Technical Papers and Presentations

Meshless methods are relative newcomers to the field of computational methods; the term “meshless method” refers to the class of numerical techniques that have the following advantages: (1) domain and boundary mesh discretization is not required; (2) domain integration is not required; (3) custom points (e.g. randomly generated or imported from a file) can be used as the domain; (4) exponential convergence for smooth boundary shapes and boundary data can be realized; (5) multi-dimensional problems are naturally handled; and (6) implementation is comparatively easy. The method is becoming more popular as researchers begin to grasp the potential power of the scheme.

The meshless method, utilizing radial basis functions (RBFs), is coupled to COMSOL Multiphysics^® simulation software, permitting large scale boundary regions to be linked to COMSOL Multiphysics^®, as shown in Fig. 1. An attractive feature of using RBFs is that variable derivatives of any order can be established by simple inner products of vectors that can be pre-built and stored. Employing multiquadric functions, the method permits easy coupling to COMSOL Multiphysics^® without having to evaluate complicated functions or discretizing large domain boundaries at every step of an iteration or time-marching scheme. In addition, the memory demands are minimal. The coupled procedure permits large regions bordering refined configurations to be linked where detailed information is required, commonly occurring in situations such as conjugate heat transfer. A set of simple heat transfer problems are used to demonstrate the model.