Final answer:
Higher mesh density is recommended in regions where a higher degree of accuracy is desired, where there are large gradients in the primary variable, and in areas of complex geometry, to increase the precision of computational simulations.
Step-by-step explanation:
When creating a computational model for analyzing physical phenomena, it is important to consider where to have a higher mesh density. Mesh density plays a crucial role in the accuracy of simulations and is especially pertinent in certain regions of the model. The mesh should not necessarily be uniform but should vary according to specific criteria.
Firstly, a higher degree of accuracy is desired in regions where the outcomes are most critical. This could include areas subject to the highest stresses in a structural analysis or regions with precision-sensitive components in a heat transfer simulation. In these areas, a more detailed mesh can capture the subtleties of the physical behavior, leading to more precise results.
Secondly, in regions with large gradients in the primary variable, whether it be temperature, pressure, velocity, or another critical field, a denser mesh is advised. Large gradients indicate rapid changes over a small spatial distance, and a finer mesh is necessary to resolve these changes accurately. Without adequate resolution, critical phenomena such as boundary layer effects or shock waves could be inaccurately represented.
Lastly, areas of complex geometry often necessitate a higher mesh density. Complex shapes have more intricate surfaces and features that require a fine mesh to correctly capture their effects on the physical system being analyzed. Features such as sharp corners, small holes, or thin walls are typical examples where a denser mesh may be required.
In summary, while a uniform mesh may seem ideal for simplicity, it is not the optimal choice for accurately capturing physical phenomena in every scenario. For regions where there is a higher degree of accuracy desired, along with large gradients in the primary variable or complex geometric features, a higher mesh density is strongly recommended.