相关论文: A generalized SAV approach with relaxation for dis…
We present a novel optimization algorithm, element-wise relaxed scalar auxiliary variable (E-RSAV), that satisfies an unconditional energy dissipation law and exhibits improved alignment between the modified and the original energy. Our…
In this paper, we consider a novel auxiliary variable method to obtain energy stable schemes for gradient flows. The auxiliary variable based on energy bounded above does not limited to the hypothetical conditions adopted in previous…
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…
In this paper, for the first time we propose two linear, decoupled, energy-stable numerical schemes for multi-component two-phase compressible flow with a realistic equation of state (e.g. Peng-Robinson equation of state). The methods are…
The Smectic-A (SmA) phase is modeled by a modified Landau-de Gennes (mLdG) model proposed by Xia et al. [Phys. Rev. Lett., 126 (2021), 177801], in which a tensor order parameter Q for the orientational order is coupled with a real scalar…
The Smectic-A (SmA) phase is modeled by a modified Landau-de Gennes (mLdG) model proposed by Xia et al. [Phys. Rev. Lett., 126 (2021), 177801], in which a tensor order parameter $\mathbf{Q}$ for the orientational order is coupled with a…
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…
In this paper, we develop a novel staggered mesh (SM) approach for general nonlinear dissipative systems with arbitrary energy distributions (including cases with known or unknown energy lower bounds). Based on this framework, we propose…
We carry out a rigorous error analysis of the first-order semi-discrete (in time) consistent splitting scheme coupled with a generalized scalar auxiliary variable (GSAV) approach for the Navier-Stokes equations with no-slip boundary…
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…
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)…
This paper studies a class of linear unconditionally energy stable schemes for the gradient flows. Such schemes are built on the SAV technique and the general linear time discretization (GLTD) as well as the linearization based on the…
We construct new first- and second-order pressure correction schemes using the scalar auxiliary variable (SAV) approach for the Navier-Stokes equations. These schemes are linear, decoupled and only require a sequence of solving Poisson type…
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…
We introduce novel entropy-dissipative numerical schemes for a class of kinetic equations, leveraging the recently introduced scalar auxiliary variable (SAV) approach. Both first and second order schemes are constructed. Since the…
In this paper, we propose and analyze semi-implicit numerical schemes for the stochastic wave equation (SWE) with general nonlinearity and multiplicative noise. These numerical schemes, called stochastic scalar auxiliary variable (SAV)…
In this paper, we propose and analyze a linear, structure-preserving scalar auxiliary variable (SAV) method for solving the Allen--Cahn equation based on the second-order backward differentiation formula (BDF2) with variable time steps. To…
It is well-known that the Allen-Cahn equation not only satisfies the energy dissipation law but also possesses the maximum bound principle (MBP) in the sense that the absolute value of its solution is pointwise bounded for all time by some…
We present an energy-stable scheme for simulating the incompressible Navier-Stokes equations based on the generalized Positive Auxiliary Variable (gPAV) framework. In the gPAV-reformulated system the original nonlinear term is replaced by a…
This paper continues to study linear and unconditionally modified-energy stable (abbreviated as SAV-GL) schemes for the gradient flows. The schemes are built on the SAV technique and the general linear time discretizations (GLTD) as well as…