Concurrent two-way coupling of global and local models across internal boundaries with non-matching discretizations

Journal Article · Sun Jun 01 00:00:00 EDT 2025 · Advances in Computational Science and Engineering

DOI:https://doi.org/10.3934/acse.2025016· OSTI ID:2589110

Kang, Soonpil ^[1]; Masud, Arif ^[2]

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1. Naval Postgraduate School, Monterey, CA (United States); Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
2. Univ. of Illinois at Urbana-Champaign, IL (United States)

Coupling local and global models enables efficient simulation of multiscale systems, where global models capture large-scale behavior and local models, with enhanced physics, resolve finer details over a smaller region. Here, this paper presents a mathematically consistent method for coupling physics-based models of varying fidelity across adjacent, non-overlapping subdomains, even when discretizations do not match at the immersed interdomain interfaces. Incompressible Navier-Stokes equations (NSE) constitute the global model while residual-based turbulence model serves as the local high-fidelity model. In addition, a scalar advection-diffusion equation that models the convection of an active scalar field is appended to the turbulence model in the local domain. This scalar field does not have its complement in the global model, giving rise to unequal number of equations at the immersed boundary between local and global models. Interdomain coupling terms are derived via the Variational Multiscale Discontinuous Galerkin (VMDG) method with new developments in scale representation and efficient fine-scale estimation. While transient laminar flows modeled with NSE in the global domain can be resolved with relatively coarse mesh, turbulent flow calculations in the local model require much finer spatial discretizations as well as smaller time-step for appropriately resolving the turbulent flow physics. The proposed framework also accommodates non-matching meshes at the immersed boundaries. Test problems in 2D and 3D numerically showcase the concurrent two-way coupling of unknown fields across the immersed boundaries. The 3D test presents a case with an unequal number of equations, where the scalar field represents the convection of contaminant concentration. This provides more detailed physics in the local region and highlights its application in climate modeling and atmospheric sciences.

• Research Organization: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
• Sponsoring Organization: USDOE National Nuclear Security Administration (NNSA)
• Grant/Contract Number: AC52-07NA27344
• OSTI ID: 2589110
• Journal Information: Advances in Computational Science and Engineering, Journal Name: Advances in Computational Science and Engineering Vol. 4; ISSN 2837-1739
• Publisher: American Institute of Mathematical Sciences (AIMS)
• Country of Publication: United States
• Language: English

Related Subjects

Variational Multiscale Discontinuous Galerkin (VMDG) method
global and local models
incompressible Navier-Stokes equations
internal interface
non-matching mesh
open boundary conditions