Link-wise artificial compressibility method

The artificial compressibility method (ACM) for the incompressible Navier–Stokes equations is (link-wise) reformulated (referred to as LW-ACM) by a finite set of discrete directions (links) on a regular Cartesian mesh, in analogy with the lattice Boltzmann method (LBM). The main advantage is the pos...

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Bibliographic Details
Published in:Journal of computational physics 2012-06, Vol.231 (15), p.5109-5143
Main Authors: Asinari, Pietro, Ohwada, Taku, Chiavazzo, Eliodoro, Di Rienzo, Antonio F.
Format: Article
Language:English
Subjects:
Artificial compressibility method (ACM)
Cartesian
Complex boundaries
Compressibility
Computation
Computational fluid dynamics
Computational techniques
Exact sciences and technology
Fluid flow
Incompressible Navier–Stokes equations
Lattice Boltzmann method (LBM)
Links
Mathematical analysis
Mathematical methods in physics
Physics
Walls
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Summary:The artificial compressibility method (ACM) for the incompressible Navier–Stokes equations is (link-wise) reformulated (referred to as LW-ACM) by a finite set of discrete directions (links) on a regular Cartesian mesh, in analogy with the lattice Boltzmann method (LBM). The main advantage is the possibility of exploiting well established technologies originally developed for LBM and classical computational fluid dynamics, with special emphasis on finite differences (at least in the present paper), at the cost of minor changes. For instance, wall boundaries not aligned with the background Cartesian mesh can be taken into account by tracing the intersections of each link with the wall (analogously to LBM technology). LW-ACM requires no high-order moments beyond hydrodynamics (often referred to as ghost moments) and no kinetic expansion. Like finite difference schemes, only standard Taylor expansion is needed for analyzing consistency. Preliminary efforts towards optimal implementations have shown that LW-ACM is capable of similar computational speed as optimized (BGK-) LBM. In addition, the memory demand is significantly smaller than (BGK-) LBM. Importantly, with an efficient implementation, this algorithm may be among the few which are compute-bound and not memory-bound. Two- and three-dimensional benchmarks are investigated, and an extensive comparative study between the present approach and state of the art methods from the literature is carried out. Numerical evidences suggest that LW-ACM represents an excellent alternative in terms of simplicity, stability and accuracy.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2012.04.027