What does LGR mean in UNCLASSIFIED

Local Grid Refinement (LGR) is a computational technique used in numerical simulations to enhance the accuracy of solutions in regions of interest while maintaining computational efficiency. It involves dynamically adapting the computational grid, refining it in areas where higher resolution is required and coarsening it in areas where coarser resolution is sufficient.

LGR allows for the efficient simulation of complex phenomena that exhibit large variations in scales, such as in fluid dynamics, combustion, and astrophysics. By adapting the grid locally, LGR provides higher resolution where necessary, capturing fine-scale details and reducing numerical errors, while using coarser resolution elsewhere, reducing computational cost.

LGR typically involves partitioning the computational domain into subdomains and adjusting the grid size within each subdomain based on local error estimates or other criteria. The grid may be refined by inserting additional points or coarsened by removing points, adapting to the evolving solution.

LGR offers several advantages over uniform grids:

• Accuracy: Adapting the grid locally improves the accuracy of solutions, particularly in regions with sharp gradients or complex features.
• Efficiency: By using a coarse grid in areas where accuracy is not critical, LGR reduces computational time and resources.
• Flexibility: LGR allows for dynamic adaptation of the grid during the simulation, enabling the resolution to be adjusted as the solution evolves.

LGR has been successfully applied in various fields, including:

• Computational Fluid Dynamics (CFD): Simulating fluid flows with complex geometries and boundary conditions.
• Combustion: Modeling combustion processes involving chemical reactions and flame propagation.
• Astrophysics: Studying astrophysical phenomena such as star formation and supernovae explosions.
• Materials Science: Investigating material properties and behavior at multiple scales.