相关论文: On the conservation properties of the two-level li…
This paper investigates the two-dimensional stochastic steady-state Navier-Stokes(NS) equations with additive random noise. We introduce an innovative splitting method that decomposes the stochastic NS equations into a deterministic NS…
We present a fully discrete approximation technique for the compressible Navier-Stokes equations that is second-order accurate in time and space, semi-implicit, and guaranteed to be invariant domain preserving. The restriction on the time…
A semi-implicit, residual-based variational multiscale (VMS) formulation is developed for the incompressible Navier--Stokes equations. The approach linearizes convection using an extrapolated (Oseen-type) convecting velocity, producing a…
In this paper, we consider a mass conservation, positivity and energy identical-relation preserving scheme for the Navier-Stokes equations with variable density. Utilizing the square transformation, we first ensure the positivity of the…
We provide optimal order pressure error estimates for the Crank-Nicolson semidiscretization of the incompressible Navier-Stokes equations. Second order estimates for the velocity error are long known, we prove that the pressure error is of…
In this paper we propose and analyze a new Finite Element method for the solution of the two- and three-dimensional incompressible Navier--Stokes equations based on a hybrid discretization of both the velocity and pressure variables. The…
We present a new hybrid direct/iterative approach to the solution of a special class of saddle point matrices arising from the discretization of the steady incompressible Navier-Stokes equations on an Arakawa C-grid. The two-level method…
We analyze two fully time-discrete numerical schemes for the incompressible Navier-Stokes equations posed on evolving surfaces in $\mathbb{R}^3$ with prescribed normal velocity using the evolving surface finite element method (ESFEM). We…
These lecture notes are devoted to solutions of hyperbolic-parabolic systems with persistent oscillations. We consider two examples both from mechanics: (i) The system of viscoelasticity of Kelvin-Voigt type with strain energies involving…
A novel numerical scheme including time and spatial discretization is offered for coupled Cahn-Hilliard and Navier-Stokes governing equation sys-tem in this paper. Variable densities and viscosities are considered in the nu-merical scheme.…
We present and analyze a linearized finite element method (FEM) for the dynamical incompressible magnetohydrodynamics (MHD) equations. The finite element approximation is based on mixed conforming elements, where Taylor--Hood type elements…
Varieties of energy-stable numerical methods have been developed for incompressible two-phase flows based on the Navier-Stokes-Cahn-Hilliard (NSCH) model in the Eulerian framework, while few investigations have been made in the Lagrangian…
The error estimates and convergence rate of a two-level MacCormack rapid solver method for solving a two-dimensional incompressible Navier-Stokes equations are analyzed. This represents a continuation of the work on the stability analysis…
In recent years, the concept of introducing physics to machine learning has become widely popular. Most physics-inclusive ML-techniques however are still limited to a single geometry or a set of parametrizable geometries. Thus, there…
A constructive numerical approximation of the two-dimensional unsteady stochastic Navier-Stokes equations of an incompressible fluid is proposed via a pseudo-compressibility technique involving a parameter $\epsilon$. Space and time are…
In this paper, we present consistent and inconsistent discontinuous Galerkin methods for incompressible Euler and Navier-Stokes equations with the kinematic pressure, Bernoulli function and EMAC function. Semi- and fully discrete energy…
We derive an expression for the energy-momentum tensor in the discrete lattice formulation of pure glue QCD. The resulting expression satisfies the continuity equation for energy conservation up to numerical errors with a symmetric…
We consider the numerical approximations for a phase field model consisting of incompressible Navier--Stokes equations with a generalized Navier boundary condition, and the Cahn-Hilliard equation with a dynamic moving contact line boundary…
We present a fully conservative, skew-symmetric finite difference scheme on transformed grids. The skew-symmetry preserves the kinetic energy by first principles, simultaneously avoiding a central instability mechanism and numerical…
In this paper, we prove the energy conservation for the weak solutions of the compressible Navier-Stokes equations for any time $t>0$, under certain conditions. The results hold for the renormalized solutions of the equations with constant…