8 papers · 1 filter
Slow--Fast Response Correction for a Compact Fourth-Order IMEX Two-Derivative Method
Zhixin Huo
A compact two-stage fourth-order two-derivative IMEX method may retain its classical non-commuting fourth-order expansion and L-stable stiff damping while losing high-order accurac…
PDE Realization and Structure-Aware Solvers for a Compact Two-Stage Fourth-Order IMEX Method
Zhixin Huo
This paper develops a PDE realization and solver framework for a compact two-stage fourth-order two-derivative implicit--explicit time discretization for stiff split problems. The…
An L-Stable Sequential Two-Stage Fourth-Order Method with ADER Trajectory Derivatives for Stiff Transport--Relaxation Systems
Zhixin Huo, Yangnan Su
A fully implicit two-stage fourth-order two-derivative time discretization was introduced previously as a temporal method. This paper closes that sequential integrator for stiff tr…
Certified Seventh-Order Two-Derivative Hermite Deferred Correction via Node-Sweep Co-Design
Zhixin Huo
Two-derivative Hermite deferred correction combines high collocation order with sequential single-state solves, but the stopped method depends jointly on the nodes and the correcti…
Arbitrary-Order Padé-Closed Anchored Two-Derivative Time Discretizations: Active Stages, Order , and -Stability
Zhixin Huo
An arbitrary-order family of implicit two-derivative one-step methods is constructed in an anchored active-stage formulation. At each information node the method uses both the vect…
A Compact Two-Stage Fourth-Order Two-Derivative IMEX Method with Mixed Compatibility, High Implicit-Solve Efficiency,and Enhanced Stiff Decay
Zhixin Huo
For additively split stiff evolution problems, classical fourth-order IMEX Runge-Kutta methods usually require several stages and complicated coupling order conditions. This paper…
A High-resolution Spatiotemporal Coupling Ghost Fluid Method for Two-Dimensional Compressible Multimedium Flows with Source Terms
Zhixin Huo
While exact and approximate Riemann solvers are widely used, they exhibit two fundamental limitations: 1) Fail to represent continuous entropy transport processes, resulting in the…
An L-Stable Implicit Two-Stage Fourth-Order Temporal Discretization Scheme for Lax-Wendroff-Type Solvers Applied to Stiff Problems
Zhixin Huo
The explicit two-stage fourth-order (TSFO) temporal-spatial coupling method is efficient and compact but suffers severe time-step restrictions for stiff problems with multiple scal…