176 citations · 199 across the 7 of their papers we have counts for
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A Geometric Local Parameterization Method for Generalized Hele-Shaw Free Boundary Problems with Source Terms
Zengyan Zhang, Wenrui Hao, John Harlim
We develop a meshfree numerical framework for Hele--Shaw free boundary problems with surface tension and source terms based on geometric local parameterization and boundary integra…
Geometric local parameterization for solving Hele-Shaw problems with surface tension
Zengyan Zhang, Wenrui Hao, John Harlim
In this work, we introduce a novel computational framework for solving the two-dimensional Hele-Shaw free boundary problem with surface tension. The moving boundary is represented…
General Numerical Framework to Derive Structure Preserving Reduced Order Models for Thermodynamically Consistent Reversible-Irreversible PDEs
Zengyan Zhang, Jia Zhao
In this paper, we propose a general numerical framework to derive structure-preserving reduced order models for thermodynamically consistent PDEs. Our numerical framework has two p…
A Remark on the Invariant Energy Quadratization (IEQ) Method for Preserving the Original Energy Dissipation Laws
Zengyan Zhang, Yuezheng Gong, Jia Zhao
In this letter, we revisit the IEQ method and provide a new perspective on its ability to preserve the original energy dissipation laws. The invariant energy quadratization (IEQ) m…
Improving the Accuracy and Consistency of the Scalar Auxiliary Variable (SAV) Method with Relaxation
Maosheng Jiang, Zengyan Zhang, Jia Zhao
The scalar auxiliary variable (SAV) method was introduced by Shen et al. and has been broadly used to solve thermodynamically consistent PDE problems. By utilizing scalar auxiliary…