Related papers: Lattice operators from discrete hydrodynamics
Finite-difference Lattice Boltzmann (LB) models are proposed for simulating gas flows in devices with microscale geometries. The models employ the roots of half-range Gauss-Hermite polynomials as discrete velocities. Unlike the standard LB…
Hydrodynamic equations for an inelastic Maxwell model are derived from the inelastic Boltzmann equation based on a systematic Chapman-Enskog perturbative scheme. Transport coefficients appear in Navier-Stokes order have been determined as a…
We present a simple and general approach to formulate the lattice BGK model for high speed compressible flows. The main point consists of two parts: an appropriate discrete equilibrium distribution function (DEDF) $\mathbf{f}^{eq}$ and a…
We introduce nonlocal flows that commute with those of the classical Toda hierarchy. We define a logarithm of the difference Lax operator and use it to obtain a Lax representation of the new flows.
Differential operators are widely used in geometry processing for problem domains like spectral shape analysis, data interpolation, parametrization and mapping, and meshing. In addition to the ubiquitous cotangent Laplacian, anisotropic…
We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal…
Transport of cold atoms in shallow optical lattices is characterized by slow, nonstationary momentum relaxation. We here develop a projector operator method able to derive in this case a generalized Smoluchowski equation for the position…
Lattice Boltzmann simulations are used to investigate spinodal decomposition in a two-dimensional binary fluid with equilibrium lamellar and droplet phases. We emphasise the importance of hydrodynamic flow to the phase separation kinetics.…
Lattice Boltzmann schemes are efficient numerical methods to solve a broad range of problems under the form of conservation laws. However, they suffer from a chronic lack of clear theoretical foundations. In particular, the consistency…
A dynamic iteration scheme for linear differential-algebraic port-Hamil\-tonian systems based on Lions-Mercier-type operator splitting methods is developed. The dynamic iteration is monotone in the sense that the error is decreasing and no…
Many transport processes exhibit direction-dependent diffusion, described macroscopically by the full-tensor anisotropic advection--diffusion equation (ADE). Numerical discretization is demanding when the principal axes are rotated relative…
In this paper we develop hydrodynamic models using spectral differential operators to investigate the spatial stability of swirling fluid systems. Including viscosity as a valid parameter of the fluid, the hydrodynamic model is derived…
We introduce a class of lattice gas models of active matter systems whose hydrodynamic description can be derived exactly. We illustrate our approach by considering two systems exhibiting two of the most studied collective behaviours in…
We consider a long-range scattering theory for discrete Schr\"odinger operators on the hexagonal lattice, which describe tight-binding Hamiltonians on the graphene sheet. We construct Isozaki-Kitada modifiers for a pair of the difference…
In this paper, we carry out the algebraic study of integrable differential-difference equations whose field variables take values in an associative (but not commutative) algebra. We adapt the Hamiltonian formalism to nonabelian difference…
We consider approximations to the solutions of differential Riccati equations in the context of linear quadratic regulator problems, where the state equation is governed by a multiscale operator. Similarly to elliptic and parabolic…
Using standard calculus, explicit formulas for the one-dimensional continuous and discrete homotopy operators are derived. It is shown that these formulas are equivalent to those in terms of Euler operators obtained from the variational…
One of the most striking draw-backs of standard lattice gas methods over lattice Boltzmann methods is a much more limited range of transport parameters that can be achieved. It is common for lattice Boltzmann methods to use over-relaxation…
We present a new Lattice Boltzmann (LB) formulation to solve the Maxwell equations for electromagnetic (EM) waves propagating in a heterogeneous medium. By using a pseudo-vector discrete Boltzmann distribution, the scheme is shown to…
We introduce a mesoscopic three-dimensional Lattice Boltzmann Model which attempts to mimick the physical features associated with cage effects in dynamically heterogeneous fluids. To this purpose, we extend the standard Lattice Boltzmann…