Topic
Lattice model (physics)
About: Lattice model (physics) is a research topic. Over the lifetime, 7803 publications have been published within this topic receiving 205094 citations.
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TL;DR: In this article, a lattice Boltzmann model is developed which has the ability to simulate flows containing multiple phases and components, each of the components can be immiscible with the others and can have different mass values.
Abstract: A lattice Boltzmann model is developed which has the ability to simulate flows containing multiple phases and components. Each of the components can be immiscible with the others and can have different mass values. The equilibrium state of each component can have a nonideal gas equation of state at a prescribed temperature exhibiting thermodynamic phase transitions. The scheme incorporated in this model is the introduction of an interparticle potential. The dynamical rules in this model are local so it is highly efficient to compute on massively parallel computers. This model has many application in large-scale numerical simulations of various types of fluid flows
2,300 citations
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TL;DR: It is shown that discrete lattice effects must be considered in the introduction of a force into the lattice Boltzmann equation, and a representation of the forcing term is proposed that derived the Navier-Stokes equation through the Chapman-Enskog expansion.
Abstract: We show that discrete lattice effects must be considered in the introduction of a force into the lattice Boltzmann equation. A representation of the forcing term is then proposed. With the representation, the Navier-Stokes equation is derived from the lattice Boltzmann equation through the Chapman-Enskog expansion. Several other existing force treatments are also examined.
1,829 citations
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TL;DR: In this paper, the problems of an Ising model in a magnetic field and a lattice gas are proved mathematically equivalent, and an example of a two-dimensional lattice model is given for which the phase transition regions in the $p\ensuremath{-}v$ diagram is exactly calculated.
Abstract: The problems of an Ising model in a magnetic field and a lattice gas are proved mathematically equivalent. From this equivalence an example of a two-dimensional lattice gas is given for which the phase transition regions in the $p\ensuremath{-}v$ diagram is exactly calculated.A theorem is proved which states that under a class of general conditions the roots of the grand partition function always lie on a circle. Consequences of this theorem and its relation with practical approximation methods are discussed. All the known exact results about the two-dimensional square Ising lattice are summarized, and some new results are quoted.
1,822 citations
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TL;DR: The basic elements of the theory of the lattice Boltzmann equation, a special lattice gas kinetic model for hydrodynamics, are reviewed in this paper, together with some generalizations which allow one to extend the range of applicability of the method to a number of fluid dynamics related problems.
1,812 citations
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TL;DR: In this article, a linear theory of deformation of an elastic solid was formulated, in which the potential energy-density is a function of the strain and its first and second gradients.
1,758 citations