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arXiv · 1303.4624

Multidimensional On-lattice Higher-order Models in the Thermal Lattice Boltzmann Theory

Jae Wan Shim
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Abstract

We present a set of uniform polynomial equations that provides multidimensional on-lattice higher-order models of the lattice Boltzmann theory, while keeping compact the number of discrete velocities. As examples, we explicitly derive two- and three-dimensional on-lattice models applicable to describing thermal compressible flows of the accuracy levels of the Navier-Stokes equations with smaller numbers of discrete velocities in comparison to the existing models. We demonstrate the accuracy and stability of the three-dimensional model by using the Riemann problem.

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Jae Wan Shim. 2013-03-19. Multidimensional On-lattice Higher-order Models in the Thermal Lattice Boltzmann Theory. https://doi.org/10.1103/physreve.88.053310

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