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

TL;DR

This paper introduces an embedded boundary method for 3D flow over terrain on staggered meshes, enhancing simulation accuracy and stability, validated against terrain-following coordinate models.

Contribution

It develops a novel EB approach for staggered meshes, extending WSRD scheme and integrating into the ERF model for improved terrain flow simulations.

Findings

Validated EB method against terrain-following coordinate simulations.

Extended WSRD scheme reduces small-cell instability.

Implemented in ERF model with adaptive mesh refinement.

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.