Metris: An Open-Source High-Order Metric-Based Remesher
Lucien Rochery, Mark Chiriac, Marshall C. Galbraith, David Darmofal, Steven R. Allmaras · 2025
This paper presents Metris, a new piece of open source metric-based mesh adaptation software. The main novelty of this software is its ability to handle high-order meshes, and to apply mesh curvature using metric fields. We present two methods for applying metric-based curvature. Firstly, prior work on closed-form formulas for Bézier node positions to obtain unit $P^2$ elements is used in conjunction with an algorithm based on Linear Programs to apply curvature while guaranteeing mesh validity. Secondly, differentiable optimization of an anisotropic quality or conformity error can be used, which is generally faster, but performs best both from a performance and unitness standpoint if applied at late stages of curving and adaptation. More generally, the algorithms within Metris are described in some detail. 2D adaptation with parametric geometry provided by a Boundary Representation (BREP) file is currently implemented. Metris can be run either through files on disk, or via memory transfer. Using the latter, a numerical solver was used to illustrate and compare adaptation with Metris and other freely-available remeshers on two test cases. One, where an analytical solution is known, to verify expected convergence is obtained. The other is a transonic flow simulation on an airfoil, with the mesh adapted to minimize an estimated drag error, to compare aerodynamics coefficients obtained with Metris and other freely-available meshers. Faster convergence of these coefficients is observed with Metris, indicating high quality meshes were produced, as corroborated by provided mesh statistics: in this case, final meshes per complexity have at least 99.64% unit length and maximum quality (in range [1, +inf[) no higher than 2.26.