Adaptive Grid Point Distribution for Fluid Flow Simulation

The patent applies local quality by transitioning from a uniform grid distribution to a non-uniform distribution where grid point spacing varies locally based on proximity to points of interest. The grid point spacing is reduced near perforations and other critical locations while maintaining larger spacing in less critical regions, thereby concentrating computational resources where they are most needed for accuracy without uniformly increasing complexity across the entire domain.

The patent implements dynamics by making the grid distribution adaptive rather than static. The grid point spacing is dynamically adjusted based on the local flow conditions and proximity to points of interest, allowing the simulation to automatically refine the mesh in regions where higher accuracy is required while coarsening it elsewhere, thus resolving the contradiction between accuracy and complexity.

The patent applies local quality by concentrating grid points only in specific regions around points of interest such as perforations and fracture intersections, rather than uniformly distributing them throughout the entire domain. This localized clustering achieves high simulation accuracy at critical locations while maintaining a coarser grid in less critical regions, thereby reducing the total number of grid points and computational resources required compared to a uniformly fine grid.

The patent applies partial action by implementing grid point clustering only where necessary (at points of interest) rather than across the entire domain. This selective refinement achieves the necessary accuracy for critical regions without the excessive computational cost of a uniformly fine grid throughout, thus resolving the contradiction between accuracy and computational resources.

The patent applies local quality by using a fine mesh only in specific regions where detailed fluid flow behavior is critical (near perforations, fracture intersections, and other points of interest) while using a coarser mesh in less critical regions. This localized refinement captures essential flow details where needed without the computational overhead of a uniformly fine mesh across the entire domain, thus resolving the contradiction between accuracy and computational efficiency.

The patent applies segmentation by dividing the computational domain into regions of different mesh densities - fine mesh regions around points of interest and coarser mesh regions elsewhere. This segmented approach allows the simulation to capture detailed flow behavior where necessary while maintaining computational efficiency in less critical areas, effectively resolving the accuracy-efficiency trade-off.