéric

doi:10.4208/cicp.2014.m350

Cited by 8 publications

(3 citation statements)

References 34 publications

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“…For a comprehensive review of models for phase-change problems with convection, see Kowalewski and Gobin (2004). Note that a different category of models was recently suggested in the literature, based on the Lattice Boltzmann Method (Luo et al, 2015;Gong et al, 2015). Such methods based on non-deterministic models are not discussed in this introduction.…”

Section: Introductionmentioning

confidence: 99%

A finite-element toolbox for the simulation of solid–liquid phase-change systems with natural convection

Rakotondrandisa

Sadaka

Danaila

2020

Computer Physics Communications

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We present and distribute a new numerical system using classical finite elements with mesh adaptivity for computing two-dimensional liquid-solid phase-change systems involving natural convection. The programs are written as a toolbox for FreeFem++ (www3.freefem.org), a free finite-element software available for all existing operating systems. The code implements a single domain approach. The same set of equations is solved in both liquid and solid phases: the incompressible Navier-Stokes equations with Boussinesq approximation for thermal effects. This model describes naturally the evolution of the liquid flow which is dominated by convection effects. To make it valid also in the solid phase, a Carman-Kozeny-type penalty term is added to the momentum equations. The penalty term brings progressively (through an artificial mushy region) the velocity to zero into the solid. The energy equation is also modified to be valid in both phases using an enthalpy (temperature-transform) model introducing a regularized latent-heat term. Model equations are discretized using Galerkin triangular finite elements. Piecewise quadratic (P2) finite-elements are used for the velocity and piecewise linear (P1) for the pressure. For the temperature both P2 or P1 discretizations are possible. The coupled system of equations is integrated in time using a second-order Gear scheme. Non-linearities are treated implicitly and the resulting discrete equations are solved using a Newton algorithm. An efficient mesh adaptivity algorithm using metrics control is used to adapt the mesh every time step. This allows us to accurately capture multiple solid-liquid interfaces present in the domain, the boundary-layer structure at the walls and the unsteady convection cells in the liquid. We present several validations of the toolbox, by simulating benchmark cases of increasing difficulty: natural convection of air, natural convection of water, melting of a phase-change material, a melting-solidification cycle, and, finally, a water freezing case. Other similar cases could be easily simulated with this toolbox, since the code structure is extremely versatile and the syntax very close to the mathematical formulation of the model.

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Section: Introductionmentioning

confidence: 99%

A finite-element toolbox for the simulation of solid–liquid phase-change systems with natural convection

Rakotondrandisa

Sadaka

Danaila

2020

Computer Physics Communications

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“…Front tracking or front fixing deforming-grid methods (e. g. Stella and Giangi (2004); Tenchev et al (2005)) would obviously introduce an algorithmic complexity penalizing parallel computing performances. Note that a different category of models was recently suggested in the literature, based on the Lattice Boltzmann Method (Luo et al, 2015;Gong et al, 2015). Such methods based on non-deterministic models are also well adapted for parallel computations.…”

Section: Introductionmentioning

confidence: 99%

Parallel finite-element codes for the simulation of two-dimensional and three-dimensional solid–liquid phase-change systems with natural convection

Sadaka

Rakotondrandisa

Tournier

et al. 2020

Computer Physics Communications

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We present and distribute a FreeFem++ Toolbox for the parallel computing of twoor three-dimensional liquid-solid phase-change systems involving natural convection. FreeFem++ (www.freefem.org) is a free finite-element software available for all existing operating systems. We use the recent library ffddm that makes available in FreeFem++ state-of-the-art scalable Schwarz domain decomposition methods (DDM). The single domain approach used in our previous contribution [A. Rakotondrandisa, G. Sadaka, I. Danaila, A finite-element Toolbox for the simulation of solid-liquid phase-change systems with natural convection, Computer Physics Communications, Vol. 253, p. 107188, 2020] is adapted for the use of the DDM method. As a result, the computational time is considerably reduced for 2D configurations and furthermore 3D problems become affordable. The numerical method is based on an enthalpy-porosity model. The same set of equations is solved in both liquid and solid phases: the incompressible Navier-Stokes equations with Boussinesq approximation for thermal effects. A Carman-Kozeny-type penalty term is added to the momentum equations to bring progressively the velocity to zero into the solid. Model equations are discretized using Galerkin triangular or tetrahedral finite elements. The coupled system of equations is integrated in time using a second-order Gear implicit scheme. The resulting discrete equations are solved using a Newton algorithm. The DDM approach is based on an overlapping Schwarz method. The mesh is first split in subdomains using Scotch or Metis libraries. The final linear system is then solved in parallel using a GMRES Krylov method, with a Restricted Additive Schwarz (RAS) preconditioner. The mesh is adapted during the computation using metrics control. The 3D-mesh adaptivity uses the mmg (www.mmgtools.org) open source library. Parallel 2D and 3D computations of benchmark cases of increasing difficulty are presented: natural convection of air, natural convection of water, melting or solidification of a phase-change material, and, finally, a water freezing case. For each case, careful validations are provided and the performance of the code is assessed. The robustness of the Toolbox in 3D is also demonstrated by adapting the number of processors to the number of tetrahedra, which can considerably vary after the mesh adaptation.

