A fourth order sharp immersed method for the incompressible Navier-Stokes equations with stationary and moving boundaries and interfaces

Ji, Xinjie; Nigel Shen, Changxiao; van Rees, Wim M.

doi:10.1016/j.jcp.2026.114806

A fourth order sharp immersed method for the incompressible Navier-Stokes equations with stationary and moving boundaries and interfaces

Journal Article · Sat Mar 07 00:00:00 EST 2026 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2026.114806· OSTI ID:3023472

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Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

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. Our algorithm employs a Runge-Kutta-based projection method that maintains high-order temporal accuracy in both velocity and pressure for steady and unsteady velocity boundary conditions. Fourth order spatial accuracy is achieved through a novel fifth order IIM discretization scheme for the advection term, as well as existing high-order interface-corrected finite difference schemes for the other differential operators. Using a set of manufactured flow problems with stationary and moving boundaries, we demonstrate fourth order convergence of velocity and pressure in the infinity norm, both inside the domain and on the immersed boundaries. The solver’s performance is further validated through a range of practical flow simulations, highlighting its efficiency over a second order scheme. Finally, we showcase the ability of our immersed discretization scheme to handle interface-coupled multiphysics problems by solving a conjugate heat transfer problem with multiple immersed solids. Overall, the proposed approach robustly combines the efficiency of high order discretization schemes with the flexibility of immersed discretizations for flow problems with complex, moving boundaries and interfaces.

View Accepted Manuscript (DOE)

Research Organization:: Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)

Grant/Contract Number:: SC0020998

OSTI ID:: 3023472

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 556; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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42 ENGINEERING
Fourth-order
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A fourth order sharp immersed method for the incompressible Navier-Stokes equations with stationary and moving boundaries and interfaces

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