Related papers: A gPAV-Based Unconditionally Energy-Stable Scheme …
In this paper, we present two multiple scalar auxiliary variable (MSAV)-based, finite element numerical schemes for the Abels-Garcke-Gr{\"u}n (AGG) model, which is a thermodynamically consistent phase field model of two-phase incompressible…
In this paper, we propose a novel family of high-order numerical schemes for the gradient flow models based on the scalar auxiliary variable (SAV) approach, which is named the high-order scalar auxiliary variable (HSAV) method. The newly…
In this paper, we propose a regularized auxiliary variable (RAV) approach and construct accurate and robust time-discrete schemes for a large class of gradient flows. By introducing an auxiliary variable $r=0$ and constructing an auxiliary…
In this paper we construct new fully decoupled and high-order implicit-explicit (IMEX) schemes for the two-phase incompressible flows based on the new generalized scalar auxiliary variable approach with optimal energy approximation…
In this paper, we consider numerical approximations for solving the nonlinear magneto-hydrodynamical system, that couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is…
We propose novel ensemble calculation methods for Navier-Stokes equations subject to various initial conditions, forcing terms and viscosity coefficients. We establish the stability of the schemes under a CFL condition involving velocity…
In this paper, we construct novel first- and second-order decoupled schemes for the Navier-Stokes equations based on the penalty method and the sequential regularization method (SRM), respectively. These schemes do not require the boundary…
We propose a novel second-order accurate, long-time unconditionally stable time-marching scheme for the forced Navier-Stokes equations. A new Forced Scalar Auxiliary Variable approach (FSAV) is introduced to preserve the underlying…
Common efficient schemes for the incompressible Navier-Stokes equations, such as projection or fractional step methods, have limited temporal accuracy as a result of matrix splitting errors, or introduce errors near the domain boundaries…
Inf-sup stable FEM applied to time-dependent incompressible Navier-Stokes flows are considered. The focus lies on robust estimates for the kinetic and dissipation energies in a twofold sense. Firstly, pressure-robustness ensures the…
We introduce a novel artificial compressibility technique to approximate the incompressible Navier-Stokes equations with variable fluid properties such as density and dynamical viscosity. The proposed scheme used the couple pressure and…
We investigate the large-time behavior of solutions to an outflow problem of the full compressible Navier-Stokes equations in the half line. The non-degenerate stationary solution is shown to be asymptotically stable under large initial…
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.…
This paper focuses on the so-called Weighted Inertia-Dissipation-Energy (WIDE) variational approach for the approximation of unsteady Leray-Hopf solutions of the incompressible Navier-Stokes system. Initiated in [56], this variational…
We investigate the large-time behavior of solutions toward the combination of the boundary layer and 3-rarefaction waves to the outflow problem for the compressible non-isentropic Navier-Stokes equations coupling with the Maxwell equations…
We construct high-order semi-discrete-in-time and fully discrete (with Fourier-Galerkin in space) schemes for the incompressible Navier-Stokes equations with periodic boundary conditions, and carry out corresponding error analysis. The…
The paper presents numerical methods for unsteady flows of a viscous incompressible fluid in internal domains with many inlet/outlet sections. The novel variants of dissipative boundary conditions augmented by the inertia terms are used at…
We propose a new numerical technique to deal with nonlinear terms in gradient flows. By introducing a scalar auxiliary variable (SAV), we construct efficient and robust energy stable schemes for a large class of gradient flows. The SAV…
This work proposes an efficient, linear, and fully decoupled pressure-correction scheme for the 2D stochastic Navier-Stokes equations with multiplicative noise and Dirichlet boundary condition. Leveraging the auxiliary variable approach,…
We present in this paper a pressure correction scheme for barotropic compressible Navier-Stokes equations, which enjoys an unconditional stability property, in the sense that the energy and maximum-principle-based a priori estimates of the…