Meshless describes computational methods, especially in engineering and scientific simulations, that do not rely on a traditional mesh (a grid of interconnected elements, like triangles or tetrahedra) to discretize the problem's domain. Instead, these methods approximate solutions based on scattered data points or particles. This approach offers advantages in handling complex geometries, adaptive refinement, and large deformations, often reducing pre-processing time compared to mesh-dependent techniques. However, they can sometimes be computationally expensive, and the accuracy might depend heavily on the point distribution and numerical scheme used.
Meshless meaning with examples
- In simulating fluid dynamics around a complex aircraft wing, a meshless method might use a large number of particles to track the fluid's movement. This eliminates the need to generate a highly refined and often computationally expensive mesh, particularly near sharp edges. This method is often preferred for this example due to it's flexibility regarding geometry.
- Researchers are developing meshless techniques for simulating earthquake ground motions in geologically complex areas. The ability to easily adapt to varying soil properties and intricate fault lines makes these approaches well-suited. These methods can capture the wave propagation with better accuracy and allow easier manipulation of the simulated properties.
- Finite element analysis, traditionally mesh-based, becomes cumbersome when modelling bone fractures and surgeries due to large deformations. meshless methods are applied in such cases. Being able to refine the numerical simulations where they matter most allows for better simulation fidelity and results.
- The increasing complexity of semiconductor manufacturing processes necessitates novel simulation tools. meshless methods offer a promising avenue for modelling the deposition and etching of materials on irregular substrates, where grid generation is challenging. This helps model the material behaviour accurately.