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“…Hong et al performed three‐dimensional LBM comparative calculations on single‐GPU and multi‐GPU of GTX Titan, Tesla C2050, and M2070. Gong et al simulated the natural convection of melted phase transitions based on GPU computations using LBM. Łaniewski‐Wołłk and Rokicki presented a topology optimization technique applicable to a broad range of flow design problems.…”

Section: Introductionmentioning

confidence: 99%

Compressible lattice Boltzmann simulations on high‐performance and low‐cost GeForce GPU

Qiu

Wang

Zhu

et al. 2019

Concurrency and Computation

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The feasibility of compressible lattice Boltzmann simulations on high-performance and low-cost NVIDIA GeForce GPU is studied to enhance computational efficiency of compressible lattice Boltzmann by using much cheaper computing hardware. The NVIDIA GeForce GTX 1080 GPU, which has similar single precision operation computing performance with NVIDIA scientific computational Tesla K80 GPU and much lower price (seven to ten times) than the latter, is used in this work. The problem of GeForce GPUs is with low double precision operation performance and lack of error-correcting code memory, which will influence the accuracy of compressible lattice Boltzmann simulations. To evaluate its feasibility, the double-distribution-function lattice Boltzmann method is adopted for compressible fluid flows. Three typical compressible problems are tested, ie, the Riemann problem, the regular shock reflection problem, and the supersonic boundary layer problem. The results by GeForce GPU with single precision operation have numerical fluctuations in the simulations with shock waves. Moreover, GeForce GPUs have similar numerical accuracy with CPUs in the regular shock reflection problem and supersonic boundary layer problem. KEYWORDS compressible flows, GPU, lattice Boltzmann method, parallel computing, shock waves INTRODUCTIONThe lattice Boltzmann method (LBM) 1,2 is a promising mesoscopic computational fluid dynamic method. It has been widely applied to various incompressible fluid flow problems, 3-7 and shows great potential for complex phenomena due to its mesoscopic features and highly efficient parallel computing. 8,9 The special streaming-collision scheme and the equilibrium distribution function of the standard LBM make it difficult to describe compressible fluid flows, which are ubiquitous in explosion physics, aerophysics, astrophysics, etc. The solving scheme and the equilibrium distribution function need to be developed for a compressible LBM. The finite-difference scheme, which can solve the problem of the streaming-collision scheme, is popular in the compressible LBM. Kataoka and Tsutahara 10 proposed a compressible model for Navier-Stokes equations, which has an adjustable specific heat ratio. Watari 11 also proposed a model for Navier-Stokes with a flexible specific heat ratio. They are within the low Mach number limit. Qu et al 12 established a lattice Boltzmann (LB) model for inviscid compressible flows, in which a circular function is applied instead of the conventional Maxwellian distribution function. This model has ability for simulation of compressible flows at a high Mach number. Li et al 13,14 introduced Qu et al's model into a coupled double-distribution-function (DDF) LB scheme for compressible flows with adjustable specific heat ratio and Prandtl number. Wang et al 15 presented another DDF LB model for compressible flows with a different total energy distribution function. Chen et al 16,17 proposed a multiple-relaxation-time (MRT) LB model for compressible flows. Gan et al 18 presented a simple and general ap...

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Numerical Simulation of Melting with Natural Convection Based on Lattice Boltzmann Method and Performed with CUDA Enabled GPU

Cited by 8 publications

References 34 publications

A finite-element toolbox for the simulation of solid–liquid phase-change systems with natural convection

A finite-element toolbox for the simulation of solid–liquid phase-change systems with natural convection

Parallel finite-element codes for the simulation of two-dimensional and three-dimensional solid–liquid phase-change systems with natural convection

Compressible lattice Boltzmann simulations on high‐performance and low‐cost GeForce GPU

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