Related papers: Incorporating variable viscosity in vorticity-base…
We construct a fully self-consistent non-equilibrium theory for the dynamics of two interacting finite-temperature atomic Bose-Einstein condensates. The condensates are described by dissipative Gross-Pitaevskii equations, coupled to quantum…
We present a new stability and error analysis of fully discrete approximation schemes for the transient Stokes equation. For the spatial discretization, we consider a wide class of Galerkin finite element methods which includes both inf-sup…
We introduce and analyze a new mixed finite element method with reduced symmetry for the standard linear model in viscoelasticity. Following a previous approach employed for linear elastodynamics, the present problem is formulated as a…
A probabilistic representation formula for general systems of linear parabolic equations, coupled only through the zero-order term, is given. On this basis, an implicit probabilistic representation for the vorticity in a 3D viscous fluid…
A finite element approximation of the Stokes equations under a certain nonlinear boundary condition, namely, the slip or leak boundary condition of friction type, is considered. We propose an approximate problem formulated by a variational…
We derive parameter-robust quasi-optimal error estimates for mixed finite element methods for the nonlinear Darcy--Forchheimer equations with mixed boundary conditions. Using the framework of operator preconditioning, we also design…
The nonlinear weakly dispersive Serre equations contain higher-order dispersive terms. This includes a mixed derivative flux term which is difficult to handle numerically. The mix spatial and temporal derivative dispersive term is replaced…
We present a mathematical proof of Einstein's formula for the effective viscosity of a dilute suspension of rigid neutrally--buoyant spheres when the spheres are centered on the vertices of a cubic lattice. We keep the size of the container…
In this paper we advance the analysis of discretizations for a fluid-structure interaction model of the monolithic coupling between the free flow of a viscous Newtonian fluid and a deformable porous medium separated by an interface. A…
This paper develops a class of robust weak Galerkin methods for the stationary incompressible convective Brinkman-Forchheimer equations. The methods adopt piecewise polynomials of degrees $m\ (m\geq1)$ and $m-1$ respectively for the…
In the spirit of the "Principle of Equipresence" introduced by Truesdell & Toupin, The Classical Field Theories (1960), we use the full version of the viscous stress tensor which was originally derived for compressible flows, instead of the…
We develop a unified continuum modeling framework for viscous fluids and hyperelastic solids using the Gibbs free energy as the thermodynamic potential. This framework naturally leads to a pressure primitive variable formulation for the…
A stationary Stokes problem with a piecewise constant viscosity coefficient in multiple subdomains is considered in the paper. For standard finite element pairs, a robust inf-sup condition is required to show the robustness of the…
In this thesis, we investigate a novel local projection based stabilized conforming virtual element method for the generalized Oseen problem using equal-order element pairs on general polygonal meshes. To ensure the stability, particularly…
We present a simulation scheme for discrete-velocity gases based on {\em local thermodynamic equilibrium}. Exploiting the kinetic nature of discrete-velocity gases, in that context, results in a natural splitting of fluxes, and the…
Embedding geometries in structured grids allows a simple treatment of complex objects in fluid simulations. Various methods for embedding geometries are available. The commonly used Brinkman-volume-penalization models geometries as porous…
We compute the first order correction of the effective viscosity for a suspension containing solid particles with arbitrary shapes. We rewrite the computation as an homogenization problem for the Stokes equations in a perforated domain.…
We formulate a quantum theory of vorticity (hydro)dynamics on a general two-dimensional bosonic lattice. In the classical limit of a bosonic condensate, it reduces to conserved plasma-like vortex-antivortex dynamics. The nonlocal…
This work proposes a new stabilized $P_1\times P_0$ finite element method for solving the incompressible Navier--Stokes equations. The numerical scheme is based on a reduced Bernardi--Raugel element with statically condensed face bubbles…
In this paper we formulate and analyze the mixed formulation of the one-dimensional equilibrium model of elastic stents. The model is based on the curved rod model for the inextensible and ushearable struts and is formulated in the weak…