LatticeBoltzmann method for nonNewtonian and nonequilibrium flows Alexander
Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows Alexander Vikhansky Department of Engineering, Queen Mary, University of London A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Lattice-Boltzmann method A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Boltzmann equation A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
NS equations A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Plan of the presentation A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Plan of the presentation A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Boltzmann equation Knudsen number: A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Chapman-Enskog expansion A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Kinetic effects: Knudsen layer (Kn 2) 1. Knudsen slip (Kn), 2. Thermal slip (Kn). A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Kinetic effects: 3. Thermal creep (Kn). A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Kinetic effects: 4. Thermal stress flow (Kn 2). A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Discrete ordinates equation A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Collision operator BGK model: A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Boundary conditions A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Boundary conditions: bounce-back rule A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Method of moments 1. Euler set: 2. Grad set: – 5 equations; – 13 equations; 3. Grad-26, Grad-45, Grad-71. A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Method of moments The error: 1. Euler set: 2. Grad set: 3. Grad-26: 4. Grad-45, Grad-71: A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Simulation of thermophoretic flows Velocity set: A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Knudsen compressor M. Young, E. P. Muntz, G. Shiflet and A. Green A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Knudsen compressor A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Effect of the boundary conditions A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Semi-implicit lattice-Boltzmann method for non-Newtonian flows From the kinetic theory of gases: Constitutive equation: A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Semi-implicit lattice-Boltzmann method for non-Newtonian flows Newtonian liquid: Bingham liquid: General case: A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Semi-implicit lattice-Boltzmann method for non-Newtonian flows Equilibrium distribution: Velocity set (3 D): Velocity set (2 D): Post-collision distribution: A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Semi-implicit lattice-Boltzmann method for non-Newtonian flows Bingham liquid Power-law liquid A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Flow of a Bingham liquid in a constant cross-section channel A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Creep flow through mesh of cylinders A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
Flow through mesh of cylinders A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
CONCLUSIONS • Continuous in time and space discrete ordinate equation is used as a link from the LB to Navier-Stokes and Boltzmann equations. This approach allows us to increase the accuracy of the method and leads to new boundary conditions. • The method was applied to simulation of a very subtle kinetic effect, namely, thermophoretic flows with small Knudsen numbers. • The new implicit collision rule for non-Newtonian rheology improves the stability of the calculations, but requires the solution of a (one-dimensional) non-linear algebraic equation at each point and at each time step. In the practically important case of Bingham liquid this equation can be solved analytically. A. Vikhansky, Lattice-Boltzmann method for non-Newtonian and non-equilibrium flows
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