An Embedded Boundary Scheme for Three-Dimensional Flow Over Terrain on a Staggered Mesh

2026-04-13

AI Summary

This study addresses numerical instabilities arising in fluid flow simulations on three-dimensional terrain when using staggered grids with embedded boundaries and small grid cells. The work presents the first adaptation of the embedded boundary method to a staggered grid framework, introducing distinct geometric treatments for velocity components—defined on cell faces—and thermodynamic scalar fields—defined at cell centers. To mitigate small-cell instability, the weighted state redistribution (WSRD) scheme is extended into this framework. Integrated within the ERF model alongside adaptive mesh refinement and performance-portable implementation, the proposed approach demonstrates excellent agreement with terrain-following coordinate simulations, achieving both high accuracy and robust numerical stability.

Technology Category

• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs

Abstract

This paper describes an embedded boundary (EB) approach for simulating three-dimensional fluid flow on a staggered mesh where the velocity components are defined on cell faces and the thermodynamic state is defined on cell centers. Most EB approaches assume that all components of the solution, including the velocity, are co-located. To compute solution quantities on faces as well as cell centers, we construct and store multiple instances of the geometric information, one for the quantities stored at cell centers and one for each velocity component. In addition, we extend the weighted state redistribution (WSRD) scheme to staggered meshes to address the small-cell instability issue. This new approach is implemented in the Energy Research and Forecasting (ERF) model that provides performance portability and adaptive mesh refinement. We validate the new EB method by comparing EB simulations to those computed using terrain-following coordinates.

Problem

• embedded boundary
• staggered mesh
• three-dimensional flow
• small-cell instability
• terrain

Innovation

• Embedded Boundary
• Staggered Mesh
• Weighted State Redistribution
• Small-Cell Stability
• Terrain-Resolving Flow