相关论文: High-efficiency and positivity-preserving stabiliz…
We consider a kind of differential equations d/dt y(t) = R(y(t))y(t) + f(y(t)) with energy conservation. Such conservative models appear for instance in quantum physics, engineering and molecular dynamics. A new class of energy-preserving…
We present several first-order and second-order numerical schemes for the Cahn-Hilliard equation with discrete unconditional energy stability. These schemes stem from the generalized Positive Auxiliary Variable (gPAV) idea, and require only…
We construct and analyze first- and second-order implicit-explicit (IMEX) schemes based on the scalar auxiliary variable (SAV) approach for the magneto-hydrodynamic equations. These schemes are linear, only require solving a sequence of…
We present a new temporal discretization paradigm for developing energy-production-rate preserving numerical approximations to thermodynamically consistent partial differential equation systems, called the supplementary variable method. The…
We present an energy-stable scheme for numerically approximating the governing equations for incompressible two-phase flows with different densities and dynamic viscosities for the two fluids. The proposed scheme employs a scalar-valued…
We carry out the convergence analysis of the Scalar Auxiliary Variable (SAV) method applied to the nonlinear Schr\"odinger equation which preserves a modified Hamiltonian on the discrete level. We derive a weak and strong convergence…
In this paper, we propose several novel numerical techniques to deal with nonlinear terms in gradient flows. These step-by-step solving schemes, termed 3S-SAV and 3S-IEQ schemes, are based on recently popular scalar auxiliary variable (SAV)…
Recently introduced invariant energy quadratization (IEQ) and scalar auxiliary variable (SAV) approaches have proven to be very powerful ways to construct energy stable schemes for phase field models. Both methods require an assumption…
In this paper, we develop a second-order, fully decoupled, and energy-stable numerical scheme for the Cahn-Hilliard-Navier-Stokes model for two phase flow with variable density and viscosity. We propose a new decoupling Constant Scalar…
For a class of fourth order gradient flow problems, integration of the scalar auxiliary variable (SAV) time discretization with the penalty-free discontinuous Galerkin (DG) spatial discretization leads to SAV-DG schemes. These schemes are…
We develop several efficient numerical schemes which preserve exactly the global constraints for constrained gradient flows. Our schemes are based on the SAV approach combined with the Lagrangian multiplier approach. They are as efficient…
In this paper, we consider a second-order scalar auxiliary variable (SAV) Fourier spectral method to solve the nonlinear fractional generalized wave equation. Unconditional energy conservation or dissipation properties of the fully discrete…
The kinetic Langevin dynamics finds diverse applications in various disciplines such as molecular dynamics and Hamiltonian Monte Carlo sampling. In this paper, a novel splitting scalar auxiliary variable (SSAV) scheme is proposed for the…
In this paper, we construct and analyze an energy stable scheme by combining the latest developed scalar auxiliary variable (SAV) approach and linear finite element method (FEM) for phase field crystal (PFC) model, and show rigorously that…
This paper introduces a novel paradigm for constructing linearly implicit and high-order unconditionally energy-stable schemes for general gradient flows, utilizing the scalar auxiliary variable (SAV) approach and the additive Runge-Kutta…
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 investigate the numerical approximation of the stochastic Allen--Cahn equation with multiplicative noise on a periodic domain. The considered scheme uses a recently proposed augmented variant of scalar auxiliary variable method for the…
We present an unconditionally energy-stable scheme for approximating the incompressible Navier-Stokes equations on domains with outflow/open boundaries. The scheme combines the generalized Positive Auxiliary Variable (gPAV) approach and a…
Consistent splitting schemes are among the most accurate pressure segregation methods, incurring no splitting errors or spurious boundary conditions. Nevertheless, their theoretical properties are not yet fully understood, especially when…
In this paper, we propose and analyze high order efficient schemes for the time fractional Allen-Cahn equation. The proposed schemes are based on the L1 discretization for the time fractional derivative and the extended scalar auxiliary…