相关论文: Fully-implicit log-conformation formulation of con…

The stable and efficient numerical simulation of viscoelastic flows has been a constant struggle due to the High Weissenberg Number Problem. While the stability for macroscopic descriptions could be greatly enhanced by the log-conformation…

We consider one dimensional isentropic compressible Navier-Stokes equations with Oldroyd-type constitutive law. By establishing uniform a priori estimates (with respect to relaxation time), we show global existence of smooth solutions with…

Logarithmic conformation reformulations for viscoelastic constitutive laws have alleviated the high Weissenberg number problem, and the exploration of highly elastic flows became possible. However, stabilized formulations for logarithmic…

We analyze the representation of viscous stresses in the one-fluid formulation of the two-phase Navier-Stokes equations, the model on which all computational approaches making use of a fixed mesh to discretize the flow field are grounded.…

First-order convergence in time and space is proved for a fully discrete semi-implicit finite element method for the two-dimensional Navier--Stokes equations with $L^2$ initial data in convex polygonal domains, without extra regularity…

We produce minimal integrity bases for both isotropic and hemitropic invariant algebras (and more generally covariant algebras) of most common bidimensional constitutive tensors and -- possibly coupled -- laws, including piezoelectricity…

The standard derivation of the Oldroyd-B model starts from a coupled system of the momentum equation for the macroscopic flow on the one hand, and Fokker-Planck dynamics for molecular dumbbells on the other. The constitutive equation is…

In this paper we show the strong convergence of a fully explicit space-time discrete approximation scheme for the solution process of the two-dimensional incompressible stochastic Navier-Stokes equations on the torus driven by additive…

The linear Navier-Stokes-Fourier (NSF) constitutive relations are capable of simulating the near-continuum flows, but fail in description of those flows which are removed far away from local equilibrium. In this paper, a diatomic nonlinear…

A numerical algorithm that computes the decomposition of any finite-dimen\-sio\-nal unitary reducible representation of a compact Lie group is presented. The algorithm, which does not rely on an algebraic insight on the group structure, is…

Modelling hydrodynamic lubrication is crucial in the design of engineering components as well as for a fundamental understanding of friction mechanisms. The cornerstone of thin-film flow modelling is the Reynolds equation -- a…

This paper presents a new numerical method for the compressible Navier-Stokes equations governing the flow of an ideal isentropic gas. To approximate the continuity equation, the method utilizes a discontinuous Galerkin discretization on…

This paper addresses the numerical solution of the two-dimensional Navier--Stokes (NS) equations with nonsmooth initial data in the $L^2$ space, which is the critical space for the two-dimensional NS equations to be well-posed. In this…

In this paper we address the problem of representing solutions of a system of scalar linear partial difference equations akin to state space equations of 1-D systems theory. We first obtain a representation formula for a special class of…

This paper is concerned with stochastic incompressible Navier-Stokes equations with multiplicative noise in two dimensions with respect to periodic boundary conditions. Based on the Helmholtz decomposition of the multiplicative noise,…

This paper introduces a robust reformulation of the incompressible Navier-Stokes equations, establishing a foundational framework for designing efficient, structure-preserving algorithms that strictly conserve the original energy…

We study the constraints imposed by conformal symmetry on the equations of fluid dynamics at second order in gradients of the hydrodynamic variables. At zeroth order conformal symmetry implies a constraint on the equation of state, E=2/3 P,…

In this paper we analyze the theoretical properties of a stochastic representation of the incompressible Navier-Stokes equations defined in the framework of the modeling under location uncertainty (LU). This setup built from a stochastic…

This article provides a reduced-order modelling framework for turbulent compressible flows discretized by the use of finite volume approaches. The basic idea behind this work is the construction of a reduced-order model capable of providing…

We introduce an immersed high-order discontinuous Galerkin method for solving the compressible Navier-Stokes equations on non-boundary-fitted meshes. The flow equations are discretised with a mixed discontinuous Galerkin formulation and are…