Finite volume TVD formulation of lattice Boltzmann simulation on unstructured mesh

Patil, Dhiraj V.; Lakshmisha, K.N.

doi:10.1016/j.jcp.2009.04.008

Cited by 106 publications

(79 citation statements)

References 60 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Patil and Lakshmisha (2009) present an alternative approach to solving the lattice Boltzmann equation on 2D unstructured meshes. Instead of using vertex-centred finite volume method, they choose the elements (triangles) as their control volumes, which is beneficial for the implementation and the performance, as it greatly simplifies the structure of the streaming and collision matrices, as well as the solid boundary conditions.…”

Section: Discussionmentioning

confidence: 99%

Detailed analysis of the lattice Boltzmann method on unstructured grids

Misztal

Hernández-García

Matin

et al. 2015

Journal of Computational Physics

View full text Add to dashboard Cite

The lattice Boltzmann method has become a standard for efficiently solving problems in fluid dynamics. While unstructured grids allow for a more efficient geometrical representation of complex boundaries, the lattice Boltzmann methods is often implemented using regular grids. Here we analyze two implementations of the lattice Boltzmann method on unstructured grids, the standard forward Euler method and the operator splitting method. We derive the evolution of the macroscopic variables by means of the Chapman-Enskog expansion, and we prove that it yields the Navier-Stokes equation and is first order accurate in terms of the temporal discretization and second order in terms of the spatial discretization. Relations between the kinetic viscosity and the integration time step are derived for both the Euler method and the operator splitting method. Finally we suggest an improved version of the bounce-back boundary condition. We test our implementations in both standard benchmark geometries and in the pore network of a real sample of a porous rock.

show abstract

Section: Discussionmentioning

confidence: 99%

Detailed analysis of the lattice Boltzmann method on unstructured grids

Misztal

Hernández-García

Matin

et al. 2015

Journal of Computational Physics

View full text Add to dashboard Cite

show abstract

“…The finite volume LBM implementation in UFS follows that of Ref. [44]. Special procedures and structures map UFS's regular Cartesian velocity grid to the LBM velocity grids.…”

Section: Lattice Boltzmann Methodsmentioning

confidence: 99%

Adaptive kinetic-fluid solvers for heterogeneous computing architectures

Zabelok

Arslanbekov

Kolobov

2015

Journal of Computational Physics

View full text Add to dashboard Cite

Abstract. We show feasibility and benefits of porting an adaptive multi-scale kinetic-fluid code to CPU-GPU systems. Challenges are due to the irregular data access for adaptive Cartesian mesh, vast difference of computational cost between kinetic and fluid cells, and desire to evenly load all CPUs and GPUs. Our Unified Flow Solver (UFS) combines Adaptive Mesh Refinement (AMR) with automatic cell-by-cell selection of kinetic or fluid solvers based on continuum breakdown criteria. Using GPUs enables hybrid simulations of mixed rarefied-continuum flows with a million of Boltzmann cells with 24x24x24 velocity mesh. We describe the implementation of CUDA kernels for three modules in UFS: the direct Boltzmann solver using discrete velocity method, the Direct Simulation Monte Carlo (DSMC) solver, and a mesoscopic solver based on Lattice Boltzmann Method, all using octree Cartesian mesh. Double digit speedups on single GPU and good scaling for multiGPUs have been demonstrated.

show abstract

“…They compared their method to the central discretization scheme of Peng et al (1999) and achieved stability at higher Reynolds numbers. Observing that central schemes can introduce non-physical oscillations, and that vertex-centered finite-volume formulations require large amounts of memory storage for the boundary fluxes, Patil and Lakshmisha (2009) introduced a cellcentered finite-volume formulation coupled to a Total Variation Diminishing scheme for the flux calculations. They concluded that their method showed better numerical stability than the central scheme.…”

Section: Intrdouctionmentioning

confidence: 99%

“…Furthermore, delaying the application of local time-stepping on the continuity equation by a few tens of thousands of iterations also improves convergence time, because it reduces solution oscillations introduced by the initial pressure waves generated at the airfoil wall. The use of a local time-stepping strategy in the context of lattice Boltzmann methods on unstructured meshes is also suggested by Patil and Lakshmisha (2009).…”

Section: Boundary Conditions and Convergence Accelerationmentioning

confidence: 99%