Related papers: Galilean Invariant Fluid-Solid Interfacial Dynamic…
Three-field Fluid-Structure Interaction (FSI) formulations for fluid and solid are applied and compared to the standard two field-one field formulation for fluid and solid, respectively. Both formulations are applied in a non linear setting…
An effort has been made to solve the Cauchy problem of the Navier-Stokes equations in the whole space by two methods. It is proved that the sum of the three vorticity components is a time-invariant in fluid motion. It has been proved that,…
The existence of two stationary solutions of the nonlinear Boltzmann equation for inelastic hard spheres or disks is investigated. They are restricted neither to weak dissipation nor to small gradients. The one-particle distribution…
In this contribution we review recent efforts on investigations of the effect of (apparent) boundary slip by utilizing lattice Boltzmann simulations. We demonstrate the applicability of the method to treat fundamental questions in…
Surface effects become important in microfluidic setups because the surface to volume ratio becomes large. In such setups the surface roughness is not any longer small compared to the length scale of the system and the wetting properties of…
We derive the partial differential equation (PDE) to which the pseudo-potential lattice Boltzmann method (P-LBM) converges under diffusive scaling, providing a rigorous basis for its consistency analysis. By establishing a direct link…
Mathematical modeling of fluid dynamics for computer graphics requires high levels of theoretical rigor to ensure visually plausible and computationally efficient simulations. This paper presents an in-depth theoretical framework analyzing…
The entropic lattice Boltzmann framework proposed the construction of the discrete equilibrium by taking into consideration minimization of a discrete entropy functional. The effect of this form of the discrete equilibrium on properties of…
The velocity circulation, a measure of the rotation of a fluid within a closed path, is a fundamental observable in classical and quantum flows. It is indeed a Lagrangian invariant in inviscid classical fluids. In quantum flows, circulation…
We consider a one-dimensional fluid-solid interaction model governed by the Burgers equation with a time varying interface. We discuss on the inverse problem of determining the shape of the interface from Dirichlet and Neumann data at one…
Multi-component fluid flow simulations in multi-scale porous structures often involve regions that are under-resolved at practical computational resolutions. Accurately capturing the contributions from these unresolved regions is critical.…
Using a Lattice Boltzmann hydrodynamic computational modeler to simulate relativistic fluid systems we explore turbulence in two-dimensional relativistic flows. We first a give a pedagogical description of the phenomenon of turbulence and…
We construct a generic coarse-grained dynamics of a thin inflexible planar layer of polar-ordered suspension of active particles, that is frictionally coupled to an embedding isotropic passive fluid medium with a friction coefficient…
A novel method to make Lagrangians Galilean invariant is developed. The method, based on null Lagrangians and their gauge functions, is used to demonstrate the Galilean invariance of the Lagrangian for Newton's law of inertia. It is…
This document reports investigations of models of multiphase flows using Lattice Boltzmann methods. The emphasis is on deriving by Chapman-Enskog techniques the corresponding macroscopic equations. The singular interface…
We present a further theoretical extension to the kinetic theory based formulation of the lattice Boltzmann method of Shan et al (2006). In addition to the higher order projection of the equilibrium distribution function and a sufficiently…
It is argued that the natural kinematics of the pilot-wave theory is Aristotelian. Despite appearances, Galilean invariance is not a fundamental symmetry of the low-energy theory. Instead, it is a fictitious symmetry that has been…
Direct numerical simulation of liquid-gas-solid flows is uncommon due to the considerable computational cost. As the grid spacing is determined by the smallest involved length scale, large grid sizes become necessary -- in particular if the…
We quantitatively characterize the metastability in a multi-phase lattice Boltzmann model. The structure factor of density fluctuations is theoretically obtained and numerically verified to a high precision, for all simulated wave-vectors…
Many numerical studies of blood flow impose a rigid wall assumption due to the simplicity of its implementation compared to a full coupling to a solid mechanics model. In this paper, we present a localised method for incorporating the…