18 citations · 37 across the 9 of their papers we have counts for
9 papers · 1 filter
Stability analysis of consistent splitting implicit-explicit multistep methods up to ninth-order accuracy for incompressible flows
Yuanyuan Kang, Hong-lin Liao, Guidong Liu
This work presents a concise, unified stability theory of high-order decoupled \lan{implicit-explicit linear multistep (IELM)} methods based on the well-known consistent splitting…
An Efficient IMEX-SDIRK2 mr-ccSAV Scheme for the Forced Navier--Stokes Equations with Uniform-in-Time Enstrophy Bounds
Honglin Liao, Haifeng Wang, Xiaoming Wang
We propose and analyze an IMEX-SDIRK2 mean-reverting concurrent-correction scalar auxiliary variable (mr-ccSAV) method for the forced two-dimensional periodic Navier--Stokes equati…
Long-time stability of implicit-explicit Runge-Kutta methods for two-dimensional incompressible flows
Hong-lin Liao, Xiaoming Wang, Xuping Wang +1
High-order adaptive time-stepping algorithms are of significant practical value and theoretical interest for accelerating long-time fluid-flow simulations and resolving complex dyn…
A semi-generating function approach to the stability of implicit-explicit multistep methods for nonlinear parabolic equations
Hong-lin Liao, Chaoyu Quan, Tao Tang +1
The rigorous stability analysis of high-order implicit-explicit linear multistep (IELM) methods for nonlinear parabolic equations by using discrete energy arguments is a long stand…
A unified framework on the original energy laws of three effective classes of Runge-Kutta methods for phase field crystal type models
Xuping Wang, Xuan Zhao, Hong-lin Liao
The main theoretical obstacle to establish the original energy dissipation laws of Runge-Kutta methods for phase-field equations is to verify the maximum norm boundedness of the st…
A class of refined implicit-explicit Runge-Kutta methods with robust time adaptability and unconditional convergence for the Cahn-Hilliard model
Hong-lin Liao, Tao Tang, Xuping Wang +1
One of main obstacles in verifying the energy dissipation laws of implicit-explicit Runge-Kutta (IERK) methods for phase field equations is to establish the uniform boundedness of…
Average energy dissipation rates of additive implicit-explicit Runge-Kutta methods for gradient flow problems
Hong-lin Liao, Xuping Wang, Cao Wen
A unified theoretical framework is suggested to examine the energy dissipation properties at all stages of additive implicit-explicit Runge-Kutta (IERK) methods up to fourth-order…
Original energy dissipation preserving corrections of integrating factor Runge-Kutta methods for gradient flow problems
Hong-lin Liao, Xuping Wang, Cao Wen
Explicit integrating factor Runge-Kutta methods are attractive and popular in developing high-order maximum bound principle preserving time-stepping schemes for Allen-Cahn type gra…
Average energy dissipation rates of explicit exponential Runge-Kutta methods for gradient flow problems
Hong-lin Liao, Xuping Wang
We propose a unified theoretical framework to examine the energy dissipation properties at all stages of explicit exponential Runge-Kutta (EERK) methods for gradient flow problems.…