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The Lattice Boltzmann EquationFor Complex States of Flowing Matter$
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Sauro Succi

Print publication date: 2018

Print ISBN-13: 9780199592357

Published to Oxford Scholarship Online: June 2018

DOI: 10.1093/oso/9780199592357.001.0001

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Extensions of the Pseudo-Potential Method

Extensions of the Pseudo-Potential Method

(p.512) 28 Extensions of the Pseudo-Potential Method
The Lattice Boltzmann Equation

Sauro Succi

Oxford University Press

This chapter provides an account of subsequent extensions of the Shan-Chen pseudo-potential method, including more elaborated potentials which extend beyond the first Brillouin cell. These extensions permit us to lift a number of limitations of the original model and considerably expand its scope and range of applications. In Chapter 27, a variety of LB techniques for nonideal fluids have been discussed. As usual, each method comes with its ups and downs, but actual evidence shows that the Shan–Chen (SC) model has enjoyed increasing popularity over the years. Interestingly, such popularity stands in the face of a fair amount of substantial criticism. In this chapter, first the Shan–Chen model is revisited in some more detail along with a discussion of ways out of the above criticism. Subsequently, the extension of the SC technique to the case of multi-range potentials extending beyond the first Brillouin cell is discussed. This extension proves pretty effective in softening many of the weaknesses of the original formulation, thereby considerably expanding its scope and range of applications.

Keywords:   pseudo-potential method, density functional theory, Shan–Chen formulation, multi-range interactions, interface dynamics, spurious currents

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