The development of a modular library for anisotropic adaptation of tetrahedral unstructured meshes is presented. The adaptive method relies on repeated application of simple edge break and collapse operations to modify a mesh such that individual edge lengths match a given anisotropic metric tensor field. The procedure maintains a continuous metric distribution through consistent interpolation of the initial metric field. Several methods are integrated within the library to preprocess the initial metric field so as to limit minimum and maximum local mesh sizes, control stretching rates of mesh size and/or anisotropy, and ensure smoothness of the resulting metric distribution. In addition, procedures to limit the metric distribution relative to the initial mesh and/or to the local geometry surface curvature are presented. Finally a linear-elastic mesh deformation method coupled with application provided geometric call-back functions is used to deform the adapted mesh to the geometry surface. The modular library implementation simplifies integration of the adaptive capability with new flow solver and mesh generation packages. Examples from multiple flow solvers and a mesh manipulation tool are presented.
Unstructured grid adaptation is a powerful tool to control Computational Fluid Dynamics (CFD) discretization error. It has enabled key increases in the accuracy, automation, and capacity of some fluid simulation applications. Slotnick et al. provide a number of case studies in the CFD Vision 2030 Study: A Path to Revolutionary Computational Aerosciences to illustrate the current state of CFD capability and capacity. The study authors forecast the potential impact of emerging High Performance Computing (HPC) environments forecast in the year 2030 and identify that mesh generation and adaptivity will continue to be significant bottlenecks in the CFD workflow. These bottlenecks may persist because very little government investment has been targeted in these areas. To motivate investment, the impacts of improved grid adaptation technologies are identified. The CFD Vision 2030 Study roadmap and anticipated capabilities in complementary disciplines are quoted to provide context for the progress made in grid adaptation in the past fifteen years, current status, and a forecast for the next fifteen years with recommended investments. These investments are specific to mesh adaptation and impact other aspects of the CFD process. Finally, a strategy is identified to di↵use grid adaptation technology into production CFD work flows.
Unstructured grid adaptation is a tool to control Computational Fluid Dynamics (CFD) discretization error. However, adaptive grid techniques have made limited impact on production analysis workflows where the control of discretization error is critical to obtaining reliable simulation results. Issues that prevent the use of adaptive grid methods are identified by applying unstructured grid adaptation methods to a series of benchmark cases. Once identified, these challenges to existing adaptive workflows can be addressed. Unstructured grid adaptation is evaluated for test cases described on the Turbulence Modeling Resource (TMR) web site, which documents uniform grid refinement of multiple schemes. The cases are turbulent flow over a Hemisphere Cylinder and an ONERA M6 Wing. Adaptive grid force and moment trajectories are shown for three integrated grid adaptation processes with Mach interpolation control and output error based metrics. The integrated grid adaptation process with a finite element (FE) discretization produced results consistent with uniform grid refinement of fixed grids. The integrated grid adaptation processes with finite volume schemes were slower to converge to the reference solution than the FE method. Metric conformity is documented on grid/metric snapshots for five grid adaptation mechanics implementations. These tools produce anisotropic boundary conforming grids requested by the adaptation process.
This paper investigates the impact of small-scale unsteadiness on adjoint-based output sensitivity analysis. In particular, when iterative methods for nonlinear flows fail to converge to a steady state, it is demonstrated that the resulting sensitivity analysis can be highly inaccurate, even when the unsteadiness in the outputs is small. The specific example considered is the viscous subsonic flow around an airfoil over a range of angles of attack. If a strengthened solver is used to solve the adjoint equation (even though the flow equations did not fully converge), it is demonstrated that the sensitivity of the lift with respect to angle of attack can vary significantly, due to linearizing about different solution iterates of the steady flow solver. Further, the unsteady iterates from the time-inaccurate steady-state solver to the time-accurate solution are compared. The unsteadiness of the time-accurate solution is markedly different from the iterate solutions of the steady-state solver. If a strengthened solver is applied to the nonlinear flow equations, steady solutions can be achieved whose lift is significantly different from the time-averaged lift of the time-accurate simulations. Time-accurate unsteady adjoint analysis is then shown to provide accurate sensitivities for the timeaveraged lift.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.