- Title Pages
- Dedication
- Preface
- Acknowledgements
- Part I Kinetic Theory of Fluids
- 1 Why a Kinetic Theory of Fluids?
- 2 Boltzmann’s Kinetic Theory
- 3 Approach to Equilibrium, the <i>H</i>-Theorem and Irreversibility
- 4 Transport Phenomena
- 5 From Kinetic Theory to Navier–Stokes Hydrodynamics
- 6 Generalized Hydrodynamics Beyond Navier–Stokes
- 7 Kinetic Theory of Dense Fluids
- 8 Model Boltzmann Equations
- 9 Stochastic Particle Dynamics
- 10 Numerical Methods for the Kinetic Theory of Fluids
- Part II Lattice Kinetic Theory
- 11 Lattice Gas-Cellular Automata
- 12 Lattice Boltzmann Models with Underlying Boolean Microdynamics
- 13 Lattice Boltzmann Models without Underlying Boolean Microdynamics
- 14 Lattice Relaxation Schemes
- 15 The Hermite–Gauss Route to LBE
- 16 LBE in the Framework of Computational-Fluid Dynamics
- Part III Fluid Dynamics Applications
- 17 Boundary Conditions
- 18 Flows at Moderate Reynolds Numbers
- 19 LBE Flows in Disordered Media
- 20 Lattice Boltzmann for Turbulent Flows
- Part IV Lattice Kinetic Theory: Advanced Topics
- 21 Entropic Lattice Boltzmann
- 22 Thermohydrodynamic LBE Schemes
- 23 Out of Legoland: Geoflexible Lattice Boltzmann Equations
- 24 Lattice Boltzmann for Turbulence Modeling
- Part V Beyond Fluid Dynamics: Complex States of Flowing Matter
- 25 LBE for Generalized Hydrodynamics
- 26 Lattice Boltzmann for reactive flows
- 27 Lattice Boltzmann for Non-Ideal Fluids
- 28 Extensions of the Pseudo-Potential Method
- 29 Lattice Boltzmann Models for Microflows
- 30 The Fluctuating Lattice Boltzmann
- 31 LB for Flows with Suspended Objects: Fluid–Solid Interactions
- Part VI Beyond Newtonian Mechanics: Quantum and Relativistic Fluids
- 32 Quantum Lattice Boltzmann (QLB)
- 33 QLB for Quantum Many-Body and Quantum Field Theory
- 34 Relativistic Lattice Boltzmann (RLB)
- 35 Advanced RLB models
- 36 Coda
- 37 Notation
- Appendices
- Part VII Hands-On
- Index

# Extensions of the Pseudo-Potential Method

# Extensions of the Pseudo-Potential Method

- Chapter:
- (p.512) 28 Extensions of the Pseudo-Potential Method
- Source:
- The Lattice Boltzmann Equation
- Author(s):
### Sauro Succi

- Publisher:
- 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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- Title Pages
- Dedication
- Preface
- Acknowledgements
- Part I Kinetic Theory of Fluids
- 1 Why a Kinetic Theory of Fluids?
- 2 Boltzmann’s Kinetic Theory
- 3 Approach to Equilibrium, the <i>H</i>-Theorem and Irreversibility
- 4 Transport Phenomena
- 5 From Kinetic Theory to Navier–Stokes Hydrodynamics
- 6 Generalized Hydrodynamics Beyond Navier–Stokes
- 7 Kinetic Theory of Dense Fluids
- 8 Model Boltzmann Equations
- 9 Stochastic Particle Dynamics
- 10 Numerical Methods for the Kinetic Theory of Fluids
- Part II Lattice Kinetic Theory
- 11 Lattice Gas-Cellular Automata
- 12 Lattice Boltzmann Models with Underlying Boolean Microdynamics
- 13 Lattice Boltzmann Models without Underlying Boolean Microdynamics
- 14 Lattice Relaxation Schemes
- 15 The Hermite–Gauss Route to LBE
- 16 LBE in the Framework of Computational-Fluid Dynamics
- Part III Fluid Dynamics Applications
- 17 Boundary Conditions
- 18 Flows at Moderate Reynolds Numbers
- 19 LBE Flows in Disordered Media
- 20 Lattice Boltzmann for Turbulent Flows
- Part IV Lattice Kinetic Theory: Advanced Topics
- 21 Entropic Lattice Boltzmann
- 22 Thermohydrodynamic LBE Schemes
- 23 Out of Legoland: Geoflexible Lattice Boltzmann Equations
- 24 Lattice Boltzmann for Turbulence Modeling
- Part V Beyond Fluid Dynamics: Complex States of Flowing Matter
- 25 LBE for Generalized Hydrodynamics
- 26 Lattice Boltzmann for reactive flows
- 27 Lattice Boltzmann for Non-Ideal Fluids
- 28 Extensions of the Pseudo-Potential Method
- 29 Lattice Boltzmann Models for Microflows
- 30 The Fluctuating Lattice Boltzmann
- 31 LB for Flows with Suspended Objects: Fluid–Solid Interactions
- Part VI Beyond Newtonian Mechanics: Quantum and Relativistic Fluids
- 32 Quantum Lattice Boltzmann (QLB)
- 33 QLB for Quantum Many-Body and Quantum Field Theory
- 34 Relativistic Lattice Boltzmann (RLB)
- 35 Advanced RLB models
- 36 Coda
- 37 Notation
- Appendices
- Part VII Hands-On
- Index