56 citations · 89 across the 18 of their papers we have counts for
18 papers
Linear, decoupled and positivity-preserving staggered mesh schemes for general dissipative systems with arbitrary energy distributions
Zhengguang Liu, Nan Zheng, Xiaoli Li
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…
Global error estimates of high-order fully decoupled schemes for the Cahn-Hilliard-Navier-Stokes model of Two-Phase Incompressible Flows
Xiaoli Li, Nan Zheng, Jie Shen +1
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…
High-efficiency and positivity-preserving stabilized SAV methods for gradient flows
Zhengguang Liu, Yanrong Zhang, Xiaoli Li
The scalar auxiliary variable (SAV)-type methods are very popular techniques for solving various nonlinear dissipative systems. Compared to the semi-implicit method, the baseline S…
An enhanced and highly efficient semi-implicit combined Lagrange multiplier approach with preserving original energy law for dissipative systems
Zhengguang Liu, Nan Zheng, Xiaoli Li
Recently, a new Lagrange multiplier approach was introduced by Cheng, Liu and Shen in \cite{cheng2020new}, which has been broadly used to solve various challenging phase field prob…
The stabilized exponential-SAV approach preserving maximum bound principle for nonlocal Allen-Cahn equation
Xiaoqing Meng, Aijie Cheng, Zhengguang Liu
The nonlocal Allen-Cahn equation with nonlocal diffusion operator is a generalization of the classical Allen-Cahn equation. It satisfies the energy dissipation law and maximum boun…
The high-order exponential semi-implicit scalar auxiliary variable approach for nonlocal Cahn-Hilliard equation
Xiaoqing Meng, Aijie Cheng, Zhengguang Liu
The nonlocal Cahn-Hilliard (NCH) equation with nonlocal diffusion operator is more suitable for the simulation of microstructure phase transition than the local Cahn-Hilliard (LCH)…
A novel energy-optimal scalar auxiliary variable (EOP-SAV) approach for gradient flows
Zhengguang Liu, Yanrong Zhang, Xiaoli Li
In recent years, the scalar auxiliary variable (SAV) approach has become very popular and hot in the design of linear, high-order and unconditional energy stable schemes of gradien…
A novel Lagrange Multiplier approach with relaxation for gradient flows
Zhengguang Liu, Xiaoli Li
In this paper, we propose a novel Lagrange Multiplier approach, named zero-factor (ZF) approach to solve a series of gradient flow problems. The numerical schemes based on the new…
Highly efficient exponential scalar auxiliary variable approaches with relaxation (RE-SAV) for gradient flows
Zhengguang Liu, Xiaoli Li
For the past few years, scalar auxiliary variable (SAV) and SAV-type approaches became very hot and efficient methods to simulate various gradient flows. Inspired by the new SAV ap…
A highly efficient and accurate exponential semi-implicit scalar auxiliary variable (ESI-SAV) approach for dissipative system
Zhengguang Liu, Xiaoli Li
The scalar auxiliary variable (SAV) approach is a very popular and efficient method to simulate various phase field models. To save the computational cost, a new SAV approach is gi…
New SAV-pressure correction methods for the Navier-Stokes equations: stability and error analysis
Xiaoli Li, Jie Shen, Zhengguang Liu
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, d…
Step-by-step solving schemes based on scalar auxiliary variable and invariant energy quadratization approaches for gradient flows
Zhengguang Liu, Xiaoli Li
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, a…
The exponential scalar auxiliary variable (E-SAV) approach for phase field models and its explicit computing
Zhengguang Liu, Xiaoli Li
In this paper, we consider an exponential scalar auxiliary variable (E-SAV) approach to obtain energy stable schemes for a class of phase field models. This novel auxiliary variabl…
Energy stable schemes for gradient flows based on novel auxiliary variable with energy bounded above
Zhengguang Liu
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 limit…
Efficient invariant energy quadratization and scalar auxiliary variable approaches without bounded below restriction for phase field models
Zhengguang Liu
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…
The fast scalar auxiliary variable approach with unconditional energy stability for nonlocal Cahn-Hilliard equation
Zhengguang liu, Aijie Cheng, Xiaoli Li
Comparing with the classical local gradient flow and phase field models, the nonlocal models such as nonlocal Cahn-Hilliard equations equipped with nonlocal diffusion operator can…
Fast procedures for Caputo fractional derivative and its applications to ordinary and partial differential equations
Zhengguang Liu, Aijie Cheng, Xiaoli Li +1
In this paper, we develop fast procedures for solving linear systems arising from discretization of ordinary and partial differential equations with Caputo fractional derivative w.…
A novel second order finite difference discrete scheme for fractal mobile/immobile transport model based on equivalent transformative Caputo formulation
Zhengguang Liu, Xiaoli Li
In this article, we present a new second order finite difference discrete scheme for fractal mobile/immobile transport model based on equivalent transformative Caputo formulation.…