3 papers
math.NA2026
Wavelet-based grid adaptation with consistent treatment of high-order sharp immersed geometries
Changxiao Nigel Shen, Wim M. van Rees
Wavelet-based grid adaptation methods use multiresolution analysis for error estimation, offering a mathematically rigorous approach to adaptive grid refinement when solving Partia…
physics.flu-dyn2025
A fourth order sharp immersed method for the incompressible Navier-Stokes equations with stationary and moving boundaries and interfaces
Xinjie Ji, Changxiao Nigel Shen, Wim M. van Rees
We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces.…
math.NA2024
A particle-in-Fourier method with semi-discrete energy conservation for non-periodic boundary conditions
Changxiao Nigel Shen, Antoine Cerfon, Sriramkrishnan Muralikrishnan
We introduce a novel particle-in-Fourier (PIF) scheme that extends its applicability to non-periodic boundary conditions. Our method handles free space boundary conditions by repla…