SubgridHeterogenität

Subgrid heterogeneity refers to variations in physical properties within a computational grid cell that are smaller than the grid resolution itself. In numerical simulations, such as those used in fluid dynamics, geosciences, or material science, computational domains are divided into discrete cells or elements. When the actual physical processes occurring within a single cell exhibit significant variations in properties like temperature, pressure, velocity, or material composition, and these variations are not explicitly resolved by the grid size, subgrid heterogeneity is present.

This phenomenon poses a challenge for numerical modeling. While the simulation solves for average quantities within each cell, the underlying subgrid-scale processes can significantly influence the overall behavior of the system. For instance, in porous media flow, the distribution of pore sizes and connectivity within a grid block can lead to non-Darcy flow behaviors that are not captured by a simple average. Similarly, in turbulent flows, unresolved turbulent eddies can affect the mixing and transport of species.

Approaches to handle subgrid heterogeneity include subgrid-scale modeling, which develops parameterized relationships to represent the effects of unresolved scales on the resolved scales. These models are often derived from theoretical considerations or from fine-scale simulations. Another approach is adaptive mesh refinement (AMR), where the grid resolution is increased in regions of high heterogeneity, effectively reducing or eliminating subgrid-scale features. Statistical methods can also be employed to describe the distribution of subgrid properties. Understanding and appropriately accounting for subgrid heterogeneity is crucial for achieving accurate and reliable simulation results.